Article

Kinetic energy change with doping upon superfluid condensation in high temperature superconductors

Authors:
To read the full-text of this research, you can request a copy directly from the authors.

Abstract

In conventional BCS superconductors, the electronic kinetic energy increases upon superfluid condensation (the change DEkin is positive). Here we show that in the high critical temperature superconductor Bi-2212, DEkin crosses over from a fully compatible conventional BCS behavior (DEkin>0) to an unconventional behavior (DEkin<0) as the free carrier density decreases. If a single mechanism is responsible for superconductivity across the whole phase diagram of high critical temperature superconductors, this mechanism should allow for a smooth transition between such two regimes around optimal doping. Comment: 3 pages, 2 figures

No full-text available

Request Full-text Paper PDF

To read the full-text of this research,
you can request a copy directly from the authors.

... It is difficult to establish, however, that high-energy anomalies below T c are related to the superfluid density rather than to superconductivity-induced changes in the scattering rate of unpaired quasiparticles [27,28] or multiband effects [29][30][31]. The validity of the FGT sum rule therefore cannot be established solely on the basis of spectra measured at or above the plasma edge [19,21,22,24,[32][33][34][35][36][37]. Direct measurements of the complex electrodynamic response reaching to very low energies are needed to accurately determine the proper distribution of SW between the superconducting δ function and the quasiparticle response. ...
... However, previously reported results for different doping levels and other cuprate families are widely divergent [21,35,51]. In particular, far-infrared reflectivity measurements in Bi 2 Sr 2 CaCu 2 O 8+δ [34,36] have suggested that integrated SW increases below T c on the underdoped side of the phase diagram and decreases in the overdoped regime, with a crossover near optimal doping. In contrast, other infrared reflectivity measurements in underdoped YBa 2 Cu 3 O 6.60 [51] found that the FGT sum rule is satisfied at c ∼ 0.6 eV, in full agreement with our data on nearoptimally doped DyBCO. ...
... Beyond optimal doping the paramagnon spectrum exhibits a sharp crossover from a regime defined by collective spin excitations to one dominated by incoherent particle-hole excitations [77]. It is possible that these findings may elucidate the similarity between the observations reported for optimally doped and underdoped RBCO [38,51], and the differences between RBCO and Bi 2 Sr 2 CaCu 2 O 8+δ [34,36]. ...
Article
Full-text available
The Ferrell-Glover-Tinkham (FGT) sum rule in superconductors defines the superfluid density, ρs, as the optical conductivity spectral weight (SW) that transfers into a δ function at ω=0 due to the opening of the energy gap below Tc. In high-Tc superconductors, strong electron-boson coupling, self-energy effects, and intertwining of energy scales can link ρs to various high-energy processes, making the question of whether or not the FGT sum rule is valid in cuprates, and at what energy scale, central to a full understanding of the pairing mechanism. Here, we report high-precision measurements of the FGT sum rule in near-optimally doped DyBa2Cu3O7−δ thin films. We resolve the low-energy balance of SW by combining submillimeter-microwave interferometry, terahertz time-domain spectroscopy, and infrared ellipsometry to independently obtain the real and imaginary parts of the complex dielectric function between 0.8 meV and 1.1 eV (6–9000 cm−1). By applying a Kramers-Kronig consistency analysis to the measured spectra we find that the FGT sum rule is obeyed, and the total intraband SW is conserved to within ±0.2% below an energy scale ∼0.6 eV. We attribute specific anomalies observed in the conductivity spectra below ∼0.6 eV to coupling of charge carriers to the spectrum of collective antiferromagnetic spin fluctuations. The procedure presented here, applied to near-optimally doped DyBa2Cu3O7−δ, lays out a protocol for how the FGT sum rule should be studied in other doping levels and compounds.
... The most striking result to a theorist may be the fact, discovered experimentally some time ago [17], that the transition to the superconducting state, particularly in the regime of low doping, δ 0.1, takes place with the kinetic energy of the system getting lowered by the transition from the paramagnetic to superconducting phase. This is shown in Fig. 7a, where the results (squares with the error marked) have been plotted against the relative doping δ − δ opt , where δ opt is the optimal doping. ...
... In the last decade, the presence of the chargeorder presence has been intensely discussed, also in the context of the appearance of hidden charge density-wave quantum critical point at the optimal doping [17]. Leaving detailed discussion aside, we have analyzed the effect of finite-range correlations within our DE-GWF method [3] on the appearance of the charge-density-wave-type (CDW) state also with possible pair-density-wave (PDW) presence. ...
... The question we are interested in is what happens if the wave functions φ i (r) are close to their atomic counterparts. In that limit, (i, j, k, l), when selected as the parent atomic-state site positions, are far enough from each other that the largest contribution to (17) comes from the term i = j = k = l, i.e., V iiii = e 2 k d 3 r d 3 r |φ i (r)| 2 |φ i (r )| 2 |r − r | . ...
Article
Full-text available
High-temperature superconductivity encompasses the cuprates, nickelates, iron pnictides, and LaHx compounds. The first three groups of compounds involve in the pairing electrons, which are strongly to moderately correlated, whereas in the last class of systems specific phonon excitations. In this overview, we concentrate first on the (semi)quantitative theory of high-TC superconductivity in the cuprates based on our original vibrational approach beyond the renormalized mean-field theory. The model we mainly explore is the t–J–U model containing superexchange (kinetic exchange) combined with strong interelectronic correlations. Selected equilibrium and dynamic–excitation properties are analyzed briefly. General questions regarding the pseudogap and two-dimensional character of those systems are raised.
... The most striking result to a theorist may be the fact, discovered experimentally some time ago [17], is that the transition to the superconducting state, particularly in the regime of low doping, δ < ∼ 0.1, takes place with the kinetic energy of the system getting lowered by the transition from the paramagnetic to superconducting phase. This is shown in Fig. 7a, where the results (squares with the error marked) have been plotted against the relative doping δ − δ opt , where δ opt is optimal doping. ...
... In the last decade, the presence of the charge-order presence has been intensely discussed, also in the context of the appearance of hidden charge density-wave quantum critical point at the optimal doping [17] . Leaving aside a detailed discussion, we have analyzed the effect of finite-range correlations within our DE-GWF method [3] on the appearance of the CDW-type state also with possible pair-density-wave presence have those states into the phase diagram. ...
... with V ijkl = d 3 rd 3 r φ * iσ (r)φ * j (r ) e 2 κ|r − r | φ k (r)φ l (r ). (17) Indices (i, j, k, l) run over all possible single-particle states φ iσ (r) i=1,2,...,N and (σ, σ ) are spin quantum numbers for particular fermions characterized by (i, j, k, l). We see that in (17) the probability densities |φ i (r)| 2 and |φ j (r )| 2 are replaced by quantities φ * i (r)φ j (r ) and φ k (r)φ l (r ), respectively. ...
Preprint
Full-text available
High temperature superconductivity encompasses the cuprates, nickelates, iron pnictides, and LaHx_x compounds. The first three groups of compounds involve in the pairing electrons, which are strongly to moderately correlated, whereas in the last class of systems specific phonon excitations. In this overview we concentrate first on the (semi)quantitative theory of high TC_{C} superconductivity in the cuprates based on our original vibrational approach beyond the renormalized mean field theory. The model we explore mainly is t-J-U model containing both the superexchange (kinetic energy) combined with strong interelectronic correlations. Selected equilibrium and dynamic-excitation properties are analyzed briefly. General questions regarding the pseudogap and two--dimensional character of those systems are raised.
... However, experiments since the 1990's have shown that cuprate superconductors are exceptions. Cuprate superconductors showed a change in the optical spectrum even at an energy scale much larger (about 100 times) than the pairing gap size during the superconducting transition [1][2][3][4][5][6][7][8][9]. Since the optical spectral sum over all energies does not change by the f -sum rule, the decreased (increased) spectral weight at high energies is transferred to (from) low energies. ...
... Since the optical spectral sum over all energies does not change by the f -sum rule, the decreased (increased) spectral weight at high energies is transferred to (from) low energies. Underdoped cuprates showed spectral weight transfers from high to low energies [1-10], while overdoped cuprates showed the opposite [5][6][7][8][9], which was reproduced in dynamical mean-field calculations [11,12]. The origin of the superconductivity-induced spectral weight transfer (also called color change [13,14] or UV-IR mixing [15]) has been debated for over 20 years and continues up to today [13][14][15][16][17][18]. ...
... In BCS theory, superconductivity decreases the interaction energy while increasing the kinetic energy. As the low-energy spectral weight is approximately given by the minus of the kinetic energy, the superconductivity-induced spectral weight transfer from low to high energies reported in overdoped cuprates [6][7][8][9] is thought to be explained within BCS theory. On the other hand, the spectral weight transfer from high to low energies implies that the kinetic energy of the conduction electrons is reduced by superconductivity [13,16]. ...
Article
Full-text available
Optical spectral weight transfer associated with the onset of superconductivity at high-energy scales compared with the superconducting gap has been observed in several systems such as high-Tc cuprates. While there are still debates on the origin of this phenomenon, a consensus is that it is due to strong correlation effects beyond the BCS theory. Here, we show that there is another route to a nonzero spectral weight transfer based on the quantum geometry of the conduction band in multiband systems. We discuss applying this idea to the cuprates and twisted multilayer graphene.
... However, experiments since the 1990s have shown that cuprate superconductors are exceptions. Cuprate superconductors showed a change in the optical spectrum even at an energy scale much larger (about 100 times) than the pairing gap size during the superconducting transition [1][2][3][4][5][6][7][8][9]. Since the optical spectral sum over all energies does not change by the f -sum rule, the decreased (increased) spectral weight at high energies is transferred to (from) low energies. ...
... Since the optical spectral sum over all energies does not change by the f -sum rule, the decreased (increased) spectral weight at high energies is transferred to (from) low energies. Underdoped cuprates showed spectral weight transfers from high to low energies [1][2][3][4][5][6][7][8][9][10], while overdoped cuprates showed the opposite [5][6][7][8][9], which was reproduced in dynamical mean-field calculations [11,12]. The origin of the superconductivity-induced spectral weight transfer (also called color change [13,14] or UV-IR mixing [15]) has been debated over 20 years and continues up to date [13][14][15][16][17][18]. ...
... Since the optical spectral sum over all energies does not change by the f -sum rule, the decreased (increased) spectral weight at high energies is transferred to (from) low energies. Underdoped cuprates showed spectral weight transfers from high to low energies [1][2][3][4][5][6][7][8][9][10], while overdoped cuprates showed the opposite [5][6][7][8][9], which was reproduced in dynamical mean-field calculations [11,12]. The origin of the superconductivity-induced spectral weight transfer (also called color change [13,14] or UV-IR mixing [15]) has been debated over 20 years and continues up to date [13][14][15][16][17][18]. ...
Preprint
Full-text available
Optical spectral weight transfer associated with the onset of superconductivity at high energy scales compared with the superconducting gap has been observed in several systems such as high-TcT_c cuprates. While there are still debates on the origin of this phenomenon, a consensus is that it is due to strong correlation effects beyond the BCS theory. Here we show that there is another route to a nonzero spectral weight transfer based on the quantum geometry of the conduction band in multiband systems. We discuss applying this idea to the cuprates and twisted multilayer graphene.
... In turn, the influence of K is generally opposite to that obtained for ′ t . Interestingly, in this case we additionally obtain a kinetic energy decrease upon condensation to the SC state, as observed with optical measurements in the cuprates [51][52][53]. Finally, the joint effect of both terms seems to be dominated by K in the underdoped regime, whereas outside of this regime ′ t takes on the leading role. ...
... One of many unconventional (i.e. different from BCS theory) features characterizing high-temperature SC in under-h-doped cuprates is the kinetic energy decrease upon condensation observed in optical experiments [51][52][53]. From a theoretical perspective this feature was already explained in the frameworks based on the Hubbard [18,64,77], t-J [78][79][80], and t-J-U [81] models. In our modeling the sign reversal of the kinetic energy change, ...
... This apparently universal (i.e. not related to the source of pairing) behavior, together with other works on this topic [18, 64, 77-81] brings us to a proposal on a possible origin of the kinetic energy gain upon condensation in cuprates [51][52][53]. It seems that the decrease in the kinetic energy upon condensation is obtained near half-filling in theoretical approaches whenever the energy of the system near the Mott state is described in a better manner. ...
Article
Full-text available
We investigate the effect of the electron-hole (e-h) symmetry breaking on d-wave superconductivity induced by non-local effects of correlations in the generalized Hubbard model. The symmetry breaking is introduced in a two-fold manner: by the next-to-nearest neighbor hopping of electrons and by the charge-bond interaction-the off-diagonal term of the Coulomb potential. Both terms lead to a pronounced asymmetry of the superconducting order parameter. The next-to-nearest neighbor hopping enhances superconductivity for h-doping, while diminishes it for e-doping. The charge-bond interaction alone leads to the opposite effect and, additionally, to the kinetic-energy gain upon condensation in the underdoped regime. With both terms included, with similar amplitudes, the height of the superconducting dome and the critical doping remain in favor of h-doping. The influence of the charge-bond interaction on deviations from [Formula: see text] symmetry of the shape of the gap at the Fermi surface in the momentum space is briefly discussed.
... The circumstance that Δ kin < 0 is regarded as a sign of non-BCS nature of the state. The DE-GWF results (continuous lines) describe the experimental data [95] quantitatively. On the contrary, neither the SGA approximation for the -model (dashed line) nor DG-GWF results for the -model match the experiment. ...
... Selected superconducting properties: (a) Kinetic energy gain Δ kin vs. relative doping − opt ( opt is the optimal doping). The microscopic parameters are = 0.2| |, = 22.6| | (blue solid lines) and = 0.2| |, = 16| | (red solid lines); the experimental points are taken from Ref.[95]. For comparison, the results obtained with SGA method (gray dashed line) and those for the -model ( = 0.25| |) in DE-GWF approximation (dash-dotted line) are also included. ...
Preprint
Full-text available
In this review, we single out selected universal features of high-TcT_c and related systems, which can be compared with experiment. We start with the concept of real-space pairing, combined with strong correlations. The discussion of concrete properties relies on variational approach, based on renormalized mean-field theory (RMFT) in the form of statistically-consistent Gutzwiller approximation (SGA), and Diagrammatic Expansion of the Variational Wave Function (DE-GWF). Two energy scales appear, one involving quasiparticles close to the Fermi energy, and the other reflecting the correlated state. Those two regimes are separated by a kink in the dispersion relation, observed in photoemission. One obtains both the doping dependent properties and renormalized quasiparticles. The reviewed ground-state characteristics for high-TcT_c systems encompass superconductivity, nematicity, charge- (and pair-) density-wave effects, as well as non-BCS kinetic energy gain in the paired state, all in quantitative manner. Calculated dynamic properties are: universal Fermi velocity, Fermi wave-vector, effective mass enhancement, pseudogap, and d-wave gap magnitude. The minimal realistic model is represented by the t-J-U Hamiltonian. Inadequacy of the t-J and Hubbard models is discussed. For heavy fermion systems we summarize superconducting, Kondo insulating, ferro- and anti-ferromagnetic states. We overview also coexistent ferromagnetic (spin-triplet) superconducting phases observed for UGe2\mathrm{UGe_2}. Finally, we extend our scheme to collective spin and charge fluctuations in high-TcT_c systems, starting from variational approach, combined with 1/N expansion (beyond random phase approximation). Spectrum of collective spin and charge excitations is determined for the Hubbard and t-J-U models, and compared quantitatively with recent experiments.
... For V > 0 the AF order competes with SC in the underdoped region and a pure AF phase wins over, as shown in figure 2. In the BCS-like region ∆E kin > 0, which is also true for the BCS theory of the phonon-mediated superconductivity, whereas ∆E kin < 0 for the non-BCS region. It should be noted that the non-BCS behavior has been detected experimentally [81,82] for the underdoped samples of the cuprate compounds. This very feature highlights the necessity of including the higher orders to describe this important aspect of cuprate superconductivity. ...
... Furthermore, the non-BCS region appears only after the inclusion of the higher-order terms within the DE-GWF and the V term pushes it to higher dopings (see figure 6). The observation of non-BCS behavior in the experiment for the cuprates [81][82][83][84] clearly shows the necessity of including the higher-order terms in the calcul ations for the considered model. ...
Article
Full-text available
In the frst part of the paper, we study the stability of antiferromagnetic (AF), charge density wave (CDW), and superconducting (SC) states within the t-J-U-V model of strongly correlated electrons by using the statistically consistent Gutzwiller approximation (SGA). We concentrate on the role of the intersite Coulomb interaction term V in stabilizing the CDW phase. In particular, we show that the charge ordering appears only above a critical value of V in a limited hole-doping range δ\delta. The effect of the V term on SC and AF phases is that a strong interaction suppresses SC, whereas the AF order is not significantly influenced by its presence. In the second part, separate calculations for the case of pure SC phase have been carried out within an extended approach (the diagrammatic expansion for the Gutzwiller wave function, DE-GWF) in order to analyze the influence of the intersite Coulomb repulsion on the SC phase with the higher-order corrections included beyond the SGA method. In the Appendices we discuss the ambiguity connected with the choice of the Gutzwiller renormalization factors within the renormalized mean field theory when either AF or CDW orders are considered. At the end we overview briefly the possible extensions of the current models to make description of the SC, AF, and CDW states on equal footing.
... Our prediction that the doped AF state is stabilized by a gain in kinetic energy for large U and by a gain in potential energy for small U can in principle be tested by optical spectroscopy in cuprates [68][69][70] . If the correlation strength U is lower in electron that in hole doped cuprates, as has been proposed 71,72 , our data suggest a potential energy driven AF in electron doped cuprates and a kinetic energy driven AF in hole doped cuprates, similar to earlier findings on the Emery model 73 . ...
Preprint
Recent quantum-gas microscopy of ultracold atoms and scanning tunneling microscopy of the cuprates reveal new detailed information about doped Mott antiferromagnets, which can be compared with calculations. Using cellular dynamical mean-field theory, we map out the antiferromagnetic (AF) phase of the two-dimensional Hubbard model as a function of interaction strength U, hole doping δ\delta and temperature T. The N\'eel phase boundary is non-monotonic as a function of U and δ\delta. Frustration induced by second-neighbor hopping reduces N\'eel order more effectively at small U. The doped AF is stabilized at large U by kinetic energy and at small U by potential energy. The transition between the AF insulator and the doped metallic AF is continuous. At large U, we find in-gap states similar to those observed in scanning tunneling microscopy. We predict that, contrary to the Hubbard bands, these states are only slightly spin polarized.
... Remarkably, the Mott transition controls the sharp crossover that we observe between a potential-energy driven AF at small U , and kineticenergy driven AF at large U . This question of the origin of the stability of the AF state relative to the normal state has hitherto received little attention compared with the same question for superconductivity [47][48][49][50][51][52][53][54][55][56][57][58][59][60][61] . Yet, both questions are related to the role of the normal-state Mott transition. ...
Preprint
The properties of a phase with large correlation length can be strongly influenced by the underlying normal phase. We illustrate this by studying the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo. Sharp crossovers in the mechanism that favors antiferromagnetic correlations and in the corresponding local density of states are observed. These crossovers occur at values of the interaction strength U and temperature T that are controlled by the underlying normal-state Mott transition.
... In the cuprates, analysis of inelastic neutron scattering [35] has suggested that superconductivity arises because of a gain in exchange energy in the t − J model. Analysis of ARPES [36] and optical data [37][38][39][40] in the context of the Hubbard model has suggested that superconductivity is kinetic-energy driven in the underdoped regime [34,35,[41][42][43]. ...
Preprint
Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature TcdT_c^d, the maximum of the condensation energy as a function of doping, the correlation between maximum TcdT_c^d and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.
... The latter effect occurs at the single meV scale, and is characterized by the sign change of kinetic energy gain at the SC transition. 17,19,20 Since the free energy landscape for TBC involves even smaller energy scales, we consider t-J-U model as an appropriate departure point for addressing unconventional SC in those systems. An attractive methodological feature of the t-J-U Hamiltonian is that calculations in restricted (projected) Hilbert space, with doubly-occupied sites excluded, are not necessary. ...
Preprint
Full-text available
We carry out a theoretical study of unconventional superconductivity in twisted bilayer cuprates (TBC) as a function of electron density and layer twist angle. The bilayer t-J-U model is employed and analyzed within the framework of a generalized variational wave function approach in the statistically-consistent Gutzwiller formulation. The constructed phase diagram encompasses both gapless d-wave state (reflecting the pairing symmetry of untwisted copper-oxides) and gapped d+eiφdd+\mathrm{e}^{i\varphi}d phase that breaks spontaneously time-reversal-symmetry (TRS) and is characterized by nontrivial Chern number. We find that d+eiφdd+\mathrm{e}^{i\varphi}d state occupies a non-convex butterfly-shaped region in the doping vs. twist-angle plane, and demonstrate the presence of previously unreported reentrant TRS-breaking phase on the underdoped side of the phase diagram. This circumstance supports the emergence of topological superconductivity for fine-tuned twist angles in TBC away from 4545^\circ. Our analysis of the microscopically derived Landau free energy functional points toward sensitivity of the superconducting order parameter to small perturbations close to the topological state boundary.
... In strongly correlated electron systems, the kinetic energy effect is important in determining the stable ground state. The kinetic energy effect in superconductivity has been examined for electronic models [103][104][105][106][107][108][109][110][111][112]. We discuss the role of the kinetic term in this subsection. ...
... (iii) The antiferromagnetic state is suppressed by hole doping, but short-range (in particular nearest-neighbor) spin correlations persist and diminish gradually as a function of increasing doping. This scenario provides the formal basis for superconductivity by kinetic energy lowering in the underdoped cuprates [8,[52][53][54][55][56][57], and for understanding why for the underdoped cuprates the Drude spectral weight increases in the superconducting state [58][59][60][61][62]. It also explains why this effect flips sign at the overdoped side, and why for overdoped cuprates the superconducting pairing is stabilized by lowering the interaction energy [47,56,57]. ...
Article
Full-text available
Explaining the mechanism of superconductivity in the high-Tc cuprates requires an understanding of what causes electrons to form Cooper pairs. Pairing can be mediated by phonons, the screened Coulomb force, spin or charge fluctuations, excitons, or by a combination of these. An excitonic pairing mechanism has been postulated, but experimental evidence for coupling between conduction electrons and excitons in the cuprates is sporadic. Here we use resonant inelastic x-ray scattering to monitor the temperature dependence of the d_d exciton spectrum of Bi2Sr2CaCu2O8−x crystals with different charge carrier concentrations. We observe a significant change of the d_d exciton spectra when the materials pass from the normal state into the superconductor state. Our observations show that the d_d excitons start to shift up (down) in the overdoped (underdoped) sample when the material enters the superconducting phase. We attribute the superconductivity-induced effect and its sign reversal from underdoped to overdoped to the exchange coupling of the site of the d_d exciton to the surrounding copper spins.
... All such features, however, were reported for UD or OP cuprates, and it has been largely assumed that such exotic features become weaker, or even vanish, on the OD side. Spectral weight transfer, for example, was found to be reversed in OD Bi2212, suggesting a possible recovery of conventional BCS condensation [62][63][64]. It was subsequently noted, however, that the vHs in Bi2212 (on one of the Fermi sheets) may markedly affect the proportionality between spectral weight transfer and the change in kinetic energy across T c , potentially masking any intrinsic kinetic-energy saving [65]. ...
Article
Full-text available
There is now compelling evidence that the normal state of superconducting overdoped cuprates is a strange metal comprising two distinct charge sectors, one governed by coherent quasiparticle excitations, the other seemingly incoherent and characterized by non-quasiparticle (Planckian) dissipation. The zero-temperature superfluid density n_s(0) n s ( 0 ) of overdoped cuprates exhibits an anomalous depletion with increased hole doping p p , falling to zero at the edge of the superconducting dome. Over the same doping range, the effective zero-temperature Hall number n_{\rm H} (0) transitions from p p to 1 + p p . By taking into account the presence of these two charge sectors, we demonstrate that in the overdoped cuprates Tl _2 2 Ba _2 2 CuO _{6+\delta} 6 + δ and La _{2-x} 2 − x Sr _x x CuO _4 4 , the growth in n_s(0) n s ( 0 ) as p p is decreased from the overdoped side may be compensated by the loss of carriers in the coherent sector. Such a correspondence is contrary to expectations from conventional BCS theory and implies that superconductivity in overdoped cuprates emerges uniquely from the sector that exhibits incoherent transport in the normal state.
... The figure indicates that ∆E kin−sc increases for large U, showing a similar behavior to ∆E kin . ∆E kin−sc can change the sign when U is small, which is consistent with the analysis for Bi 2 Sr 2 CaCu 2 O 8+δ [79]. ...
Article
Full-text available
We investigate the role of kinetic energy for the stability of superconducting state in the two-dimensional Hubbard model on the basis of an optimization variational Monte Carlo method. The wave function is optimized by multiplying by correlation operators of site off-diagonal type. This wave function is written in an exponential-type form given as ψλ=exp(−λK)ψG for the Gutzwiller wave function ψG and a kinetic operator K. The kinetic correlation operator exp(−λK) plays an important role in the emergence of superconductivity in large-U region of the two-dimensional Hubbard model, where U is the on-site Coulomb repulsive interaction. We show that the superconducting condensation energy mainly originates from the kinetic energy in the strongly correlated region. This may indicate a possibility of high-temperature superconductivity due to the kinetic energy effect in correlated electron systems.
... Our prediction that the doped AF state is stabilized by a gain in kinetic energy for large U and by a gain in potential energy for small U can in principle be tested by optical spectroscopy in cuprates [68][69][70] . If the correlation strength U is lower in electron that in hole doped cuprates, as has been proposed 71,72 , our data suggest a potential energy driven AF in electron doped cuprates and a kinetic energy driven AF in hole doped cuprates, similar to earlier findings on the three-band Emery model 73 . ...
Article
Full-text available
Recent quantum-gas microscopy of ultracold atoms and scanning tunneling microscopy of the cuprates reveal new detailed information about doped Mott antiferromagnets, which can be compared with calculations. Using cellular dynamical mean-field theory, we map out the antiferromagnetic (AF) phase of the two-dimensional Hubbard model as a function of interaction strength U, hole doping δ\delta and temperature T. The N\'eel phase boundary is non-monotonic as a function of U and δ\delta. Frustration induced by second-neighbor hopping reduces N\'eel order more effectively at small U. The doped AF is stabilized at large U by kinetic energy and at small U by potential energy. The transition between the AF insulator and the doped metallic AF is continuous. At large U, we find in-gap states similar to those observed in scanning tunneling microscopy. We predict that, contrary to the Hubbard bands, these states are only slightly spin polarized.
... Remarkably, the hidden Mott transition controls the sharp crossover that we observe between a potential-energy driven AF at small U , and kinetic-energy driven AF at large U . This question of the origin of the stability of the AF state relative to the normal state has hitherto received little attention compared with the same question for superconductivity in models of interacting electrons [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. Yet, both questions are intimately related to the role of the normal-state Mott transition. ...
Article
The properties of a phase with large correlation length can be strongly influenced by the underlying normal phase. We illustrate this by studying the half-filled two-dimensional Hubbard model using cellular dynamical mean-field theory with continuous-time quantum Monte Carlo. Sharp crossovers in the mechanism that favors antiferromagnetic correlations and in the corresponding local density of states are observed. These crossovers occur at values of U and T that are controlled by the underlying normal-state Mott transition.
... In the cuprates, analysis of inelastic neutron scattering [35] has suggested that superconductivity arises because of a gain in exchange energy in the t − J model. Analysis of ARPES [36] and optical data [37][38][39][40] in the context of the Hubbard model has suggested that superconductivity is kinetic-energy driven in the underdoped regime [34,35,[41][42][43]. ...
Article
Full-text available
Superconductivity in the cuprates exhibits many unusual features. We study the two-dimensional Hubbard model with plaquette dynamical mean-field theory to address these unusual features and relate them to other normal-state phenomena, such as the pseudogap. Previous studies with this method found that upon doping the Mott insulator at low temperature a pseudogap phase appears. The low-temperature transition between that phase and the correlated metal at higher doping is first-order. A series of crossovers emerge along the Widom line extension of that first-order transition in the supercritical region. Here we show that the highly asymmetric dome of the dynamical mean-field superconducting transition temperature , the maximum of the condensation energy as a function of doping, the correlation between maximum and normal-state scattering rate, the change from potential-energy driven to kinetic-energy driven pairing mechanisms can all be understood as remnants of the normal state first-order transition and its associated crossovers that also act as an organizing principle for the superconducting state.
... single-particle) energy [2, 18, 19]. Interestingly, it turns out that in underdoped samples of the cuprates the " kinetic " energy behaves oppositely to the BCS prediction (i.e. is decreased by the normal to superconducting transition), while on the overdoped side it behaves consistently with BCS (i.e. is increased) [20, 21], which is in fact consistent with numerical calculations based on the Hubbard model and the t − J model222324. However, one should beware of assuming that the " kinetic " (single-particle) energy which enters the sum rule (7) is necessarily the expectation value of the sum of the single-particle termsˆTtermsˆ termsˆT andˆUandˆ andˆU in Eq. (1); the tight-binding description leading to Eq. (7) is at a different level from that of the Hamiltonian (1), and it is for example not excluded that the Coulomb term in (1) may affect the effective tunnelling matrix elements in the tight-binding description. ...
Article
Full-text available
We performed an experimental study of the temperature and doping dependence of the energy-loss function of the bilayer and trilayer Bi-cuprate family. The primary aim is to obtain information on the energy stored in the Coulomb interaction between the conduction electrons, on the temperature dependence thereof, and on the change of Coulomb interaction when Cooper-pairs are formed. We performed temperature-dependent ellipsometry measurements on several Bi2_2Sr2_2CaCu2_2O8x_{8-x} single crystals: under-doped with Tc=60,70T_c=60, 70 and 83~K, optimally doped with Tc=91T_c=91~K, overdoped with Tc=81,70T_c=81, 70 and 58~K, as well as optimally doped Bi2_2Sr2_2Ca2_2Cu3_3O10+x_{10+x} with Tc=110T_c=110~K. Our first observation is that, as the temperature drops through TcT_c, the loss function in the range up to 2~eV displays an abrupt change of temperature dependence as compared to the temperature dependence in the normal state. This effect at -- or close to -- TcT_c depends strongly on doping, with a sign-change for weak overdoping. A second observation is that in the underdoped and optimally doped regime, when cooling down from much higher temperature, the loss function integral shows a gradual loss of spectral weight in a temperature range up to twice TcT_c, coinciding with the range where other experiments have indicated the existence of strongly enhanced pair-correlations.
Article
We carry out a theoretical study of unconventional superconductivity in twisted bilayer cuprates (TBCs) as a function of electron density and layer twist angle. The bilayer t−J−U model is employed and analyzed within the framework of a generalized variational wave function approach in the statistically consistent Gutzwiller formulation. The constructed phase diagram encompasses both a gapless d-wave state (reflecting the pairing symmetry of untwisted copper-oxides) and gapped d+eiφd phase that breaks spontaneously time reversal symmetry (TRS) and is characterized by a nontrivial Chern number. We find that the d+eiφd state occupies a nonconvex butterfly-shaped region in the doping versus twist-angle plane and demonstrate the presence of a reentrant TRS-breaking phase on the underdoped side of the phase diagram. This circumstance supports the emergence of topological superconductivity for fine-tuned twist angles in TBC away from 45∘. Our analysis of the microscopically derived Landau free-energy functional points toward sensitivity of the superconducting order parameter to small perturbations close to the topological state boundary.
Article
The principal purpose of this topical review is to single out some of the universal features of high-temperature (high-Tc) and related strongly-correlated systems, which can be compared with experiment in a quantitative manner. The description starts with the concept of exchange-interaction-mediated (real-space) pairing, combined with strong correlations among narrow band electrons, for which the reference state is that of the Mott–Hubbard insulator. The physical discussion of concrete properties relies on variational approach, starting from generalized renormalized mean-field theory (RMFT) in the form of statistically-consistent Gutzwiller approximation (SGA), and its subsequent generalization, i.e., a systematic Diagrammatic Expansion of the Variational (Gutzwiller-type) Wave Function (DE-GWF). The solution leads to the two energy scales, one involving unconventional quasiparticles close to the Fermi energy, and the other reflecting the fully correlated state, involving electrons deeper below the Fermi surface. Those two regimes are separated by a kink in the dispersion relation, which is observed in photoemission. As a result, one obtains both the doping dependent properties in the correlated state, and effective renormalized quasiparticles. The reviewed ground-state characteristics for high-Tc systems encompass high-Tc superconductivity, nematicity, charge- (and pair-) density-wave effects, as well as non-BCS kinetic energy gain in the paired state. The calculated dynamic properties are: the universal Fermi velocity, the Fermi wave-vector, the effective mass enhancement, the pseudogap; and the d-wave gap magnitude. We discuss that, within the variational approach, the minimal realistic model is represented by the so-called t-J-U Hamiltonian. Inadequacy of the t-J and Hubbard models, particularly of their RMFT versions, is discussed explicitly. For heavy fermion systems, modeled by the Anderson lattice model and with the DE-GWF approach, we discuss the phase diagram, encompassing superconducting, Kondo insulating, ferro- and anti-ferromagnetic states. The superconducting state is then a two-d-wave gap system. If the orbital degeneracy of f-electrons is included, the coexistent ferromagnetic- (spin–triplet) superconducting phases appear and match those observed for UGe2 in a semiquantitative manner. Finally, in the second part, we generalize our approach to the collective spin and charge fluctuations in high-Tc systems, starting from variational approach, defining the saddle-point state, and combining it with 1/N expansion. The present scheme differs essentially from that starting from the saddle-point Hartree–Fock approximation, and incorporating the fluctuations in the random phase approximation (RPA). The spectrum of collective spin and charge excitations is determined for the Hubbard and t-J-U models, and subsequently compared quantitatively with recent experiments. The Appendices provide formal details to make this review self-contained.
Article
We investigated kinetic properties of correlated pairing states in strongly correlated phase of the Hubbard model in two space dimensions. We employ an optimization variational Monte Carlo method, where we use the improved wave function ψ λ = e −λK ψ G for the Gutzwiller wave function ψ G with K being the kinetic part of the Hamiltonian. The Gutzwiller-BCS state is stabilized as the potential energy driven superconductivity because the Coulomb interaction energy is lowered while the kinetic energy increases in this state. In contrast, we show that in the ψ λ-BCS wave function ψ λ−BC S = e −λK P G ψ BC S , the Coulomb energy increases and instead the kinetic energy is lowered in the strongly correlated phase where the Coulomb repulsive interaction U is large. The correlated superconducting state is realized as a kinetic energy driven pairing state and this indicates the enhancement of superconductivity due to kinetic-energy effect.
Article
We study the effect of the correlated hopping term and the intersite Coulomb interaction term on principal features of the d-wave superconducting (SC) state, in both the electron and hole doped regimes within the t-J-U model. In our analysis we use the approach based on the diagrammatic expansion of the Gutzwiller wave function (DE-GWF) which allows us to go beyond the renormalized mean field theory (RMFT). We show that the correlated hopping term enhances the pairing at the electron-doped side of the phase diagram. Moreover, the so-called non-BCS regime (which manifests itself by the negative kinetic energy gain at the transition to the SC phase) is narrowed down with the increasing magnitude of the correlated hopping K\sim K. Also, the doping dependences of the nodal Fermi velocity and Fermi momentum, as well as the average number of double occupancies, are analyzed with reference to the experimental data for selected values of the parameter K. For the sake of completeness, the influence of the intersite Coulomb repulsion on the obtained results is provided. Additionally, selected results concerning the Hubbard-model case are also presented. A complete model with all two-site interactions is briefly discussed in the Appendix for reference.
Article
Full-text available
The influence of Mott physics on the doping–temperature phase diagram of copper oxides represents a major issue that is the subject of intense theoretical and experimental efforts. Here, we investigate the ultrafast electron dynamics in prototypical single-layer Bi-based cuprates at the energy scale of the O-2p Cu-3d charge-transfer (CT) process. We demonstrate a clear evolution of the CT excitations from incoherent and localized, as in a Mott insulator, to coherent and delocalized, as in a conventional metal. This reorganization of the high-energy degrees of freedom occurs at the critical doping pcr≈ 0.16 irrespective of the temperature, and it can be well described by dynamical mean-field theory calculations. We argue that the onset of low-temperature charge instabilities is the low-energy manifestation of the underlying Mottness that characterizes the p < pcr region of the phase diagram. This discovery sets a new framework for theories of charge order and low-temperature phases in underdoped copper oxides.
Article
We examine the nature of thermal flow during the annealing process of a recently reported method to produce films of the high-T c superconducting compound YBa 2 Cu 3 O x wherein the oxygen content (x) spatially varies across the length of the sample. In this context, we discuss contrasting annealing results that can be expected under differing annealing configurations-including the formation of discrete regions of pressure stabilized oxygen content associated with known lattice superstructures. We also examine characteristic energy scales associated with the corresponding normal and superconducting states of these stabilized superstructures. A relationship between ratios of the superconducting gap energy, superconducting electronic kinetic energy, and the BCS-Eliashberg coupling constant associated with each lattice superstructure is found. The near integer ratios observed suggest that the superstructures can be viewed as “quantum structural” lattice states in the sense that oxygen doping levels in between are composed of a superposition of ordered structures.
Article
We show, that in contrast to the free electron model (standard BCS model), a particular gap in the spectrum of multiband superconductors opens at some distance from the Fermi energy, if conduction band is composed of hybridized atomic orbitals of different symmetries. This gap has composite superconducting-hybridization origin, because it exists only if both the superconductivity and the hybridization between different kinds of orbitals are present. So for many classes of superconductors with multiorbital structure such spectrum changes should take place. These particular changes in the spectrum at some distance from the Fermi level result in slow convergence of the spectral weight of the optical conductivity even in quite conventional superconductors with isotropic s-wave pairing mechanism.
Article
Selected universal experimental properties of high-temperature superconducting (HTS) cuprates have been singled out in the last decade. One of the pivotal challenges in this field is the designation of a consistent interpretation framework within which we can describe quantitatively the universal features of those systems. Here we analyze in a detailed manner the principal experimental data and compare them quantitatively with the approach based on a single-band model of strongly correlated electrons supplemented with strong antiferromagnetic (super)exchange interaction (the so-called t−J−U model). The model rationale is provided by estimating its microscopic parameters on the basis of the three-band approach for the Cu-O plane. We use our original full Gutzwiller wave-function solution by going beyond the renormalized mean-field theory (RMFT) in a systematic manner. Our approach reproduces very well the observed hole doping (δ) dependence of the kinetic-energy gain in the superconducting phase, one of the principal non-Bardeen-Cooper-Schrieffer features of the cuprates. The calculated Fermi velocity in the nodal direction is practically δ-independent and its universal value agrees very well with that determined experimentally. Also, a weak doping dependence of the Fermi wave vector leads to an almost constant value of the effective mass in a pure superconducting phase which is both observed in experiment and reproduced within our approach. An assessment of the currently used models (t−J, Hubbard) is carried out and the results of the canonical RMFT as a zeroth-order solution are provided for comparison to illustrate the necessity of the introduced higher-order contributions.
Article
We consider the one-band Hubbard model on the square lattice by using variational and Green's function Monte Carlo methods, where the variational states contain Jastrow and backflow correlations on top of an uncorrelated wave function that includes BCS pairing and magnetic order. At half filling, where the ground state is antiferromagnetically ordered for any value of the on-site interaction U, we can identify a hidden critical point UMottU_{\rm Mott}, above which a finite BCS pairing is stabilized in the wave function. The existence of this point is reminiscent of the Mott transition in the paramagnetic sector and determines a separation between a Stoner insulator (at small values of U), where magnetism induces a potential energy gain, and a Mott insulator (at large values of U), where magnetic correlations drive a kinetic energy gain. Most importantly, the existence of UMottU_{\rm Mott} has crucial consequences when doping the system: we observe a tendency to phase separation into a hole-rich and a hole-poor region only when doping the Stoner insulator, while the system is uniform by doping the Mott insulator. Superconducting correlations are clearly observed above UMottU_{\rm Mott}, leading to the characteristic dome structure in doping. Furthermore, we show that the energy gain due to the presence of a finite BCS pairing above UMottU_{\rm Mott} shifts from the potential to the kinetic sector by increasing the value of the Coulomb repulsion.
Article
The universal experimental properties of high temperature superconducting (HTS) cuprates have been singled out in the last decade. One of the pivotal challenges in this field is the designation of a consistent interpretation framework within which we can describe quantitatively the universal features of those systems. Here we analyze in a detailed manner the principal experimental data and compare them quantitatively with the approach based on a single band of strongly correlated electrons supplemented with strong antiferromagnetic exchange interaction. We use our original full Gutzwiller-wave-function solution and demonstrate the indispensability of going beyond the renormalized mean field theory (RMFT). Our approach reproduces very well the observed doping (δ\delta) dependence of the kinetic-energy gain in the superconducting phase, one of the principal non-Bardeen-Cooper-Schrieffer features of the cuprates. The calculated Fermi velocity in the nodal direction is practically δ\delta- independent and its universal value agrees excellently with that determined experimentally. Also, a weak doping dependence of the Fermi wave-vector leads to an almost constant value of the effective mass in a pure superconducting phase which is both observed in the experiment and reproduced within our approach. An assessment of the currently used models is carried out and the results of the canonical RMFT are provided for comparison to illustrate the indispensability of introduced by us higher order corrections.
Article
Non-equilibrium spectroscopies of strongly correlated materials have evolved in the last two decades from avant-garde studies to a crucial tool for understanding strongly correlated materials. In particular, the possibility of obtaining both spectral and temporal information simultaneously leads to insights which are complementary (and in some instances beyond to) those attainable by conventional equilibrium experiments. The new time-resolved methods brought in novel tools to investigate the time-evolution of broken symmetry phases and the bosonic excitations which mediate the electronic interactions and eventually lead to superconductivity and other exotic phases. Furthermore, the recent development of a theoretical framework to model the dynamical response function of materials made it possible to monitor the time-evolution of both the single-particle and collective excitations under different conditions. New non-equilibrium phenomena can thus be induced and manipulated by short laser pulses, opening the way toward a new physics in correlated electron systems far from equilibrium. Here we will review the most recent advances in the experimental and theoretical studies for probing the electronic, optical, structural and magnetic non-equilibrium properties of correlated materials in the sub-picosecond time domain. We will mainly focus on the prototypical case of correlated oxides, which exhibit superconducting and other exotic phases at low temperature, although the discussion will extend also to other topical systems, such as iron-based and organic superconductors, MgB2_2, charge-transfer insulators along with other materials. It will clearly emerge that the dramatically growing experimental information will trigger the development of new theoretical concepts, methods and models.
Article
The normal state of strongly coupled superconductors is characterized by the presence of "preformed" Cooper pairs well above the superconducting critical temperature. In this regime, the electrons are paired, but they lack the phase coherence necessary for superconductivity. The existence of preformed pairs implies the existence of a characteristic energy scale associated to a pseudogap. Preformed pairs are often invoked to interpret systems where some signatures of pairing are present without actual superconductivity, but an unambiguous theoretical characterization of a preformed-pair system is still lacking. To fill this gap, we consider the response to an external pairing field of an attractive Hubbard model, which hosts one of the cleanest realizations of a preformed pair phase, and a repulsive model where s-wave superconductivity can not be realized. Using dynamical mean-field theory to study this response, we identify the characteristic features which distinguish the reaction of a preformed pair state from a normal metal without any precursor of pairing. The theoretical detection of preformed pairs is associated with the behavior of the second derivative of the order parameter with respect to the external field, as confirmed by analytic calculations in limiting cases. Our findings provide a solid testbed for the interpretation of state-of-the-art calculations for the normal state of the doped Hubbard model in terms of d-wave preformed pairs and, in perspective, of non-equilibrium experiments in high-temperature superconductors.
Article
We study the BCS-Bose Einstein Condensation (BEC) crossover of a three-dimensional spin polarized Fermi gas with Rashba spin-orbital coupling (SOC). At finite temperature, the effects of non-condensed pairs due to the thermal excitation are considered based on the G0G pair fluctuation theory. These fluctuations generate a pseudogap even persistent above Tc. Within this framework, the Sarma state or the spin polarized superfluid state and polarized pseudogap state are explored in detail. The resulting Tc curves show that the enhancement of pairing due to the SOC roughly cancels out the suppression of pairing due to the population imbalance. Thus we observed that in a large portion of the parameter space, the polarized superfluid state are stabilized by the SOC.
Article
Full-text available
A recent experiment has shown a macroscopic quantum coherent condensate at 203 K, about 19 degrees above the coldest temperature recorded on the Earth, 184 K, in pressurized sulfur hydride. This discovery is relevant not only in material science and condensed matter but also in other fields ranging from quantum computing to quantum physics of living matter. It has given the start to a gold rush looking for other macroscopic quantum coherent condensates in hydrides at the temperature range of living matter 200<Tc<400K. We present here a review of the experimental results and the theoretical works and we discuss the Fermiology of H3S focusing on Lifshitz transitions as a function of pressure. We discuss the possible role of the shape resonance near a neck disrupting Lifshitz transition, in the Bianconi-Perali Valletta (BPV) theory, for rising the critical temperature in a multigap superconductor, as the Feshbach resonance rises the critical temperature in Fermionic ultracold gases.
Article
Full-text available
We present the full Gutzwiller-wave-function solution of the Anderson lattice model in two dimensions that leads to the correlation-driven multigap superconducting (SC) ground state with the dominant dx2y2d_{x^2-y^2}-wave symmetry. The results are consistent with the principal properties of the heavy-fermion superconductor CeCoIn5_5. We regard the pairing mechanism as universal and thus applicable to other Ce-based heavy-fermion compounds. Additionally, a gain in kinetic energy in the SC state takes place, as is also the case for high-temperature superconductors.
Article
We present a review on the developments in the photoemission spectrometer with a vacuum ultraviolet laser at Institute for Solid State Physics at the University of Tokyo. The advantages of high energy resolution, high cooling ability, and bulk sensitivity enable applications with a wide range of materials. We introduce some examples of fine electronic structures detected by laser photoemission spectroscopy and discuss the prospects of research on low-transition-temperature superconductors exhibiting unconventional superconductivity.
Article
We discuss effects of surface perturbations on equilibrium surface currents which contribute to orbital magnetization and orbital angular momentum in systems without time reversal symmetry. We show that, in a U(1) particle number conserving system, disorder and other perturbations at a surface do not affect the equilibrium surface current and corresponding orbital magnetization due to a sum rule which is analogous to Luttinger's theorem. On the other hand, for a superfluid, the sum rule is no longer applicable and hence the surface mass current and corresponding orbital angular momentum can depend on details of a surface.
Article
Full-text available
Beliaev damping in a superfluid is the decay of a collective excitation into two lower frequency collective excitations; it represents the only decay mode for a bosonic collective excitation in a superfluid at T = 0. The standard treatment for this decay assumes a linear spectrum, which in turn implies that the final state momenta must be collinear to the initial state. We extend this treatment, showing that the inclusion of a gradient term in the Hamiltonian yields a realistic spectrum for the bosonic excitations; we then derive a formula for the decay rate of such excitations, and show that even moderate nonlinearities in the spectrum can yield substantial deviations from the standard result. We apply our result to an attractive Fermi gas in the BCS-BEC crossover: here the low-energy bosonic collective excitations are density oscillations driven by the phase of the pairing order field. These collective excitations, which are gapless modes as a consequence of the Goldstone mechanism, have a spectrum which is well established both theoretically and experimentally, and whose linewidth, we show, is determined at low temperatures by the Beliaev decay mechanism.
Article
The study of Majorana fermions is of great importance for the implementation of a quantum computer. These modes are topologically protected and very stable. It is now well known that a p-wave superconducting wire can sustain, in its topological non-trivial phase, Majorana quasi-particles at its ends. Since this type of superconductor is not found in nature, many methods have been devised to implement it. Most of them rely on the spin-orbit interaction. In this paper we study the superconducting properties of a two-band system in the presence of antisymmetric hybridization. We consider inter-band attractive interactions and also an attractive interaction in one of the bands. We show that superconducting fluctuations with p-wave character are induced in the non-interacting band due to the combined effects of inter-band coupling and hybridization. In the case of a wire, this type of induced superconductivity gives rise to four Majorana modes at its ends. The long range correlation between the different charge states of these modes offers new possibilities for the implementation of protected q-bits.
Article
We scrutinize the real-frequency structure of the self-energy in the superconducting state of the attractive Hubbard model within the dynamical mean-field theory. Within the strong-coupling superconducting phase which has been understood in terms of the Bose-Einstein condensation in the literature, we find two qualitatively different regions crossing over each other. In one region close to zero temperature, the self-energy depends on the frequency only weakly at low energy. On the other hand, in the region close to the critical temperature, the self-energy shows a pole structure. The latter region becomes more dominant as the interaction becomes stronger. We reveal that the self-energy pole in the latter region is generated by a coupling to a hidden fermionic excitation. The hidden fermion persists in the normal state, where it yields a pseudogap. We compare these properties with those of the repulsive Hubbard model relevant for high-temperature cuprate superconductors, showing that hidden fermions are a key common ingredient in strongly correlated superconductivity.
Article
Full-text available
Elastic phase transitions of crystals and phase transitions whose order parameter couples linearly to elastic degrees of freedom are reviewed with particular focus on instabilities at zero temperature. A characteristic feature of these transitions is the suppression of critical fluctuations by long-range shear forces. As a consequence, at an elastic crystal symmetry-breaking quantum phase transition the phonon velocity vanishes only along certain crystallographic directions giving rise to critical phonon thermodynamics described by a stable Gaussian fixed point. At an isostructural solid-solid quantum critical end point, on the other hand, the complete suppression of critical fluctuations results in true mean-field critical behavior without a diverging correlation length. Whenever an order parameter couples bilinearly to the strain tensor, the critical properties are eventually governed by critical crystal elasticity. This is, for example, the case for quantum critical metamagnetism but also for the classical critical Mott end point at finite T. We discuss and compare the solid-solid end points expected close to the Mott transition in V2_2O3_3 and κ\kappa-(BEDT-TTF)2X_2 X.
Article
The spatial structures of the chiral symmetry breaking(χSB)−quark−antiquark(qq¯) pair and two-color superconducting(2SC)−quark−quark(qq), antiquark−antiquark(q¯q¯), and hole−hole(hh) pairs are investigated. At low density, it is found that the qq¯ pair is well localized with average bond length of the order 1fm. It is then suggested that the pions, which are excitations arising from flavor-space phase fluctuations, exhibit the spatial structure of the underlying qq¯-paired ground state. At intermediate density where the quarks form a 2SC state, it is found that the qq and hh pairs are extended and oscillating in real space while the q¯q¯ pair remains well localized.
Article
Full-text available
We present a theoretical study of the ground state of the BCS-BEC crossover in dilute two-dimensional Fermi gases. While the mean-field theory provides a simple and analytical equation of state, the pressure is equal to that of a noninteracting Fermi gas in the entire BCS-BEC crossover, which is not consistent with the features of a weakly interacting Bose condensate in the BEC limit and a weakly interacting Fermi liquid in the BCS limit. The inadequacy of the 2D mean-field theory indicates that the quantum fluctuations are much more pronounced than those in 3D. In this work, we show that the inclusion of the Gaussian quantum fluctuations naturally recovers the above features in both the BEC and the BCS limits. In the BEC limit, the missing logarithmic dependence on the boson chemical potential is recovered by the quantum fluctuations. Near the quantum phase transition from the vacuum to the BEC phase, we compare our equation of state with the known grand canonical equation of state of 2D Bose gases and determine the ratio of the composite boson scattering length aBa_{\rm B} to the fermion scattering length a2Da_{\rm 2D}. We find aB0.56a2Da_{\rm B}\simeq 0.56 a_{\rm 2D}, in good agreement with the exact four-body calculation. We compare our equation of state in the BCS-BEC crossover with recent results from the quantum Monte Carlo simulations and the experimental measurements and find good agreements.
Article
We have measured isofield curves for the kinetic energy density (E k) in the superconducting state of a Bi2Sr2CaCu2O8+δ (Bi-2212) single crystal. These curves were determined from magnetization versus temperature experiments that were analyzed according to the prescription of the virial theorem of superconductivity. The magnetization measurements were carried out using the zero field cooling (ZFC) and field cooled cooling (FCC) protocols. This procedure allows the determination of the temperature interval where the magnetization behaves reversibly. This study is limited to the temperature region where the pinning effects are negligible. The field-induced kinetic energy is associated with the currents circulating around the vortices. The obtained results allow the estimation of the upper critical field and are in accordance to the expectations of the Abrikosov theory for type-II superconductors.
Article
Full-text available
We provide a new perspective on the pseudogap physics for attractive fermions as described by the three-dimensional Hubbard model. The pseudogap in the single-particle spectral function, which occurs for temperatures above the critical temperature TcT_c of the superfluid transition, is often interpreted in terms of preformed, uncondensed pairs. Here we show that the occurrence of pseudogap physics can be consistently understood in terms of local excitations which lead to a splitting of the quasiparticle peak for sufficiently large interaction. This effect becomes prominent at intermediate and high temperatures when the quantum mechanical hopping is incoherent. We clarify the existence of a conjectured temperature below which pseudogap physics is expected to occur. Our results are based on approximating the physics of the three-dimensional Hubbard model by dynamical mean field theory calculations and a momentum independent self-energy. Our predictions can be tested with ultracold atoms in optical lattices with currently available temperatures and spectroscopic techniques.
Article
We give a comprehensive introduction into a diagrammatic method that allows for the evaluation of Gutzwiller wave functions in finite spatial dimensions. We discuss in detail some numerical schemes that turned out to be useful in the real-space evaluation of the diagrams. The method is applied to the problem of d-wave superconductivity in a two-dimensional single-band Hubbard model. Here, we discuss in particular the role of long-range contributions in our diagrammatic expansion. We further reconsider our previous analysis on the kinetic energy gain in the superconducting state.
Article
In the standard Bardeen-Cooper-Schrieffer model, the optical sum rule establishes the relation between the superfluid density and the change in the integral of the real part of the conductivity over the frequency after the transition to the superconducting state. In conventional low-temperature superconductors, these two values become equal if the conductivity is integrated up to a frequency of the order of several widths of the superconducting gap. Optical experiments for high-T c cuprate superconductors performed by many research groups over the world demonstrate that the integration up to a much higher frequency (of the order of the band width) is needed to reproduce the spectral weight of the superfluid component. An interpretation of these experiments has been proposed with allowance for the complex crystal structure of cuprates, in which several orbitals of different symmetries approach the Fermi level.
Article
We report on experimental measurements of the magnetically induced kinetic energy density (E k ) in single-crystal samples of YBa 2Cu 3O x (YBCO), with the oxygen contents x=6.72, 6.78, 6.85, and 6.90. Our study is restricted to the reversible region near the critical temperature (T c ), where the pinning force acting on the vortices is negligible. We use the expression E k =−M⋅B (M is the magnetization and B is the magnetic induction) to calculate the kinetic energy density from magnetization measurements carried out in magnetic fields up to 5 T. We analyze the behavior of E k as a function of the temperature for several isofield curves and construct E k versus B curves as well. We find that E k rises with the increase of the charge carriers density. Granularity effects and dimensionality of the order parameter can also be important factors contributing to the kinetic energy density.
Article
Full-text available
We theoretically investigate the equation of state and Tan's contact of a non-degenerate three dimensional Bose gas near a broad Feshbach resonance, within the framework of large-N expansion. Our results agree with the path-integral Monte Carlo simulations in the weak-coupling limit and recover the second-order virial expansion predictions at strong interactions and high temperatures. At resonance, we find that the chemical potential and energy are significantly enhanced by the strong repulsion, while the entropy does not change significantly. With increasing temperature, the two-body contact initially increases and then decreases like T1T^{-1} at large temperature, and therefore exhibits a peak structure at about 4Tc04T_{c0}, where Tc0T_{c0} is the Bose-Einstein condensation temperature of an ideal, non-interacting Bose gas. These results may be experimentally examined with a non-degenerate unitary Bose gas, where the three-body recombination rate is substantially reduced. In particular, the non-monotonic temperature dependence of the two-body contact could be inferred from the momentum distribution measurement.
Article
Full-text available
We study the dynamic response of an s-wave BCS-BEC (atomic-molecular) condensate to detuning quenches within the two channel model beyond the weak coupling BCS limit. At long times after the quench, the condensate ends up in one of three main asymptotic states (nonequilibrium phases), which are qualitatively similar to those in other fermionic condensates defined by a global complex order parameter. In phase I the amplitude of the order parameter vanishes as a power law, in phase II it goes to a nonzero constant, and in phase III it oscillates persistently. We construct exact quench phase diagrams that predict the asymptotic state (including the many-body wavefunction) depending on the initial and final detunings and on the Feshbach resonance width. Outside of the weak coupling regime, both the mechanism and the time dependence of the relaxation of the amplitude of the order parameter in phases I and II are modified. Also, quenches from arbitrarily weak initial to sufficiently strong final coupling do not produce persistent oscillations in contrast to the behavior in the BCS regime. The most remarkable feature of coherent condensate dynamics in various fermion superfluids is an effective reduction in the number of dynamic degrees of freedom as the evolution time goes to infinity. As a result, the long time dynamics can be fully described in terms of just a few new collective dynamical variables governed by the same Hamiltonian only with "renormalized" parameters. Combining this feature with the integrability of the underlying (e.g. the two channel) model, we develop and consistently present a general method that explicitly obtains the exact asymptotic state of the system.
Article
Full-text available
The in-plane infrared and visible (3meV-3eV) reflectivity of Bi2Sr2CaCu2O8+delta (Bi-2212) thin films is measured between 300K and 10K for different doping levels with unprecedented accuracy. The optical conductivity is derived through an accurate fitting procedure. We study the transfer of spectral weight from finite energy into the superfluid as the system becomes superconducting. In the overdoped regime, the superfluid develops at the expense of states lying below 60meV , which is a conventional energy of the order of a few times the superconducting gap. In the underdoped regime, spectral weight is removed from up to 2eV , far beyond any conventional scale. The intraband spectral weight change between the normal and superconducting state, if analyzed in terms of a change of kinetic energy, is ˜1meV . Compared to the condensation energy, this figure addresses the issue of a kinetic-energy driven mechanism.
Article
Full-text available
Recently, high-resolution angle-resolved photoemission spectroscopy has been used to determine the detailed momentum dependence of the superconducting gap in the high-temperature superconductor Bi2Sr2CaCu2O8. In this paper, we first describe tight-binding fits to the normal-state dispersion and superlattice modulation effects. We then discuss various theoretical models in light of the gap measurements. We find that the simplest model which fits the data is the anisotropic s-wave gap cos(kx)cos(ky), which within a one-band BCS framework suggests the importance of next-near-neighbor Cu-Cu interactions. Various alternative interpretations of the observed gap are also discussed, along with the implications for microscopic theories of high-temperature superconductors.
Article
Full-text available
The Ferrell-Glover-Tinkham (FGT) sum rule has been applied to the temperature dependence of the in-plane optical conductivity of optimally-doped YBa_2Cu_3O_{6.95} and underdoped YBa_2Cu_3O_{6.60}. Within the accuracy of the experiment, the sum rule is obeyed in both materials. However, the energy scale \omega_c required to recover the full strength of the superfluid \rho_s in the two materials is dramatically different; \omega_c \simeq 800 cm^{-1} in the optimally doped system (close to twice the maximum of the superconducting gap, 2\Delta_0), but \omega_c \gtrsim 5000 cm^{-1} in the underdoped system. In both materials, the normal-state scattering rate close to the critical temperature is small, \Gamma < 2\Delta_0, so that the materials are not in the dirty limit and the relevant energy scale for \rho_s in a BCS material should be twice the energy gap. The FGT sum rule in the optimally-doped material suggests that the majority of the spectral weight of the condensate comes from energies below 2\Delta_0, which is consistent with a BCS material in which the condensate originates from a Fermi liquid normal state. In the underdoped material the larger energy scale may be a result of the non-Fermi liquid nature of the normal state. The dramatically different energy scales suggest that the nature of the normal state creates specific conditions for observing the different aspects of what is presumably a central mechanism for superconductivity in these materials.
Article
Full-text available
A brief introduction is given in the generic microscopic framework of superconductivity. The consequences for the temperature dependence of the kinetic energy, and the correlation energy are discussed for two cases: The BCS scenario and the non-Fermi liquid scenario. A quantitative comparison is made between the BCS-prediction for d-wave pairing in a band with nearest neighbor and next-nearest neighbor hoppping and the experimental specific heat and the optical intraband spectral weight along the plane. We show that the BCS-prediction produces the wrong sign for the kink at T c of the intraband spectral weight, even though the model calculation agrees well with the specific heat.
Article
Full-text available
We report on generic trends in the behavior of the interlayer penetration depth λc\lambda_c of several different classes of quasi two-dimensional superconductors including high-Tc_c cuprates, Sr2_2RuO4_4, transition metal dichalcogenides and organic materials of the (BEDTTTF)2X(BEDT-TTF)_2X - series. Analysis of these trends reveals two distinct patterns in the scaling between the values of λc\lambda_c and the magnitude of the c-axis DC conductivity σDC\sigma_{DC}: one realized in the systems with a ground state formed out of well defined quasiparticles and the other seen in systems in which the quasiparticles are not well defined. The latter pattern is found primarily in under-doped cuprates and indicates a dramatic enhancement (factor 102\simeq 10^2) of the energy scale ΩC\Omega_C associated with the formation of the condensate compared to the data for conventional materials. We discuss the implication of these results on the understanding of superconductivity in high-TcT_c cuprates. Comment: 7 pages, 3 figures
Article
Full-text available
The in-plane optical conductivity of Bi2Sr2CaCu2O8+d thin films with small carrier density (underdoped) up to large carrier density (overdoped) is analyzed with unprecedented accuracy. Integrating the conductivity up to increasingly higher energies points to the energy scale involved when the superfluid condensate builds up. In the underdoped sample, states extending up to 2 eV contribute to the superfluid. This anomalously large energy scale may be assigned to a change of in-plane kinetic energy at the superconducting transition, and is compatible with an electronic pairing mechanism. Comment: 11 pages, 3 figures
Article
Three general theorems of statistical mechanics are used to calculate the differences, between the normal and superconducting states of a metal in (i) the mean kinetic energy of the electrons, (ii) the mean kinetic energy of the lattice, and (iii) the mean potential energy of the entire system. The word "mean" implies thermal average at a given temperature and pressure. The formal properties of these differences are established and a numerical calculation is carried out in the case of tin. The most important results of this investigation are that (a) all three differences are of the same order of magnitude (∼10-3 cal/mole for a typical superconductor) at all temperatures, (b) they all vanish at the transition temperature, (c) the mean kinetic energy of the electrons is greater in the superconducting state than in the normal state and depends strongly on the isotopic mass, (d) the mean kinetic energy of the lattice is less in the superconducting state than in the normal state and depends equally strongly on the electron mass, and (e) the mean potential energy of the entire system is also less in the superconducting state than in the normal state. In the final section these results are discussed from a physical point of view.
Article
Electrical transport measurements were carried out on ultrathin films of high temperature superconductor at extremely low temperatures and in high magnetic fields. These films were fabricated by molecular-beam-epitaxy (MBE). Normal state Hall effect measurements were carried out on both ultrathin and thin films. The Hall number (R[sub H](exp -1)) was a linear function of temperature in thin films and was less temperature dependent in ultrathin films. The Hall angle (cot theta(sub H)) on the other hand exhibited the same T2 dependence in both cases, in accordance with Anderson's Luttinger liquid phenomenology. When the transition temperature decreased to zero the Hall number decreased to a limiting value which corresponded approximately to one pair per coherence volume. The superconductor-insulator transition was studied both in zero magnetic field and in a finite magnetic field. The zero field transition was achieved either by considering a sequence of films of decreasing thicknesses, or by successive thermal cycling of a single film in vacuum. The critical resistance was found to be very close to universal constant h/4e(exp 2) (6.5 k-omega). This result supports the notion that the critical resistance in the superconductor-insulator transition in two dimensions is universal. Anomalous magnetoresistance was observed in films having resistances with values near that of zero-field superconductor-insulator transition. This unusual behavior may result from an interaction between carriers and antiferromagnetically ordered Cu2+ spins of the CuO2 planes. Upon application of a magnetic field three successive superconductor-insulator transitions were found. The first two at low critical fields appear to result from the film sheet resistance being modulated by the applied magnetic field, possibly by scattering of the carriers from reorienting spins. The third one may represent the new type of superconductor-insulator transition proposed by Fisher.
Article
In spiral galaxies where the molecular phase dominates the interstellar medium, the molecular gas as traced by CO emission will approximately obey the continuity equation on orbital timescales. The Tremaine-Weinberg method can then be used to determine the pattern speed of such galaxies. We have applied the method to single-dish CO maps of three nearby spirals, M51, M83 and NGC 6946 to obtain estimates of their pattern speeds: 38 +/- 7 km/s/kpc, 45 +/- 8 km/s/ kpc and 39 +/- 8 km/s/kpc, respectively, and we compare these results to previous measurements. We also analyze the major sources of systematic errors in applying the Tremaine-Weinberg method to maps of CO emission. Characterization the atmospheric surface layer is an important and often overlooked step in site selection for small telescopes. Turbulence in the surface layer can contribute half or more of the total atmospheric image degradation encountered at a typical astronomical site. The overall image quality of the site feeds back into the design of both the optical system and instruments of telescopes in significant ways, both scientific and financial. Existing methods of characterizing turbulence in the surface layer measure non- optical quantities and rely heavily on turbulence theory that is unlikely to apply in surface layer conditions at astronomical sites. Therefore, it was undertaken to develop new optical methods to focus specifically on characterizing turbulence in the first thirty meters of the surface layer. The Two Source Differential Image Motion Monitor (2SDIMM) measures the apparent separation of a pair of transmitters suspended from the top of a tower, extending the traditional Differential Image Motion Monitor concept to surface layer studies. The Structure Function Monitor (SFM) adapts the Gerchberg-Saxton phase retrieval algorithm to the recovery of the phase of the incoming wavefront from an artifical source across the aperture of a small telescope. >From the wavefront phase, all relevant atmospheric turbulence parameters can be obtained on all spatial scales available to the aperture.
Article
We consider a gas of fermions interacting via an attractive potential. We study the ground state of that system and calculate the critical temperature for the onset of superconductivity as a function of the coupling strength. We compare the behavior of continuum and lattice models and show that the evolution from weak to strong coupling superconductivity is smooth.
Article
Optical data are reported on a spectral weight transfer over a broad frequency range of Bi2Sr2CaCu2O8+delta, when this material became superconducting. Using spectroscopic ellipsometry, we observed the removal of a small amount of spectral weight in a broad frequency band from 10(4) cm(-1) to at least 2 x 10(4) cm(-1), due to the onset of superconductivity. We observed a blue shift of the ab-plane plasma frequency when the material became superconducting, indicating that the spectral weight was transferred to the infrared range. Our observations are in agreement with models in which superconductivity is accompanied by an increased charge carrier spectral weight. The measured spectral weight transfer is large enough to account for the condensation energy in these compounds.
Article
We review the field of high temperature cuprate superconductors, with an emphasis on the nature of their electronic properties. After a general overview of experiment and theory, we concentrate on recent results obtained by angle resolved photoemission, inelastic neutron scattering, and optical conductivity, along with various proposed explanations for these results. We conclude by reviewing efforts which attempt to identify the energy savings involved in the formation of the superconducting ground state. Comment: 76 pages, 53 figures, submitted to Rep. Prog. Phys
Article
We consider the condensation energy in superconductors where the pairing is electronic in origin and is mediated by a collective bosonic mode. We use magnetically-mediated superconductivity as an example, and show that for large spin-fermion couplings, the physics is qualitatively different from the BCS theory as the condensation energy results from the feedback on spin excitations, while the electronic contribution to the condensation energy is positive due to an ``undressing'' feedback on the fermions. The same feedback effect accounts for the gain of the kinetic energy at strong couplings. Comment: 4 pages, revtex 4, 3 eps figures
Article
Using a simple model for the frequency dependent scattering rate, we evaluate the in-plane optical integral for cuprate superconductors in the normal and superconducting states. In the overdoped region, this integral is conserved. In the optimal and underdoped region, though, the optical integrals differ, implying a lowering of the in-plane kinetic energy in the superconducting state. This sum rule violation, due to the difference of the non Fermi liquid normal state and the superconducting Fermi liquid state, has a magnitude comparable to recent experimental results. Comment: 5 pages, revtex, 4 encapsulated postscript figures
Article
Underdoped high-Tc superconductors are frequently characterised by a temperature, T*, below which the normal-state pseudogap opens. Two different "phase diagrams" based on the doping (p) dependence of T* are currently considered: one where T* falls to zero at a critical doping state and the other where T* merges with Tc in the overdoped region. By examining the temperature dependence of the NMR Knight shift and relaxation rate, entropy, resistivity, infrared conductivity, Raman scattering, ARPES and tunnelling data it is concluded that the second scenario is not at all supported. Neither can one distinguish a small and a large pseudogap as is often done. T* is an energy scale which falls abruptly to zero at p=0.19. Comment: 13 pages, 11 figures, a response to confusion at M^2S Conference, Houston, regarding the phase behaviour of the HTS cuprates. Submitted to Physica C, 2 May 2000. More references added as well as section on c-axis resistivity
where Ekinhas been calculated versus doping in a specific model. However, our experimental data shown in this graph were taken from Ref.[2], where the positive sign of ∆Ekinin the over-doped sample was overlooked
  • M Norman
A similar graph was shown in M. Norman and C. P´ epin, Phys. Rev. B 66, 100506(R) (2002), where Ekinhas been calculated versus doping in a specific model. However, our experimental data shown in this graph were taken from Ref.[2], where the positive sign of ∆Ekinin the over-doped sample was overlooked.
A. Leggett, in Modern Trends in the the-ory of condensed matter
  • P Nozi
  • S Schmitt
  • J Rink
  • Low
  • Temp
P. Nozi` eres and S. Schmitt-Rink, J. Low. Temp. Physics 59, 195 (1985); A. Leggett, in Modern Trends in the the-ory of condensed matter, Ed. A Bekalksky and J. Przys-pawa (Springer Verlag, 1980), pp.13-27.
  • A F Santander-Syro
A.F. Santander-Syro et al., Phys. Rev. B 70, 134504 (2004).
  • C C Homes
C. C. Homes et al., Phys. Rev. B 69, 024514 (2004).
  • S Dordevic
S. Dordevic et al., Phys. Rev. B 65, 134511 (2002).
  • A F Santander-Syro
A.F. Santander-Syro et al., Europhys. Lett 62, 568 (2003).
where E kin has been calculated versus doping in a specific model. However, our experimental data shown in this graph were taken from Ref
  • M Norman
  • C Pépin
A similar graph was shown in M. Norman and C. Pépin, Phys. Rev. B 66, 100506(R) (2002), where E kin has been calculated versus doping in a specific model. However, our experimental data shown in this graph were taken from Ref.[2], where the positive sign of ∆E kin in the overdoped sample was overlooked.
These authors present a quantitative analysis for optimally doped YBCO and claim a similar behaviour for slightly underdoped Bi-2212. Their analysis and the resulting conclusions are objected by D. van der Marel
  • Boris
The sign of ∆E kin in underdoped and close to optimally doped Bi-2212 (Ref.[1, 2, 3]) has been challenged by Boris et al., Science 304, 708 (2004). These authors present a quantitative analysis for optimally doped YBCO and claim a similar behaviour for slightly underdoped Bi-2212. Their analysis and the resulting conclusions are objected by D. van der Marel (private communication), A.F. Santander-Syro and N. Bontemps.
  • H J A Molegraaf
H. J. A. Molegraaf et al., Science 295, 2239 (2002).
  • M R Norman
M. R. Norman et al., Phys. Rev. B 52, 615 (1995).
  • J L Tallon
  • J W Loram
J. L. Tallon and J. W. Loram, Physica C 349, 53 (2001).
  • J W Loram
J. W. Loram et al., Physica C 341-348, 831 (2001).
  • P Nozières
  • S Schmitt-Rink
P. Nozières and S. Schmitt-Rink, J. Low. Temp. Physics 59, 195 (1985);