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Energy scales of CDW, superconducting and pseudogap orders a, ΔCDW (filled symbols) and TCDW (open symbols) for Hg-1223 (triangles) and Y-123 (squares) cuprates showing different doping trends. The data for Hg-1223 and Y-123 cuprates are extracted from Figs. 1 and 2 and from Supplementary Section E (Supplementary Fig. 4). The continuous and dotted lines are guides for the eyes. b, ΔCDW, ΔSC and ΔPG display the same doping dependence; in particular, ΔSC and ΔCDW are close in energy. The error bars represent standard deviations of the superconducting peak, the CDW hump and the pseudogap end measured on the Raman spectra.
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The cuprate high-temperature superconductors develop spontaneous charge density wave (CDW) order below a temperature TCDW and over a wide range of hole doping (p). An outstanding challenge in the field is to understand whether this modulated phase is related to the more exhaustively studied pseudogap and superconducting phases1,2. To address this i...
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An account is given of the main steps that led the research group in Rome, to which the author belongs, to the formulation of the charge-density-wave scenario for high- T c superconducting cuprates. The early finding of the generic tendency of strongly correlated electron systems with short range interactions to undergo electron phase separation wa...
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... Pseudogap states have been observed in various materials with strong electronic correlation [1][2][3][4][5][6][7][8][9][10] including a notable example of high-temperature superconductors. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] A few different mechanisms have been proposed as origins of pseudogap states, which involve competing orders, [8][9][10]20] preformed Cooper pairs, [21][22][23] and disorder. [1][2][3][4][5][6][7][17][18][19]21,22,[24][25][26] Pseudogap states have also been observed in CDW materials with emerging superconductivity such as 1T-TaS 2 [4] and 2H-TaSe 2 , [9] which have been related to the impurity-induced disorder and the CDW fluctuation, respectively. ...
... Pseudogap states have been observed in various materials with strong electronic correlation [1][2][3][4][5][6][7][8][9][10] including a notable example of high-temperature superconductors. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26] A few different mechanisms have been proposed as origins of pseudogap states, which involve competing orders, [8][9][10]20] preformed Cooper pairs, [21][22][23] and disorder. [1][2][3][4][5][6][7][17][18][19]21,22,[24][25][26] Pseudogap states have also been observed in CDW materials with emerging superconductivity such as 1T-TaS 2 [4] and 2H-TaSe 2 , [9] which have been related to the impurity-induced disorder and the CDW fluctuation, respectively. ...
The emergence of a pseudogap is a hallmark of anomalous electronic states formed through substantial manybody interaction but the mechanism of the pseudogap formation and its role in related emerging quantum states such as unconventional superconductivity remain largely elusive. Here, the emergence of an unusual pseudogap in a representative van der Waals chiral charge density wave (CDW) materials with strong electron correlation, 1T‐TaS2 is reported, through isoelectronic substitute of S. The evolution of electronic band dispersions of 1T‐TaS2 − xSex (0 ⩽ x ⩽ 2) is systematically investigated using angle‐resolved photoemission spectroscopy (ARPES). The results show that the Se substitution induces a quantum transition from an insulating to a pseudogap metallic phase with the CDW order preserved. Moreover, the asymmetry of the pseudogap spectral function is found, which reflects the chiral nature of CDW structure. The present observation is contrasted with the previous suggestions of a Mott transition driven by band width control or charge transfer. Instead, the pseudogap phase is attributed to a disordered Mott insulator in line with the recent observation of substantial lateral electronic disorder. These findings provide a unique electronic system with chiral pseudogap, where the complex interplay between CDW, chirality, disorder, and electronic correlation may lead to unconventional emergent physics.
... Before presenting our model for the R H (p, T ) we need to address the role of planar charge instabilities 9 , which have been observed in various forms, such as stripe phases 10 , checkerboard order 11 , puddles 12 , and nematic phases 13 , across several materials and compounds 14 . Initially, this phenomenon was attributed solely to weakly doped compounds, particularly around p = 1/8 Cu atom, where the CDW, or incommensurate charge order (CO) is more intense [15][16][17][18] , while overdoped compounds were traditionally considered to be Fermi liquid materials. However, this perspective is evolving due to numerous recent discoveries of CDW phases and local inhomogeneities in overdoped La 2−x Sr x CuO 4 (LSCO), with doping levels reaching p ≡ x = 0.21 13,19,20 and potentially up to p = 0.27 in the form of puddles 21 . ...
Measurements of the Hall coefficient in LaSrCuO, ranging from the undoped () Mott insulator to overdoped compounds, exhibit a temperature dependence that offers insights into their electronic structure. We interpret these results using a model based on the theory of phase-separation (PS) dynamics, which begins at half-filled () and at a temperature , near the pseudogap temperature . The holes have low mobility and provide the modulations of the charge density waves (CDW). As doping increases from , these modulations guide the additional p holes to occupy alternating CDW domains. This charge inhomogeneity may facilitate the formation of localized superconducting amplitudes below the critical onset temperature . Using thermal activation expressions, along with quantum tunnelling between the charge domains, we successfully reproduce all Hall coefficient measurements and highlight the relevant energies of cuprates. The calculations confirm three significant electronic features: the phase-separating role of the pseudogap temperature, the superconducting state achieved through phase coherence, and the two types of charge carriers whose energies and mobilities become comparable at , where . This results in a crossover from to . These findings, along with the calculations from insulating to overdoped compounds, underscore the critical role of the electronic phase separation in the properties of cuprates.
... The electron-electron (e-e) correlation is considered to be at the heart of CDW in cuprates [10,11]. Moreover, pseudogap and superconducting phase are believed to be intimately related with a CDW [27,28]. In this case, lattice modulation is believed to be driven by e-e interaction and charge redistribution. ...
Using high-energy-resolution inelastic x-ray scattering, we observe anomalous softening and damping of the transverse acoustic phonon in UPtSi as the system is cooled towards the charge density wave (CDW) transition temperature, T. The phonon exhibits a marked Kohn type anomaly around the CDW wave vector, Q, and becomes over-damped within a finite momentum range already well above T. The dispersion anomaly is consistent with a potential Fermi surface nesting, which together with the extended phonon collapse indicate strong electron-phonon coupling. The transition temperature estimated from the phonon softening is markedly lower than T, further corroborating a primarily electronic instability rather than a phonon-driven transition. Our results establish UPtSi as an exemplary case of an electronically driven strongly correlated CDW system.
... Connections between certain aspects of the pseudogap and the short-range CDW have been unveiled in earlier studies [16][17][18][19][20][21][22] but our findings offer a complementary perspective. Although they fall short of χ spin (q = 0). ...
A fundamental obstacle to understanding high-temperature superconducting cuprates is that the occurrence of superconductivity hinders the observation of the normal-state properties at low temperature. One important property illustrating this issue is the spin susceptibility: its decrease upon cooling in the normal state is considered as evidence of pseudogap behaviour. However, unambiguous interpretation of this decrease has been impossible, as the crucial low-temperature data inevitably reflect the superconducting pairing rather than the normal state. Here we measure the spin susceptibility of YBa2Cu3Oy at low temperature while suppressing superconductivity in high magnetic field. We found that there are two thermally activated contributions, each of which comes from a different gap, alongside a residual component due to gapless excitations. We relate these two distinct gaps to short-range charge density waves and to the formation of singlets, as occurs in certain quantum spin systems. Both phenomena contribute to the pseudogap at low temperature, supplementing the short-lived antiferromagnetism that initiates pseudogap behaviour at high temperatures. We, therefore, propose that the pseudogap should be regarded as a composite property and that, when not undergoing spin-stripe ordering, underdoped cuprates tend to form short-range spin singlets.
... Due to the incommensuracy of the quantum order or competing phases, the volume of quantum materials is partitioned into multiple domains. 6,7 This electronic inhomogeneity in the material results in a non-local optical response. 8,9 Here, we study such non-local optical response of 1T-TaS 2 , a layered quantum material supporting charge density waves (CDWs) at room temperature, [10][11][12][13] and probe the competition between two CDW stacking configurations using low-intensity illumination. ...
... The summation in Eq. (8) is taken over all the first-order neighbors. We use h AL(LA) to denote the Dyadic Green's function components isolated from complex exponential terms in Eq. (4)-(7) in g AL(LA) and cosine terms in Eq. (6). The expression in Eq. (8) indicates the susceptibility is a function of incident light direction. ...
Light–matter interaction in quantum materials presents a new paradigm as light can tip the balance between many competing quantum many-body phases to result in new phenomena. Describing the optical response of such materials requires complex models. Here, we develop a non-local model to describe the optical response of a quantum material, 1T- TaS 2. 1T- TaS 2 is a charge density wave material that supports competing stacking configurations of its charge domains. The presence of various stacking domains results in an inhomogeneity that necessitates a non-local dielectric function. We experimentally measure the non-local optical response of 1T- TaS 2 films under various illumination intensities and validate our model. The non-local parameter extracted from our measurements sheds light on the competition between the two stacking configurations of 1T- TaS 2. Our technique of measuring non-local optical response serves as a quick, simple, and non-invasive method to probe the energy landscape of strong correlations in many such quantum materials.
... The hallmark feature of multilayer cuprates is the universal n-dependence of the superconducting critical temperature T c : it is often maximum for the tri-layer (n = 3) compounds [60]. The tri-layer nHBCCO even yields the record of T c at ambient pressure among all known superconductors [61,62]. Moreover, the inner CuO 2 planes are protected from inhomogeneity and disorder [60,63,64], allowing the direct observation of Fermi pockets and the opening of the superconducting gap at low doping [63,64]. ...
Significant progress towards a theory of high-temperature superconductivity in cuprates has been achieved via the study of effective one- and three-band Hubbard models. Nevertheless, material-specific predictions, while essential for constructing a comprehensive theory, remain challenging due to the complex relationship between real materials and the parameters of the effective models. By combining cluster dynamical mean-field theory and density functional theory in a charge-self-consistent manner, here we show that the goal of material-specific predictions for high-temperature superconductors from first principles is within reach. We take on the challenge of explaining the remarkable physics of multilayer cuprates by focusing on the two representative CaCuOCl and HgBaCaCuO families. We shed light on the microscopic origin of many salient features of multilayer cuprates, in particular the n-dependence of their superconducting properties. The maximum of for the tri-layer compounds is explained by an intertwined analysis of the charge-transfer gap, superexchange J, and inhomogeneous doping between the CuO planes. We highlight the existence of a minimal doping (4\%) required for superconductivity to emerge. We capture material-specific properties such as the larger propensity of HgBaCaCuO to superconduct compared with CaCuOCl. We also find the coexistence of arcs and pockets observed with photoemission, the charge redistribution between copper and oxygen, and the link to the pseudogap. Our work establishes a framework for comprehensive studies of cuprates, enables detailed comparisons with experiment, and, through its \emph{ab initio} settings, unlocks opportunities for theoretical material design of high-temperature superconductors.
... It is widely documented that superconductivity emerges near the quantum critical point (QCP) of symmetry-broken phases. [1][2][3][4][5][6][7][8][9] This competing behavior, or the presence of a competing order, has led to notable speculation that quantum fluctuations of the order could play a role in superconductivity formation, thereby pairing electrons into Cooper pairs. For instance, spin fluctuation has been considered a pairing mediator in cuprate, iron-based, and heavy fermion superconductors where spin ordering competes with superconductivity [10][11][12][13][14][15][16] . ...
... For instance, spin fluctuation has been considered a pairing mediator in cuprate, iron-based, and heavy fermion superconductors where spin ordering competes with superconductivity [10][11][12][13][14][15][16] . A CDW, an ordering of itinerant charge carriers, also exhibits competing behavior with the superconductivity [1][2][3][4][5][6][7][8][9] . Therefore, similar to the other cases, it is natural to speculate that a CDW-associated low-energy excitation could pair the electrons and induce the superconductivity, which has not been sufficiently visited. ...
In most charge density wave (CDW) systems of different material classes, ranging from traditional correlated systems in low‐dimension to recent topological systems with Kagome lattice, superconductivity emerges when the system is driven toward the quantum critical point (QCP) of CDW via external parameters of doping and pressure. Despite this rather universal trend, the essential hinge between CDW and superconductivity has not been established yet. Here, the evidence of coupling between electron and CDW fluctuation is reported, based on a temperature‐ and intercalation‐dependent kink in the angle‐resolved photoemission spectra of 2H‐PdxTaSe2. Kinks are observed only when the system is in the CDW phase, regardless of whether a long‐ or short‐range order is established. Notably, the coupling strength is enhanced upon long‐range CDW suppression, albeit the coupling energy scale is reduced. Interestingly, the estimation of the superconducting critical temperature by incorporating the observed coupling characteristics into McMillan's equation yields results closely resembling the known values of the superconducting dome. The results thus highlight a compelling possibility that this new coupling mediates Cooper pairs, which provides new insights into the competing relationship not only for CDW but also for other competing orders.
... A gap opens up in the electronic density of states, which is often reflected in the physical properties, such as the electrical resistivity and magnetic susceptibility, and in spectroscopic experiments. 3,4,7,9,10 There are various techniques to probe the CDW state, such as X-ray diffraction (XRD), 10,11 scanning tunnelling microscopy (STM), 4,12 transmission electron microscopy (TEM), 13 angle resolved X-ray photoelectron spectroscopy (ARPES), 4 nuclear magnetic resonance (NMR), 14 Raman spectroscopy 15 and ultrafast pump-probe experiments. 16 A metal-to-insulator transition (MIT), obvious in the electrical resistivity, together with the appearance of superlattice reflections in XRD are the typical characteristic features pointing toward a CDW state. ...
Charge density wave (CDW) systems are proposed to exhibit application potential for electronic and optoelectronic devices. However, CDWs often develop at cryogenic temperatures, which hinders their applications. Therefore, identifying new materials that exhibit a CDW state at room temperature is crucial for the development of CDW-based devices. Here, we present a nonlayered tetragonal polymorph of Gd 2 Os 3 Si 5 , which exhibits a CDW state at room temperature. Gd 2 Os 3 Si 5 assumes the tetragonal Sc 2 Fe 3 Si 5 structure type with the space group P4/mnc. Single-crystal X-ray diffraction (SXRD) analysis shows that Gd 2 Os 3 Si 5 possesses an incommensurately modulated structure with modulation wave vector q = (0.53, 0, 0), while the modulation reduces the symmetry to orthorhombic Cccm(σ00)0s0. This differs from isostructural Sm 2 Ru 3 Ge 5 , where the modulated phase has been reported to possess monoclinic symmetry Pm(α0γ)0. Reinvestigation of Sm 2 Ru 3 Ge 5 suggests that its modulated crystal structure can alternatively be described by Cccm(σ00)0s0, with modulations similar to Gd 2 Os 3 Si 5. The temperature-dependent magnetic susceptibility indicates an antiferromagnetic transition at T N ≈ 5.5 K. Furthermore, it shows an anomaly at around 345 K, suggesting a CDW transition at T CDW = 345 K, in agreement with high-temperature SXRD measurements. The temperature-dependent electrical resistivity has a maximum at a lower temperature, which we nevertheless identify with the CDW transition and can be described as an insulator-to-metal transition. The calculated electronic band structure indicates q-dependent electron−phonon coupling as the dominant mechanism of CDW formation in tetragonal Gd 2 Os 3 Si 5. The modulated structure then indicates a major involvement of the Si2a atom in the CDW modulations. Compounds RE 2 T 3 X 5 (RE = rare earth, T = transition metal, X = Si, Ge) have been reported with either the tetragonal Sc 2 Fe 3 Si 5 structure type or the orthorhombic U 2 Co 3 Si 5 structure type. Not all of these compounds undergo CDW phase transitions. We find that RE 2 T 3 X 5 compounds will exhibit a CDW transition if the condition < < c ab 0.526 / 0.543 is satisfied.
... This is due to their prevalence in various topical platforms of quantum matter. CDW order has been found to coexist and/or couple to diverse emergent phases, whether in transition-metal dichalcogenides [1], cuprate and iron-based unconventional superconductors [2][3][4], or in systems with complex (topological) forms of magnetic order [5][6][7]. Crucially, the ability to induce, suppress, or modify CDWs could be a powerful means to tune emergent order parameters of correlated electron systems. ...
EuAl 4 is a rare-earth intermetallic in which competing itinerant and/or indirect exchange mechanisms give rise to a complex magnetic phase diagram, including a centrosymmetric skyrmion lattice. These phenomena arise not in the tetragonal parent structure but in the presence of a charge-density wave (CDW), which lowers the crystal symmetry and renormalizes the electronic structure. Microscopic knowledge of the corresponding atomic modulations and their driving mechanism is a prerequisite for a deeper understanding of the resulting equilibrium of electronic correlations and how it might be manipulated. Here, we use synchrotron single-crystal x-ray diffraction, inelastic x-ray scattering, and lattice-dynamics calculations to clarify the origin of the CDW in EuAl 4 . We observe a broad softening of a transverse acoustic phonon mode that sets in well above room temperature and, at T CDW = 142 K, freezes out in an atomic displacement mode described by the superspace group I m m m ( 00 γ ) s 00 . In the context of previous work, our observation is a clear confirmation that the CDW in EuAl 4 is driven by electron-phonon coupling. This result is relevant for a wider family of BaAl 4 and ThCr 2 Si 2 -type rare-earth intermetallics known to combine CDW instabilities and complex magnetism.
Published by the American Physical Society 2024
... Here, we address this question and show that the dielectric function has to be non-local to accurately describe the lightmatter interaction. Due to the incommensuracy of the quantum order or competing phases, the volume of quantum materials is partitioned into multiple domains [5,6]. This electronic inhomogeneity in the material results in a non-local optical response [7,8]. ...
Light-matter interaction in quantum materials presents a new paradigm as light can tip the balance between many competing quantum many-body phases to result in new phenomena. Describing the optical response of such materials requires complex models. Here, we develop a non-local model to describe the optical response of a quantum material, 1T-TaS. 1T-TaS is a nearly commensurate charge-density-wave material at room temperature. The competing stacking configurations of the charge domains in this layered material result in significant optical inhomogeneity that necessitates a non-local dielectric function. We experimentally measure the non-local optical response of 1T-TaS films under various illumination intensities and validate our model. The non-local parameter extracted from our measurements sheds light on the competition between the two stacking configurations of 1T-TaS. Our technique of measuring non-local optical response serves as a quick, simple, and non-invasive method to probe the energy landscape of strong correlations in many such quantum materials.
