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Intimate link between charge density wave, pseudogap and superconducting energy scales in cuprates

Authors:
Bastien Loret at Paris Diderot University
Bastien Loret
Nicolas Auvray at Paris Diderot University
Nicolas Auvray
Y. Gallais
Y. Gallais
Y. Gallais
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M. Cazayous
M. Cazayous
M. Cazayous
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Abstract and Figures

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 issue, it is important to extract the energy scale ΔCDW associated with the CDW order, and to compare it with the pseudogap ΔPG and with the superconducting gap ΔSC. However, while TCDW is well characterized from earlier work³, little is currently known about ΔCDW. Here, we report the extraction of ΔCDW for several cuprates using electronic Raman spectroscopy. We find that on approaching the parent Mott state by lowering p, ΔCDW increases in a manner similar to the doping dependence of ΔPG and ΔSC. This reveals that these three phases have a common microscopic origin. In addition, we find that ΔCDW ≈ ΔSC over a substantial doping range, which suggests that CDW and superconducting phases are intimately related; for example, they may be intertwined or connected by an emergent symmetry1,4–9.
Nodal Raman responses (B2g) of several cuprates a, The white region represents the tight-binding Fermi volume of hole-doped cuprates in the first Brillouin zone calculated from ref. ²² (see Supplementary Section F). The red arcs indicate the actual experimental Fermi surface observed, for example, by photoemission2,34. The Qx and Qy ordering vectors reproduce the bi-collinear CDW, as observed for example with X-rays³. The green zones highlight the nodal regions that are probed in the B2g Raman response. b, Temperature dependence of the B2g (nodal) Raman responses of the Hg-1223 compound above Tc = 117 K. c, The same responses, after subtracting the one at 290 K to highlight the CDW gap structure (dip and hump). d, The difference between the calculated B2g Raman responses with and without the CDW potential (see Supplementary Section F), which highlights the dip–hump CDW feature. e,f, Temperature dependence of the B2g Raman response of Hg-1201 with Tc = 72 K (e) and Y-123 with Tc = 54 K (f).
Nodal Raman responses (B2g) of several cuprates a, The white region represents the tight-binding Fermi volume of hole-doped cuprates in the first Brillouin zone calculated from ref. ²² (see Supplementary Section F). The red arcs indicate the actual experimental Fermi surface observed, for example, by photoemission2,34. The Qx and Qy ordering vectors reproduce the bi-collinear CDW, as observed for example with X-rays³. The green zones highlight the nodal regions that are probed in the B2g Raman response. b, Temperature dependence of the B2g (nodal) Raman responses of the Hg-1223 compound above Tc = 117 K. c, The same responses, after subtracting the one at 290 K to highlight the CDW gap structure (dip and hump). d, The difference between the calculated B2g Raman responses with and without the CDW potential (see Supplementary Section F), which highlights the dip–hump CDW feature. e,f, Temperature dependence of the B2g Raman response of Hg-1201 with Tc = 72 K (e) and Y-123 with Tc = 54 K (f).
… 
Temperature dependence of the CDW Raman signal a–c, Results for Hg-1223 (a), Hg-1201 (b) and Y-123 (c). The black arrow indicates the temperature onset TCDW for each compound (details of the integrated hump area calculation are given Supplementary Section B). The error bars represent standard deviations of the integrated hump area. The vertical dotted line indicates the superconducting transition temperature, Tc.
Temperature dependence of the CDW Raman signal a–c, Results for Hg-1223 (a), Hg-1201 (b) and Y-123 (c). The black arrow indicates the temperature onset TCDW for each compound (details of the integrated hump area calculation are given Supplementary Section B). The error bars represent standard deviations of the integrated hump area. The vertical dotted line indicates the superconducting transition temperature, Tc.
… 
Doping and temperature dependence of the CDW Raman signal a, Temperature dependence of the B2g Raman responses of several under-doped Hg-1223 compounds. Tc = 105 K (p = 0.11), Tc = 117 K (p = 0.12), Tc = 127 K (p = 0.14) and Tc = 133 K (p = 0.16). b, The difference between the superconducting Raman response at the lowest temperature and the Raman response at TCDW. The shaded red form is a guide for the eyes to follow the 2ΔCDW hump with doping. c–e, T–p phase diagrams of Hg-1223 (c), Y-123 (d) and Hg-1201 (e). The T* values plotted in these three phase diagrams come from the references listed in Supplementary Section C. The error bars originate from standard deviations from our data and those of the references cited below and in Supplementary Section C. In c, the TCDW(p) values (red filled circles) extracted from Hg-1223 Raman spectra match well with the 1/T1T(p) values (orange triangles) deduced from NMR data20,21. It was recently realized that the maximum in the ⁶³Cu 1/T1T curve (where T1 is the spin-lattice relaxation time) coincides with TCDW in YBCO14,35. This suggests that 1/T1T is related to the CDW order rather than the pseudogap. d, TCDW values extracted from the Y-123 Raman spectra fit well with X-ray diffraction and NMR data whose references are given in Supplementary Section C. e, The TCDW value obtained from the Hg-1201 Raman spectra fits with the X-ray and transient reflectivity25,27.
Doping and temperature dependence of the CDW Raman signal a, Temperature dependence of the B2g Raman responses of several under-doped Hg-1223 compounds. Tc = 105 K (p = 0.11), Tc = 117 K (p = 0.12), Tc = 127 K (p = 0.14) and Tc = 133 K (p = 0.16). b, The difference between the superconducting Raman response at the lowest temperature and the Raman response at TCDW. The shaded red form is a guide for the eyes to follow the 2ΔCDW hump with doping. c–e, T–p phase diagrams of Hg-1223 (c), Y-123 (d) and Hg-1201 (e). The T* values plotted in these three phase diagrams come from the references listed in Supplementary Section C. The error bars originate from standard deviations from our data and those of the references cited below and in Supplementary Section C. In c, the TCDW(p) values (red filled circles) extracted from Hg-1223 Raman spectra match well with the 1/T1T(p) values (orange triangles) deduced from NMR data20,21. It was recently realized that the maximum in the ⁶³Cu 1/T1T curve (where T1 is the spin-lattice relaxation time) coincides with TCDW in YBCO14,35. This suggests that 1/T1T is related to the CDW order rather than the pseudogap. d, TCDW values extracted from the Y-123 Raman spectra fit well with X-ray diffraction and NMR data whose references are given in Supplementary Section C. e, The TCDW value obtained from the Hg-1201 Raman spectra fits with the X-ray and transient reflectivity25,27.
… 
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.
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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Letters
https://doi.org/10.1038/s41567-019-0509-5
1Laboratoire Matériaux et Phénomènes Quantiques (UMR 7162 CNRS), Université Paris Diderot-Paris 7, Bat.Condorcet, Paris, France. 2Service de
Physique de l’État Condensé, DSM/IRAMIS/SPEC (UMR 3680 CNRS), CEA Saclay, Gif sur Yvette Cedex, France. 3Laboratoire National des Champs
Magnétiques Intenses, CNRS-Université Grenoble Alpes-Université Paul Sabatier-Institut National des Sciences Appliquées, European Magnetic
Field Laboratory, Grenoble, France. 4Laboratoire de Physique des Solides, CNRS, Université Paris-Sud, Université Paris-Saclay, Orsay Cedex, France.
*e-mail: alain.sacuto@univ-paris-diderot.fr
The cuprate high-temperature superconductors develop
spontaneous charge density wave (CDW) order below a tem-
perature 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 stud-
ied pseudogap and superconducting phases1,2. To address this
issue, it is important to extract the energy scale ΔCDW asso-
ciated with the CDW order, and to compare it with the pseu-
dogap ΔPG and with the superconducting gap ΔSC. However,
while TCDW is well characterized from earlier work3, little is
currently known about ΔCDW. Here, we report the extraction
of ΔCDW for several cuprates using electronic Raman spec-
troscopy. We find that on approaching the parent Mott state
by lowering p, ΔCDW increases in a manner similar to the dop-
ing dependence of ΔPG and ΔSC. This reveals that these three
phases have a common microscopic origin. In addition, we find
that ΔCDW ≈ ΔSC over a substantial doping range, which sug-
gests that CDW and superconducting phases are intimately
related; for example, they may be intertwined or connected by
an emergent symmetry1,4–9.
In recent years, many experiments and different techniques have
established the ubiquity of CDW order in cuprates3. In particular,
these works have determined TCDW(p), which displays a dome-like
shape in the temperature–doping (T–p) phase diagram, in a fashion
reminiscent of the superconducting dome TSC(p), even though the
CDW order is present over a narrower p range, and mostly below
optimal doping. The CDW was found to compete with supercon-
ductivity10–16 but there are indications that the interplay between the
two phenomena might be more complex than a simple competition.
The energy scale ΔCDW associated with the CDW has attracted
much less experimental attention, even though knowledge of this
quantity is crucial to address several important questions. First,
can the CDW be understood within a scenario of weakly interact-
ing electrons for which mean-field theory is adequate? A telltale
signature of it would be if TCDW(p) ∝ ΔCDW(p). On the other hand,
a more intricate physics is implied if their doping trends are dif-
ferent, as is famously the case for high-Tc superconductivity, where
TSC(p) displays a dome whereas ΔSC(p) increases with lower doping.
Here we show that this is also the case for CDW, and that ΔCDW(p)
and TCDW(p) have very different doping trends. Second, what is the
relationship between the CDW, superconducting and pseudogap
phases that can be understood through a comparison of the magni-
tudes and the doping dependencies of their energy scales ΔCDW(p),
ΔSC(p) and ΔPG(p)? We show that these three energy scales have sim-
ilar doping evolutions, implying that it is likely that they originate
from the same electronic interaction. Moreover, we find that the
magnitude of ΔCDW(p) and that of ΔSC(p) are nearly the same over
a significant doping range. This is a signature either of competing
superconducting and CDW orders connected by an approximate
emergent symmetry, or of these orders cooperating via a micro-
scopic intertwining1,4–9.
A typical signature of a density wave in Raman spectroscopy
is the loss of spectral weight of the electronic continuum at low
energy, followed by a recovery of spectral weight at higher energy,
as the order sets in as a function of temperature17. However, in the
cuprates, TCDW is below T*, the characteristic pseudogap tempera-
ture, so one technical challenge is to distinguish CDW from the loss
of spectral weight due to the pseudogap itself.
This difficulty can be overcome by studying the B2g Raman
response, which preferentially probes the nodal regions of the
Brillouin zone (Fig. 1a), and where pseudogap effects are known to
be minimal. This intuition is further aided by the fact that the Bloch
states that are expected to show the largest reconstruction due to
the CDW are in between the nodal and the anti-nodal regions, as
indicated by the CDW ordering vectors Qx and Qy on Fig. 1a3,18.
Therefore, the B2g Raman geometry should be able to capture the
signature of the CDW.
Consequently, we have performed electronic Raman scatter-
ing measurements on cuprates in the B2g geometry. We have first
investigated HgBa2Ca2Cu3O8+δ (Hg-1223) single crystals grown
with a single-step synthesis19. From a materials point of view,
its inner CuO2 plane is likely to be the cleanest CuO2 plane of all
cuprates because it is homogeneously doped and screened from
out-of-plane disorder by the outer planes, as demonstrated by the
analysis of the 63Cu-NMR linewidth20,21. Having obtained promis-
ing results in Hg-1223 (see below), we also measured single crystals
from HgBa2CuO4+δ (Hg-1201) and YBa2Cu3O7−δ (Y-123) to dem-
onstrate that the CDW signature in the Raman response is present
in different cuprate families. The experimental details are given in
Supplementary Section A.
Our first central observation is that the B2g Raman response
χ ω′′ T(, )
Bg2 of an underdoped Hg-1223 crystal displays a well-
Intimate link between charge density wave,
pseudogap and superconducting energy scales
in cuprates
B. Loret1, N. Auvray1, Y. Gallais1, M. Cazayous1, A. Forget2, D. Colson2, M.-H. Julien3, I. Paul1, M. Civelli4
and A. Sacuto 1*
NATURE PHYSICS | VOL 15 | AUGUST 2019 | 771–775 | www.nature.com/naturephysics 771
Content courtesy of Springer Nature, terms of use apply. Rights reserved
... 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. ...
Chiral Pseudogap Metal Emerging from a Disordered Van der Waals Mott Insulator 1T‐TaS2 − xSex
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View
... 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. ...
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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.
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... 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. ...
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... 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 . ...
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View
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View
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Full-text available
  • Aug 2019
Charge density modulations have been observed in all families of high-critical temperature (Tc) superconducting cuprates. Although they are consistently found in the underdoped region of the phase diagram and at relatively low temperatures, it is still unclear to what extent they influence the unusual properties of these systems. Using resonant x-ray scattering, we carefully determined the temperature dependence of charge density modulations in YBa2Cu3O7-δ and Nd1+ x Ba2- x Cu3O7-δ for several doping levels. We isolated short-range dynamical charge density fluctuations in addition to the previously known quasi-critical charge density waves. They persist up to well above the pseudogap temperature T*, are characterized by energies of a few milli-electron volts, and pervade a large area of the phase diagram.
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Synchrotron x-ray scattering study of charge-density-wave order in HgBa 2 CuO 4 + δ
Article
Full-text available
  • Oct 2017
We present a detailed synchrotron x-ray scattering study of the charge-density-wave (CDW) order in simple tetragonal HgBa2CuO4+δ (Hg1201). Resonant soft x-ray scattering measurements reveal that short-range order appears at a temperature that is distinctly lower than the pseudogap temperature and in excellent agreement with a prior transient reflectivity result. Despite considerable structural differences between Hg1201 and YBa2Cu3O6+δ, the CDW correlations exhibit similar doping dependencies, and we demonstrate a universal relationship between the CDW wave vector and the size of the reconstructed Fermi pocket observed in quantum oscillation experiments. The CDW correlations in Hg1201 vanish already below optimal doping, once the correlation length is comparable to the CDW modulation period, and they appear to be limited by the disorder potential from unit cells hosting two interstitial oxygen atoms. A complementary hard x-ray diffraction measurement, performed on an underdoped Hg1201 sample in magnetic fields along the crystallographic c axis of up to 16 T, provides information on the form factor of the CDW order. As expected from the single-CuO2-layer structure of Hg1201, the CDW correlations vanish at half-integer values of L and appear to be peaked at integer L. We conclude that the atomic displacements associated with the short-range CDW order are mainly planar, within the CuO2 layers.
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Is charge order induced near an antiferromagnetic quantum critical point?
Article
Full-text available
  • Oct 2017
We investigate the interplay between charge order and superconductivity near an antiferromagnetic quantum critical point using sign-problem-free Quantum Monte Carlo simulations. We establish that, when the electronic dispersion is particle-hole symmetric, the system has an emergent SU(2) symmetry that implies a degeneracy between d-wave superconductivity and charge order with d-wave form factor. Deviations from particle-hole symmetry, however, rapidly lift this degeneracy, despite the fact that the SU(2) symmetry is preserved at low energies. As a result, we find a strong suppression of charge order caused by the competing, leading superconducting instability. Across the antiferromagnetic phase transition, we also observe a shift in the charge order wave-vector from diagonal to axial. We discuss the implications of our results to the universal phase diagram of antiferromagnetic quantum-critical metals and to the elucidation of the charge order experimentally observed in the cuprates.
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The rate of quasiparticle recombination probes the onset of coherence in cuprate superconductors
Article
Full-text available
  • Jan 2016
The condensation of an electron superfluid from a conventional metallic state at a critical temperature TcT_c is described well by the BCS theory. In the underdoped copper-oxides, high-temperature superconductivity condenses instead from a nonconventional metallic "pseudogap" phase that exhibits a variety of non-Fermi liquid properties. Recently, it has become clear that a charge density wave (CDW) phase exists within the pseudogap regime, appearing at a temperature TCDWT_{CDW} just above TcT_c. The near coincidence of TcT_c and TCDWT_{CDW}, as well the coexistence and competition of CDW and superconducting order below TcT_c, suggests that they are intimately related. Here we show that the condensation of the superfluid from this unconventional precursor is reflected in deviations from the predictions of BSC theory regarding the recombination rate of quasiparticles. We report a detailed investigation of the quasiparticle (QP) recombination lifetime, τqp\tau_{qp}, as a function of temperature and magnetic field in underdoped HgBa2_{2}CuO4+δ_{4+\delta} (Hg-1201) and YBa2_{2}Cu3_{3}O6+x_{6+x} (YBCO) single crystals by ultrafast time-resolved reflectivity. We find that τqp(T)\tau_{qp}(T) exhibits a local maximum in a small temperature window near TcT_c that is prominent in underdoped samples with coexisting charge order and vanishes with application of a small magnetic field. We explain this unusual, non-BCS behavior by positing that TcT_c marks a transition from phase-fluctuating SC/CDW composite order above to a SC/CDW condensate below. Our results suggest that the superfluid in underdoped cuprates is a condensate of coherently-mixed particle-particle and particle-hole pairs.
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Sensitivity of T c to pressure and magnetic field in the cuprate superconductor YBa 2 Cu 3 O y : Evidence of charge-order suppression by pressure
Article
  • Aug 2018
Cuprate superconductors have a universal tendency to form charge density-wave (CDW) order which competes with superconductivity and is strongest at a doping p≃0.12. Here we show that in the archetypal cuprate YBa2Cu3Oy (YBCO) pressure suppresses charge order but does not affect the pseudogap phase. This is based on transport measurements under pressure, which reveal that the onset of the pseudogap at T* is independent of pressure, while the negative Hall effect, a clear signature of CDW order in YBCO, is suppressed by pressure. We also find that pressure and magnetic field shift the superconducting transition temperature Tc of YBCO in the same way as a function of doping—but in opposite directions—and most effectively at p≃0.12. This shows that the competition between superconductivity and CDW order can be tuned in two ways, either by suppressing superconductivity with field or suppressing CDW order by pressure. Based on existing high-pressure data and our own work, we observe that when CDW order is fully suppressed at high pressure, the so-called “1/8 anomaly” in the superconducting dome vanishes, revealing a smooth Tc dome which now peaks at p≃0.13. We propose that this Tc dome is shaped by the competing effects of the pseudogap phase below its critical point p★∼0.19 and spin order at low doping.
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Crystal Growth and Characterization of HgBa 2 Ca 2 Cu 3 O 8+δ Superconductors with the Highest Critical Temperature at Ambient Pressure
Article
  • Aug 2017
We report an original procedure for the elaboration of very high-quality single crystals of superconducting HgBa2Ca2Cu3O8+δ mercury cuprates. These single crystals are unique, with very high-quality surface paving the way for spectroscopic, transport, and thermodynamic probes in order to understand the hole-doped cuprate phase diagram. Annealing allows one to optimize Tc up to Tc(max) = 133 K. The superconductivity transition width of about 2 K indicates that they are homogeneous. We show for the first time that, with adequate heat treatment, Hg-1223 can be largely underdoped and its doping level controlled. Importantly, the crystal structure was studied in detail by single-crystal X-ray diffraction, and we have identified the signature of the underdoping by a detailed sample characterization and micro-Raman spectroscopy measurements.
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Charge density wave modulation and gap measurements in CeTe$_3
Article
  • Jun 2016
We present a study of charge density wave (CDW) ordering in CeTe3_3 at room temperature using a scanning tunneling microscope and Raman spectroscopy. Two characteristic CDW ordering wavevectors obtained from the Fourier analysis are assessed to be ∣c∗−q∣=4.19 nm−1|{\bf \textbf{c}}^\ast-{\bf q}|=4.19\,{\rm nm}^{-1} and ∣q∣=10.26 nm−1|{\bf q}|=10.26\,{\rm nm}^{-1} where ∣c∗∣=2π/c|{\bf c}^\ast| = 2\pi/c is the reciprocal lattice vector. The scanning tunneling spectroscopy measurements, along with inelastic light (Raman) scattering measurements, show a CDW gap Δmax\Delta_{\rm max} of approximately 0.37 eV. In addition to the CDW modulation, we observe an organization of the Te sheet atoms in an array of alternating V- and N- groups along the CDW modulation, as predicted in the literature.
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Unconventional high-energy-state contribution to the Cooper pairing in under-doped copper-oxide superconductor HgBa2_2Ca2_2Cu3_3O$_{8+\delta}
Article
  • Jan 2016
We study the temperature-dependent electronic B1g Raman response of a slightly under-doped single crystal HgBa2_2Ca2_2Cu3_3O8+δ_{8+\delta} with a superconducting critical temperature Tc=122 K. Our main finding is that the superconducting pair-breaking peak is associated with a dip on its higher-energy side, disappearing together at Tc. This result hints at an unconventional pairing mechanism, whereas spectral weight lost in the dip is transferred to the pair-breaking peak at lower energies. This conclusion is supported by cellular dynamical mean-field theory on the Hubbard model, which is able to reproduce all the main features of the B1g Raman response and explain the peak-dip behavior in terms of a nontrivial relationship between the superconducting and the pseudo gaps.
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Resonant X-Ray Scattering Studies of Charge Order in Cuprates
Article
  • Sep 2015
X-ray techniques have been used for more than a century to study the atomic and electronic structure in virtually any type of material. The advent of correlated electron systems, in particular complex oxides, brought about new scientific challenges and opportunities for the advancement of conventional x-ray methods. In this context, the need for new approaches capable of selectively sensing new forms of orders involving all degrees of freedom -- charge, orbital, spin, and lattice -- paved the way for the emergence and success of resonant x-ray scattering, which has become an increasingly popular and powerful tool for the study of electronic ordering phenomena in solids. Here we review the recent resonant x-ray scattering breakthroughs in the copper oxide high-temperature superconductors, in particular regarding the phenomenon of charge order -- a broken-symmetry state occurring when valence electrons self-organize into periodic structures. After a brief historical perspective on charge order, we outline the milestones in the development of resonant x-ray scattering, as well as the basic theoretical formalism underlying its unique capabilities. The rest of the review will focus on the recent contributions of resonant scattering to the tremendous advancements in our description and understanding of charge order. To conclude, we propose a series of present and upcoming challenges, and discuss the future outlook for this technique.
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