Underdoped Cuprate Superconductors Research Articles

Nodal-antinodal dichotomy from anisotropic quantum critical continua in holographic models

We demonstrate that the absence of stable quasiparticle excitations on parts of the Fermi surface, similar to the “nodal-antinodal dichotomy” in underdoped cuprate superconductors, can be reproduced in models of strongly correlated electrons defined via a holographic dual. We show analytically that the anisotropy of the quantum critical continuum, which is a feature of these models, may lead to washing out the quasiparticle peak in one direction while leaving it intact in the perpendicular one. The effect relies on the qualitatively different scaling of the self-energy in different directions. Using the explicit example of the anisotropic Q-lattice model, we demonstrate how this effect emerges due to specific features of the near horizon geometry of the black hole in the dual description.

Low-energy gap emerging from confined nematic states in extremely underdoped cuprate superconductors

The pairing mechanism of high-temperature superconductivity in cuprates is regarded as one of the most challenging issues in condensed matter physics. The core issue concerns how the Cooper pairs are formed. Here we report spin-resolved tunneling measurements on extremely underdoped Bi2Sr2−xLaxCuO6+δ. Our data reveal that, when holes are doped into the system, the antiferromagnetic order is destroyed, while at the same time an increasing density of states (DOS) peaked at around 200 meV appears within the charge transfer gap. Meanwhile, an electronic structure with 4a0 × 4a0 basic plaquettes emerges inhomogeneously, with an area fraction that grows with hole doping. In each plaquette, there are some unidirectional bars (along the Cu-O bond) which are most pronounced at energies near peaks in the DOS around at 25 meV, with an intensity that is especially pronounced at oxygen sites. We argue that the atomically resolved low-energy DOS and related gap are closely associated with some kinds of density waves, possibly reflecting modulations of the electron density, or a pair-density wave, i.e. a modulation of the local pairing. Our work sheds new light on the doping induced electronic evolution from the “parent” insulator of the cuprate superconductors.

Nematic single-component superconductivity and loop-current order from pair-density wave instability

We investigate the nematic and loop-current type orders that may arise as vestigial precursor phases in a model with an underlying pair-density wave (PDW) instability. We discuss how such a vestigial phase gives rise to a highly anisotropic stiffness for a coexisting single-component superconductor with low intrinsic stiffness, as is the case for the underdoped cuprate superconductors. Next, focusing on a regime with a mean-field PDW ground state with loop-current and nematic $xy$ (B$_{2g}$) order, we find a preemptive transition into a low and high-temperature vestigial phase with loop-current and nematic order corresponding to $xy$ (B$_{2g}$) and $x^2-y^2$ (B$_{1g}$) symmetry respectively. Near the transition between the two phases, a state of soft nematic order emerges for which we expect that the nematic director is readily pinned away from the high-symmetry directions in the presence of an external field. Results are discussed in relation to findings in the cuprates, especially to the recently inferred highly anisotropic superconducting fluctuations [W{\aa}rdh {\em et al.}, ``Colossal transverse magnetoresistance due to nematic superconducting phase fluctuations in a copper oxide'', arXiv:2203.06769], giving additional evidence for an underlying ubiquitous PDW instability in these materials.

Unified approach to electrical and thermal transport in high- Tc superconductors

In this paper, we present a consolidated equation for all low-field transport coefficients, based on a reservoir approach developed for noninteracting quasiparticles. This formalism allows us to treat the two distinct types of charged (fermionic and bosonic) quasiparticles that can be simultaneously present, as, for example, in superconductors. Indeed, in the underdoped cuprate superconductors, these two types of carriers result in two onset temperatures with distinct features in transport: ${T}^{*}$, where the fermions first experience an excitation (pseudo)gap, and ${T}_{c}$, where bosonic conduction processes are dominant and often divergent. This provides the central goal of this paper, which is to address the challenges in thermoelectric transport that stem from having two characteristic temperatures as well as two types of charge carriers whose contributions can in some instances enhance each other and in others compete. We show how essential features of the cuprates (their bad-metal character and the presence of Fermi arcs) provide an explanation for the classic pseudogap onset signatures at ${T}^{*}$ in the longitudinal resistivity, ${\ensuremath{\rho}}_{xx}$. Based on the fits to the temperature-dependent ${\ensuremath{\rho}}_{xx}$, we present the implications for all of the other thermoelectric transport properties.

Magnetic anisotropy from linear defect structures in correlated electron systems

Correlated electron systems, particularly iron-based superconductors, are extremely sensitive to strain, which inevitably occurs in the crystal growth process. Built-in strain of this type has been proposed as a possible explanation for experiments where nematic order has been observed at high temperatures corresponding to the nominally tetragonal phase of iron-based superconductors. Strain is assumed to produce linear defect structures, e.g. dislocations, which are quite similar to O vacancy chainlets in the underdoped cuprate superconductor YBCO. Here we investigate a simple microscopic model of dislocations in the presence of electronic correlations, which create defect states that can drive magnetic anisotropy of this kind, if spin orbit interaction is present. We estimate the contribution of these dislocations to magnetic anisotropy as detected by current torque magnetometry experiments in both cuprates and Fe-based systems.

Intrinsic hallmarks of phonon-induced charge order in cuprates

Charge-density wave (CDW) modulations in underdoped high-temperature cuprate superconductors remain a central puzzle in condensed matter physics. However, despite a substantial experimental verification of this ubiquitous phase in a large class of high ${T}_{c}$ cuprates, a complete theoretical explanation of this phase is still missing. Here, we build upon our recent proposal that the CDW in underdoped cuprates (Y- and Bi- based compounds) emerges from a unique cooperation of the ${\phantom{\rule{4pt}{0ex}}B}_{1g}$ bond-buckling phonon with strong electronic correlations. We assume a static mean-field lattice distortion with ${\mathrm{B}}_{1g}$ symmetry, regardless of its origin, with a commensurate wave vector ${\mathbf{q}}^{*}=(2\ensuremath{\pi}/3,0)/(0,2\ensuremath{\pi}/3)$. We show that such a phonon-induced CDW (both uni- and biaxial) reconstructs the Fermi surface, leading to electron and hole pockets, with relevant quantum oscillation frequencies in close consistency with the experiments. Furthermore, a systematic analysis of the symmetry of the intra-unit-cell charge modulations on the copper-oxygen planes is provided. We find that the atomic charge modulation on the $\mathrm{Cu}{\mathrm{O}}_{2}$ unit cell is predominantly of $s$-wave character, in support of the recent experimental observation.

Magnetic field reveals vanishing Hall response in the normal state of stripe-ordered cuprates

The origin of the weak insulating behavior of the resistivity, i.e. {rho }_{xx}propto {mathrm{ln}},(1/T), revealed when magnetic fields (H) suppress superconductivity in underdoped cuprates has been a longtime mystery. Surprisingly, the high-field behavior of the resistivity observed recently in charge- and spin-stripe-ordered La-214 cuprates suggests a metallic, as opposed to insulating, high-field normal state. Here we report the vanishing of the Hall coefficient in this field-revealed normal state for all T < (2-6){T}_{{rm{c}}}^{0}, where {T}_{{rm{c}}}^{0} is the zero-field superconducting transition temperature. Our measurements demonstrate that this is a robust fundamental property of the normal state of cuprates with intertwined orders, exhibited in the previously unexplored regime of T and H. The behavior of the high-field Hall coefficient is fundamentally different from that in other cuprates such as YBa2Cu3O6+x and YBa2Cu4O8, and may imply an approximate particle-hole symmetry that is unique to stripe-ordered cuprates. Our results highlight the important role of the competing orders in determining the normal state of cuprates.

Quantum oscillations from a pair-density wave

A pair-density wave state has been suggested to exist in underdoped cuprate superconductors, with some supporting experimental evidence emerging over the past few years from scanning tunneling spectroscopy. Several studies have also linked the observed quantum oscillations in these systems to a reconstruction of the Fermi surface by a pair-density wave. Here, we show, using semiclassical analysis and numerical calculations, that a Fermi pocket created by first-order scattering from a pair-density wave cannot induce such oscillations. In contrast, pockets resulting from second-order scattering can cause oscillations. We consider the effects of a finite pair-density wave correlation length on the signal, and demonstrate that it is only weakly sensitive to disorder in the form of $\pi$-phase slips. Finally, we discuss our results in the context of the cuprates and show that a bidirectional pair-density wave may produce observed oscillation frequencies.

Anomalous softening of phonon dispersion in cuprate superconductors

A softening of phonon-dispersion has been observed experimentally in under-doped cuprate superconductors at the charge-density wave (CDW) ordering wave vector. Interestingly, the softening occurs below the superconducting (SC) transition temperature T$_{c}$, in contrast to the metallic systems, where the softening occurs usually below the CDW onset temperature T$_{\text{CDW}}$. An understanding of the `anomalous' nature of the phonon-softening and its connection to the pseudo-gap phase in under-doped cuprates remain open questions. Within a perturbative approach, we show that a complex interplay among the ubiquitous CDW, SC orders and life-time of quasi-particles associated to thermal fluctuations, can explain the anomalous phonon-softening below T$_{c}$. Furthermore, our formalism captures different characteristics of the low temperature phonon-softening depending on material specificity.

Unconventional quantum vortex matter state hosts quantum oscillations in the underdoped high-temperature cuprate superconductors

A central question in the underdoped cuprates pertains to the nature of the pseudogap ground state. A conventional metallic ground state of the pseudogap region has been argued to host quantum oscillations upon destruction of the superconducting order parameter by modest magnetic fields. Here, we use low applied measurement currents and millikelvin temperatures on ultrapure single crystals of underdoped [Formula: see text] to unearth an unconventional quantum vortex matter ground state characterized by vanishing electrical resistivity, magnetic hysteresis, and nonohmic electrical transport characteristics beyond the highest laboratory-accessible static fields. A model of the pseudogap ground state is now required to explain quantum oscillations that are hosted by the bulk quantum vortex matter state without experiencing sizable additional damping in the presence of a large maximum superconducting gap; possibilities include a pair density wave.

Field-dependent specific heat of the canonical underdoped cuprate superconductor hbox {YBa}_2hbox {Cu}_4hbox {O}_8

The cuprate superconductor hbox {YBa}_2hbox {Cu}_4hbox {O}_8, in comparison with most other cuprates, has a stable stoichiometry, is largely free of defects and may be regarded as the canonical underdoped cuprate, displaying marked pseudogap behaviour and an associated distinct weakening of superconducting properties. This cuprate ‘pseudogap’ manifests as a partial gap in the electronic density of states at the Fermi level and is observed in most spectroscopic properties. After several decades of intensive study it is widely believed that the pseudogap closes, mean-field like, near a characteristic temperature, T^*, which rises with decreasing hole concentration, p. Here, we report extensive field-dependent electronic specific heat studies on hbox {YBa}_2hbox {Cu}_4hbox {O}_8 up to an unprecedented 400 K and show unequivocally that the pseudogap never closes, remaining open to at least 400 K where T^* is typically presumed to be about 150 K. We show from the NMR Knight shift and the electronic entropy that the Wilson ratio is numerically consistent with a weakly-interacting Fermion system for the near-nodal states. And, from the field-dependent specific heat, we characterise the impact of fluctuations and impurity scattering on the thermodynamic properties.

First-Principles Calculation of Copper Oxide Superconductors That Supports the Kamimura-Suwa Model

In 1986 Bednorz and Műller discovered high temperature superconductivity in copper oxides by chemically doping holes into La2CuO4 (LCO), the antiferromagnetic insulator. Despite intense experimental and theoretical research during the past 34 years, no general consensus on the electronic-spin structures and the origin of pseudogap has been obtained. In this circumstance, we performed a first-principles calculation of underdoped cuprate superconductors La2-xSrxCuO4 (LSCO) within the meta-generalized gradient approximation of the density functional theory. Our calculations clarify first the important role of the anti Jahn-Teller (JT) effect, the backward deformation against the JT distortion in La2CuO4 by doping extra holes. The resulting electronic structure agrees with the two-component theory provided by the tight-binding model of Kamimura and Suwa (K-S), which has been also used to elucidate the d-wave superconductivity. Our first-principles calculation thus justifies the K-S model and demonstrates advanced understanding of cuprates. For example, the remarkable feature of our calculations is the appearance of the spin-polarized band with a nearly flat-band character, showing the peaky nature in the density of states at the Fermi level.

Preformed Cooper Pairs in Layered FeSe-Based Superconductors.

Superconductivity arises from two distinct quantum phenomena: electron pairing and long-range phase coherence. In conventional superconductors, the two quantum phenomena generally take place simultaneously, while in the underdoped high- T_{c} cuprate superconductors, the electron pairing occurs at higher temperature than the long-range phase coherence. Recently, whether electron pairing is also prior to long-range phase coherence in single-layer FeSe film on SrTiO_{3} substrate is under debate. Here, by measuring Knight shift and nuclear spin-lattice relaxation rate, we unambiguously reveal a pseudogap behavior below T_{p}∼60 K in two kinds of layered FeSe-based superconductors with quasi2D nature. In the pseudogap regime, a weak diamagnetic signal and a remarkable Nernst effect are also observed, which indicates that the observed pseudogap behavior is related to superconducting fluctuations. These works confirm that strong phase fluctuation is an important character in the 2D iron-based superconductors as widely observed in high-T_{c} cuprate superconductors.

Multiorbital charge-density wave excitations and concomitant phonon anomalies in Bi2Sr2LaCuO6+δ

Charge-density waves (CDWs) are ubiquitous in underdoped cuprate superconductors. As a modulation of the valence electron density, CDWs in hole-doped cuprates possess both Cu-3d and O-2p orbital character owing to the strong hybridization of these orbitals near the Fermi level. Here, we investigate underdoped Bi2Sr1.4La0.6CuO6+δ using resonant inelastic X-ray scattering (RIXS) and find that a short-range CDW exists at both Cu and O sublattices in the copper-oxide (CuO2) planes with a comparable periodicity and correlation length. Furthermore, we uncover bond-stretching and bond-buckling phonon anomalies concomitant to the CDWs. Comparing to slightly overdoped Bi2Sr1.8La0.2CuO6+δ, where neither CDWs nor phonon anomalies appear, we highlight that a sharp intensity anomaly is induced in the proximity of the CDW wavevector (QCDW) for the bond-buckling phonon, in concert with the diffused intensity enhancement of the bond-stretching phonon at wavevectors much greater than QCDW Our results provide a comprehensive picture of the quasistatic CDWs, their dispersive excitations, and associated electron-phonon anomalies, which are key for understanding the competing electronic instabilities in cuprates.

Unusual Dynamic Charge Correlations in Simple-Tetragonal HgBa2CuO4+δ

The charge-density-wave (CDW) instability in the underdoped, pseudogap part of the cuprate phase diagram has been a major recent research focus, yet measurements of dynamic, energy-resolved CDW correlations are still in their infancy. We report a high-resolution resonant inelastic X-ray scattering (RIXS) study of the underdoped cuprate superconductor HgBa$_{2}$CuO$_{4+\delta}$ ($T_c = 70$ K). At $T=250$ K, above the CDW order temperature $T_\mathrm{CDW} \approx 200$ K, we observe significant dynamic CDW correlations at about 40 meV. This energy scale is comparable to both the superconducting gap and the previously reported low-energy pseudogap. At $T = T_c$, a strong elastic CDW peak appears, but the dynamic correlations around 40 meV remain virtually unchanged. In addition, we observe a new feature: dynamic correlations at significantly higher energy, with a characteristic scale of about 160 meV. A similar scale was previously identified in other experiments as a high-energy pseudogap. The existence of three distinct features in the charge response is highly unusual for a CDW system, and suggests that charge order in the cuprates is closely related to the pseudogap phenomenon and more complex than previously thought. We further observe the paramagnon dispersion along [1,0], across the two-dimensional CDW wavevector $\boldsymbol{q}_\mathrm{CDW}$, which is consistent with magnetic excitations measured by inelastic neutron scattering. Unlike for some other cuprates, our results point to the absence of a discernible coupling between CDW and magnetic excitations.

Fallacies on pairing symmetry and intrinsic electronic Raman spectrum in high-Tc cuprate superconductors

Certain significant fallacies are involved in discussions of the high-[Formula: see text] mechanism unsolved for over 30 years in cuprate superconductors. These fallacies are explored with the aim of unraveling this mechanism. Moreover, using polarized electronic Raman scattering in inhomogeneous underdoped cuprate superconductors, the intrinsic nonlinear Raman spectrum is obtained by subtracting the pseudogap characteristic of a nonlinear from the linear Raman spectrum measured in the [Formula: see text] mode of the node area below the critical temperature. The intrinsic nonlinear behavior implies the existence of the nodal superconducting gap denying [Formula: see text]-wave pairing symmetry. An origin of the nodal superconducting gap is discussed.

Incipient loop-current order in the underdoped cuprate superconductors

There are growing experimental evidence which indicate discrete symmetry breaking like time-reversal ($\mathcal{T}$), parity ($\mathcal{P}$) and C$_{4}$ lattice rotation in the pseudo-gap state of the under-doped copper-oxide based (cuprate) superconductors. The discrete symmetry breaking manifests a true phase transition to an ordered state. A detailed thermodynamic understanding of these orders can answer various puzzles related to the nature of the transition at the pseudo-gap temperature T$^*$. In this work, we investigate thermodynamic signature of $\mathcal{T-P}$ symmetry breaking considering superconductivity (SC) and bond-density wave (BDW) as two primary orders. The BDW can generate both modulating charge and current densities. This framework takes into account an intricate competition between the ubiquitous charge density wave and SC, which is prominent in various cuprates in the under-doped regime. We demonstrate that within mean-field approach of competing BDW and SC orders, a $\mathcal{T-P}$ breaking ground state of coexisting BDW and SC can be stabilized, provided the BDW itself breaks $\mathcal{T}-\mathcal{P}$. But this ground state ceases to occur at higher temperatures. However, we show that fluctuations in SC and BDW can drive emergence of a new unusual translational symmetry preserving order due to a preemptive phase transition by spontaneously breaking $\mathcal{T-P}$ at a higher temperature before the primary orders set in. We refer this order to be magneto-electric loop current (MELC) order. We present possible nature of phase transition for this new incipient MELC order and discuss some experimental relevance.

Origin of hour-glass magnetic dispersion in underdoped cuprate superconductors

In the present work we explain the hour-glass magnetic dispersion in underdoped cuprates. The dispersion arises due to the Lifshitz-type magnetic criticality. Superconductivity also plays a role, but the role is secondary. We list six major experimental observations related to the hour-glass and explain all of them. The theory provides a unified picture of the evolution of magnetic excitations in various cuprate families, including "hour-glass" and "wine-glass" dispersions and an emergent static incommensurate order. We propose the Lifshitz spin liquid "fingerprint" sum rule, and show that the latest data confirm the validity of the sum rule.

Bulk Superconductivity and Role of Fluctuations in the Iron-Based Superconductor FeSe at High Pressures.

The iron-based superconductor FeSe offers a unique possibility to study the interplay of superconductivity with purely nematic as well magnetic-nematic order by pressure (p) tuning. By measuring specific heat under p up to 2.36GPa, we study the multiple phases in FeSe using a thermodynamic probe. We conclude that superconductivity is bulk across the entire p range and competes with magnetism. In addition, whenever magnetism is present, fluctuations exist over a wide temperature range above both the bulk superconducting and the magnetic transitions. Whereas the magnetic fluctuations are likely temporal, the superconducting fluctuations may be either temporal or spatial. These observations highlight similarities between FeSe and underdoped cuprate superconductors.

Cooper pairing of incoherent electrons: An electron-phonon version of the Sachdev-Ye-Kitaev model

We introduce and solve a model of interacting electrons and phonons that is a natural generalization of the Sachdev-Ye-Kitaev-model and that becomes superconducting at low temperatures. In the normal state two Non-Fermi liquid fixed points with distinct universal exponents emerge. At weak coupling superconductivity prevents the onset of low-temperature quantum criticality, reminiscent of the behavior in several heavy-electron and iron-based materials. At strong coupling, pairing of highly incoherent fermions sets in deep in the Non-Fermi liquid regime, a behavior qualitatively similar to that in underdoped cuprate superconductors. The pairing of incoherent time-reversal partners is protected by a mechanism similar to Anderson's theorem for disordered superconductors. The superconducting ground state is characterized by coherent quasiparticle excitations and higher-order bound states thereof, revealing that it is no longer an ideal gas of Cooper pairs, but a strongly coupled pair fluid. The normal-state incoherency primarily acts to suppress the weight of the superconducting coherence peak and reduce the condensation energy. Based on this we expect strong superconducting fluctuations, in particular at strong coupling.