high-Tc Cuprate Superconductors Research Articles

Planckian behavior of cuprates at the pseudogap critical point simulated via flat electron-boson spectral density

Planckian behavior has been recently observed in La1·76Sr0·24CuO4 at the pseudogap critical point. The Planckian behavior takes place in an intriguing quantum metallic state at a quantum critical point. Here, the Planckian behavior was simulated with an energy-independent (or flat) and weakly temperature-dependent electron-boson spectral density (EBSD) function by using a generalized Allen's (Shulga's) formula. We obtained various optical quantities from the flat EBSD function, such as the optical scattering rate, the optical effective mass, and the optical conductivity. These quantities are well fitted with the recently observed Planckian behavior. Fermi-liquid behavior was also simulated with an energy-linear and temperature-independent EBSD function. The EBSD functions agree well with the overall doping- and temperature-dependent trends of the EBSD function obtained from the optically measured spectra of cuprate systems, which can be crucial for understanding the microscopic electron-pairing mechanism for high-Tc superconductivity in cuprates.

Rotational symmetry breaking in superconducting nickelate Nd0.8Sr0.2NiO2 films

The infinite-layer nickelates, isostructural to the high-Tc cuprate superconductors, have emerged as a promising platform to host unconventional superconductivity and stimulated growing interest in the condensed matter community. Despite considerable attention, the superconducting pairing symmetry of the nickelate superconductors, the fundamental characteristic of a superconducting state, is still under debate. Moreover, the strong electronic correlation in the nickelates may give rise to a rich phase diagram, where the underlying interplay between the superconductivity and other emerging quantum states with broken symmetry is awaiting exploration. Here, we study the angular dependence of the transport properties of the infinite-layer nickelate Nd0.8Sr0.2NiO2 superconducting films with Corbino-disk configuration. The azimuthal angular dependence of the magnetoresistance (R(φ)) manifests the rotational symmetry breaking from isotropy to four-fold (C4) anisotropy with increasing magnetic field, revealing a symmetry-breaking phase transition. Approaching the low-temperature and large-magnetic-field regime, an additional two-fold (C2) symmetric component in the R(φ) curves and an anomalous upturn of the temperature-dependent critical field are observed simultaneously, suggesting the emergence of an exotic electronic phase. Our work uncovers the evolution of the quantum states with different rotational symmetries in nickelate superconductors and provides deep insight into their global phase diagram.

Ferromagnetic Fluctuations in the Heavily Overdoped Regime of Single-Layer High-Tc Cuprate Superconductors.

To investigate proposed ferromagnetic fluctuations in the so-called single-layer Bi-2201 and La-214 high-Tc cuprates, we performed magnetization and electrical resistivity measurements using single-layer Tl-2201 cuprates Tl2Ba2CuO6+δ and La-214 La2-xSrxCuO4 in the heavily overdoped regime. Magnetization of Tl2Ba2CuO6+δ and La2-xSrxCuO4 exhibited the tendency to be saturated in high magnetic fields at low temperatures, suggesting the precursor behavior toward the formation of a ferromagnetic order. It was found that the power of temperature n obtained from the temperature dependence of the electrical resistivity is ~4/3 and ~5/3 for Bi-2201 and La2-xSrxCuO4, respectively, and is ~4/3 at high temperatures and ~5/3 at low temperatures in Tl2Ba2CuO6+δ. These results suggest that two- and three-dimensional ferromagnetic fluctuations exist in Bi-2201 and La2-xSrxCuO4, respectively. In Tl2Ba2CuO6+δ, it is suggested that the dimension of ferromagnetic fluctuations is two at high temperatures and three at low temperatures, respectively. The dimensionality of ferromagnetic fluctuations is understood in terms of the dimensionality of the crystal structure and the bonding of atoms in the blocking layer.

Investigating the Cuprates as a platform for high-order Van Hove singularities and flat-band physics

Beyond the two-dimensional saddle-point Van Hove singularities (VHSs) with logarithmic divergences in the density of states, recent studies have identified higher-order VHSs with faster-than-logarithmic divergences that can amplify electron correlation effects. Here we show that the cuprate high-Tc superconductors harbor high-order VHSs in their electronic spectra and unveil a new correlation that the cuprates with high-order VHSs display higher Tc’s. Our analysis indicates that the normal and higher-order VHSs can provide a straightforward new marker for identifying propensity of a material toward the occurrence of correlated phases such as the excitonic insulators and supermetals. Our study suggests cuprates and related high-Tc superconductors as materials for exploring the interplay between high-order VHSs, superconducting transition temperatures, and electron correlation effects.

Spin resonances in heavy-fermion superconductors

Historically heavy-fermion superconductors have been the first discovered unconventional superconductors and can to some extent be regarded as model systems for high-Tc superconductors. A hallmark of the unconventional superconductivity in high-Tc cuprates has been the observation of a spin resonance in the magnetic excitation spectrum probed by inelastic neutron scattering. We review the situation in heavy-fermion superconductors, the possible existence of a spin resonance in the superconducting state and its implications.

Energy-scale considerations of unconventional superconductors—implications to condensation and pairing

Discovery of high-Tc cuprate superconductors (HTSC) in 1986 by Bednorz and Muller, followed by synthesis of A3C60, iron-pnictides/chalcogenides and other exotic superconducting (SC) systems, introduced unconventional superconductors (UCSC) having their mechanisms of condensation and/or pairing distinctly different from those of simpler metals which can be explained by BCS theory. This article will show how one can demonstrate their new mechanisms by examining correlations among key energy-scale parameters, including the transition temperature Tc, the superfluid density ns/m*, the effective Fermi energy εF, the excitation energy of the magnetic resonance mode (MRM), the onset temperatures of Nernst effect and light-induced transient superconductivity, and the spin fluctuation energy scale ℏωsf, and by resorting to analogy / comparisons with superfluid 4He as a representative system undergoing Bose Einstein Condensation (BEC). We will propose a paring mechanism in HTSC based on resonance of spin (ℏωsf) and charge (εF) energy scales, and apply that concept for explaining unusual behaviors in the overdoped region. We will also discuss modifications of a simple BEC-BCS crossover picture to account for actual situations with additional effects of competing order and phase separation.

Unveiling phase diagram of the lightly doped high-Tc cuprate superconductors with disorder removed

The currently established electronic phase diagram of cuprates is based on a study of single- and double-layered compounds. These CuO2 planes, however, are directly contacted with dopant layers, thus inevitably disordered with an inhomogeneous electronic state. Here, we solve this issue by investigating a 6-layered Ba2Ca5Cu6O12(F,O)2 with inner CuO2 layers, which are clean with the extremely low disorder, by angle-resolved photoemission spectroscopy (ARPES) and quantum oscillation measurements. We find a tiny Fermi pocket with a doping level less than 1% to exhibit well-defined quasiparticle peaks which surprisingly lack the polaronic feature. This provides the first evidence that the slightest amount of carriers is enough to turn a Mott insulating state into a metallic state with long-lived quasiparticles. By tuning hole carriers, we also find an unexpected phase transition from the superconducting to metallic states at 4%. Our results are distinct from the nodal liquid state with polaronic features proposed as an anomaly of the heavily underdoped cuprates.

Structure and equation of state of Bi2Sr2Can−1CunO2n+4+δ from x-ray diffraction to megabar pressures

Pressure is a unique tuning parameter for probing the properties of materials, and it has been particularly useful for studies of electronic materials such as high-temperature cuprate superconductors. Here we report the effects of quasihydrostatic compression produced by a neon pressure medium on the structures of bismuth-based high-Tc cuprate superconductors with the nominal composition Bi2Sr2Can−1CunO2n+4+δ (n=1,2,3) up to 155 GPa. The structures of all three compositions obtained by synchrotron x-ray diffraction can be described as pseudotetragonal over the entire pressure range studied. We show that previously reported pressure-induced distortions and structural changes arise from the large strains that can be induced in these layered materials by nonhydrostatic stresses. The pressure-volume equations of state (EOS) measured under these quasihydrostatic conditions cannot be fit to single phenomenological formulation over the pressure ranges studied, starting below 20 GPa. This intrinsic anomalous compression as well as the sensitivity of Bi2Sr2Can−1CunO2n+4+δ to deviatoric stresses provide explanations for the numerous inconsistencies in reported EOS parameters for these materials. We conclude that the anomalous compressional behavior of all three compositions is a manifestation of the changes in electronic properties that are also responsible for the remarkable nonmonotonic dependence of Tc with pressure, including the increase in Tc at the highest pressures studied so far for each. Transport and spectroscopic measurements up to megabar pressures are needed to fully characterize these cuprates and explore higher possible critical temperatures in these materials.1 MoreReceived 15 December 2022Accepted 5 May 2023DOI:https://doi.org/10.1103/PhysRevMaterials.7.064803©2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasEquations of stateHigh-pressure studiesPhysical SystemsCupratesTechniquesX-ray diffractionCondensed Matter, Materials & Applied Physics

A testable theory for high-Tc superconductivity in cuprates

A number of theories for the superconductivity in cuprates, have been proposed in the more than 30 years that have elapsed since its discovery. A common feature of these theories is the small number, or even the absence, of quantitative predictions that could be compared to a vast number of experimental data, which are, conversely, available. Such theories are, consequently non-testable. We describe the foundations and a number of applications of a theory describing High-Tc Superconductivity in cuprates, which we proposed recently, that besides being testable, has proven to meet successfully the tests to which it has been submitted so far.

Periodic Atomic Displacements and Visualization of the Electron-Lattice Interaction in the Cuprate

Traditionally, X-ray scattering techniques have been used to detect the breaking of the structural symmetry of the lattice, which accompanies a periodic displacement of the atoms associated with charge density wave (CDW) formation in the cuprate pseudogap states. Similarly, the Spectroscopic Imaging Scanning Tunneling Microscopy (SI-STM) has visualized the short-range CDW. However, local coupling of electrons to the lattice in the form of a short-range CDW has been a challenge to visualize, thus a link between these measurements has been missing. Here, we introduce a novel STM-based technique to visualize the local bond length variations obtained from topographic imaging with picometer precision. Application of this technique to the high-Tc cuprate superconductor Bi2Sr2CaCu2O8+{\delta} revealed a high-fidelity local lattice distortion of the BiO lattice as large as 2%. In addition, analysis of local breaking of rotational symmetry associated with the bond lengths reveals modulations around four-unit-cell periodicity in both B1 and E representations in the C4v group of the lattice, which coincides with the uni-directional d-symmetry CDW (dCDW) previously identified within the CuO2 planes, thus providing direct evidence of electron-lattice coupling in the pseudogap state and a link between the X-ray scattering and STM measurements. Overall, our results suggest that the periodic lattice displacements in E representations correspond to a locally-frozen version of the soft phonons identified by the X-ray scattering measurements, and a fluctuation of the bond length is reflected by the fluctuation of the dCDW formation near the quantum critical point.

Visualizing the Atomic Configuration of Carbonate Groups in a (Cu,C)Ba2 Ca3 Cu4 O11+δ Superconductor.

Carbonates (CO3 2- ) have always been known as impurities to degrade the superconductivity in cuprate high-Tc superconductors. Herein, the atomic arrangement of carbonates is directly visualized in (Cu,C)Ba2 Ca3 Cu4 O11+δ via integrated differential phase contrast (iDPC) combined with state-of-the-art scanning transmission electron microscopy. The carbon atoms replace Cu atoms in the charge-reservoir layers, contributing to the formation of carbonates through strong orbital hybridization with the surrounding oxygen atoms. Using first-principles calculations, the spatial configuration of the carbonate groups is confirmed and their influence on the local crystal lattice and electronic states is further investigated. The carbonates not only accommodate distortions by improving the flatness of the outer CuO2 layers but also reduce the density of states at the Fermi level. These two factors play competitive roles to affect the superconductivity. This study provides direct evidence of the presence of CO3 2- groups and gains an insight into the underlying mechanism of superconductivity in oxycarbonate superconductors.

Fano interference between collective modes in cuprate high-Tc superconductors

Cuprate high-Tc superconductors are known for their intertwined interactions and the coexistence of competing orders. Uncovering experimental signatures of these interactions is often the first step in understanding their complex relations. A typical spectroscopic signature of the interaction between a discrete mode and a continuum of excitations is the Fano resonance/interference, characterized by the asymmetric light-scattering amplitude of the discrete mode as a function of the electromagnetic driving frequency. In this study, we report a new type of Fano resonance manifested by the nonlinear terahertz response of cuprate high-Tc superconductors, where we resolve both the amplitude and phase signatures of the Fano resonance. Our extensive hole-doping and magnetic field dependent investigation suggests that the Fano resonance may arise from an interplay between the superconducting fluctuations and the charge density wave fluctuations, prompting future studies to look more closely into their dynamical interactions.

Possible Manifestation of Q-Ball Mechanism of High-Tc Superconductivity in X-ray Diffraction

It is demonstrated, that recently proposed by the author Q-ball mechanism of the pseudogap state and high-Tc superconductivity in cuprates may be detected in micro X-ray diffraction, since it imposes inverse correlations between the size and scattering intensities of the Q-ball charge-density-wave (CDW) fluctuations in these compounds. The Q-ball charge Q gives the number of condensed elementary bosonic excitations in a CDW fluctuation of finite amplitude. The attraction between these excitations inside Euclidean Q-balls is self-consistently triggered by the simultaneous condensation of Cooper/local pairs. Euclidean Q-ball solutions, analogous to the famous Q-balls of squarks in the supersymmetric standard model, arise due to the global invariance of the effective theory under the U(1) phase rotation of the Fourier amplitudes of the short-range CDW fluctuations. A conserved ‘Noether charge’ Q along the Matsubara time axis equals Q∝TM2V, where the temperature T, Q-ball’s volume V, and fluctuation amplitude M enter. Several predictions are derived in an analytic form that follow from this picture. The conservation of the charge Q leads to an inverse proportionality between the volume V and X-ray scattering intensity ∼M2 of the CDW puddles found in micro X-ray scattering experiments. The theoretical temperature dependences of the most probable Q value of superconducting Q-balls and their size and scattering amplitudes fit well the recent X-ray diffraction data in the pseudogap phase of high-Tc cuprates.

Non-Centrosymmetric Sr2IrO4 Obtained Under High Pressure.

Sr2IrO4 with strong spin-orbit coupling and Hubbard repulsion (U) hosts Mott insulating states. The similar crystal structure and magnetic and electronic properties, particularly the d-wave gap observed in Sr2IrO4 enhanced the analogies to the cuprate high-Tc superconductor, La2CuO4. The incomplete analogy was due to the lack of broken inversion symmetry phases observed in Sr2IrO4. Here, under high-pressure and high-temperature conditions, we report a noncentrosymmetric Sr2IrO4. The crystal structure and its noncentrosymmetric character were determined by single-crystal X-ray diffraction and high-resolution scanning transmission electron microscopy. The magnetic characterization confirms the Ir4+ with S = 1/2 at low temperature in Sr2IrO4 with magnetic ordering occurring at around 86 K, where a larger moment is observed than the ambient pressure Sr2IrO4. Moreover, the resistivity measurement shows three-dimensional Mott variable-range hopping (VRH) existed in the system. This noncentrosymmetric Sr2IrO4 phase appears to be a unique material that offers a further understanding of high-Tc superconductivity.

Methods of Modeling of Strongly Correlated Electron Systems

The discovery of high-Tc superconductivity in cuprates in 1986 moved strongly correlated systems from exotic worlds interesting only for pure theorists to the focus of solid-state research. In recent decades, the majority of hot topics in condensed matter physics (high-Tc superconductivity, colossal magnetoresistance, multiferroicity, ferromagnetism in diluted magnetic semiconductors, etc.) have been related to strongly correlated transition metal compounds. The highly successful electronic structure calculations based on density functional theory lose their predictive power when applied to such compounds. It is necessary to go beyond the mean field approximation and use the many-body theory. The methods and models that were developed for the description of strongly correlated systems are reviewed together with the examples of response function calculations that are needed for the interpretation of experimental information (inelastic neutron scattering, optical conductivity, resonant inelastic X-ray scattering, electron energy loss spectroscopy, angle-resolved photoemission, electron spin resonance, and magnetic and magnetoelectric properties). The peculiarities of (quasi-) 0-, 1-, 2-, and 3- dimensional systems are discussed.

Two distinctive temperature dependences of the London penetration depth in high-Tc cuprate superconductors as support for the theory of Bose-liquid superconductivity

In the framework of the theory of Bose-liquid superconductivity, we show that in high-Tc cuprate superconductors the magnetic field penetration depth (known as the London penetration depth λL(T)) decreases first exponentially below the superconducting transition temperature Tc with decreasing the temperature T and then λL(T) decreases like a certain power of T at lower temperatures due to the vanishing of the energy gap Δg(T) in the excitation spectrum of a superfluid Bose-liquid at a characteristic temperature Tc⁎ lower than Tc. Below Tc, the London penetration depth λL(T) has an exponential temperature dependence down to Tc⁎, which is different from a BCS- like exponential temperature dependence, and then λL(T) will follow a power law temperature dependence down to T=0, which is also different from power-law temperature dependences predicted by some BCS-like (d-wave) pairing theories. In unconventional (bosonic) cuprate superconductors characterized by the strong interboson coupling constant (γB≳1), λL(T) exhibits the distinctly different temperature dependences in different temperature intervals 0≤T≤Tc⁎<<Tc and Tc⁎<T<Tc when the energy gap Δg(T) vanishes at a temperature Tc⁎ well below Tc. In the weak interboson coupling (γB<<1) the energy gap Δg(T) vanishes at a temperature Tc⁎ close to Tc and the reduced London penetration depth λL(T)/λL(0) has an unusual Tn power-law temperature dependence in a wide temperature range 0<T<Tc⁎ below Tc, i.e. the expression λL(T)/λL(0)≃[1−aL(T)(T/Tc)n]−1/2 (where n≳4 and aL(T)≲1) is valid only below Tc⁎ and is similar to the well-known empirical Gorter-Casimir law. Our theoretical predictions of the distinctive power-law and exponential temperature dependences of λL(T)/λL(0) are in good agreement with the experimental results reported for GdBa2Cu3O7−δ ceramics and YBa2Cu3O7−δ films. The peculiar temperature dependences of λL(T)/λL(0) observed in these high-Tc materials at low and high temperatures do not follow the predictions of the s- and d-wave BCS-like theories of Fermi-liquid superconductivity and give evidence for the predictions of the theory of Bose-liquid superconductivity.

Possible Benefits from Phonon/Spin-Wave Induced Gaps below or above EF for Superconductivity in High-TC Cuprates

A phonon of appropriate momentum kF will open a band gap at the Fermi energy EF. The gap within the electronic density-of-states (DOS), N(EF), leads to a gain in electronic energy and a loss of elastic energy because of the gap-generating phonon. A BCS-like simulation shows that the energy gain is larger than the loss for temperatures below a certain transition temperature, TC. Here, it is shown that the energy count can be almost as favorable for gaps a little below or above EF. Such gaps can be generated by auxiliary phonons (or even spin- and charge-density waves) with k-vectors slightly different from kF. Gaps not too far from EF will add to the energy gain at the superconducting transition. In addition, a DOS-peak can appear at EF and thereby increase N(EF) and TC. A dip in the DOS below EF will result for temperatures below TC, which is similar to what often is observed in cuprate superconductors. The roles of spin waves and thermal disorders are discussed.

High critical current density and high-tolerance superconductivity in high-entropy alloy thin films

High-entropy alloy (HEA) superconductors—a new class of functional materials—can be utilized stably under extreme conditions, such as in space environments, owing to their high mechanical hardness and excellent irradiation tolerance. However, the feasibility of practical applications of HEA superconductors has not yet been demonstrated because the critical current density (Jc) for HEA superconductors has not yet been adequately characterized. Here, we report the fabrication of high-quality superconducting (SC) thin films of Ta–Nb–Hf–Zr–Ti HEAs via a pulsed laser deposition. The thin films exhibit a large Jc of >1 MA cm−2 at 4.2 K and are therefore favorable for SC devices as well as large-scale applications. In addition, they show extremely robust superconductivity to irradiation-induced disorder controlled by the dose of Kr-ion irradiation. The superconductivity of the HEA films is more than 1000 times more resistant to displacement damage than that of other promising superconductors with technological applications, such as MgB2, Nb3Sn, Fe-based superconductors, and high-Tc cuprate superconductors. These results demonstrate that HEA superconductors have considerable potential for use under extreme conditions, such as in aerospace applications, nuclear fusion reactors, and high-field SC magnets.

Antinodal kink in the band dispersion of electron-doped cuprate La2\u2212xCexCuO4\xb1\u03b4

Angle-resolved photoemission spectroscopy (ARPES) measurements have established the phenomenon of kink in band dispersion of high-Tc cuprate superconductors. However, systematic studies of the kink in electron-doped cuprates are still lacking experimentally. We performed in situ ARPES measurements on La2−xCexCuO4±δ (LCCO) thin films over a wide electron doping (n) range from 0.05 to 0.23. While the nodal kink is nearly invisible, an antinodal kink around 45 meV, surviving above 200 K, is observed for n ~ 0.05–0.19, whose position is roughly independent of doping. The fact that the antinodal kink observed at high temperatures and in the highly overdoped region favors the phonon mechanism with contributions from the Cu–O bond-stretching mode and the out-of-plane oxygen buckling mode.

Anomalous phase separation in a correlated electron system: Machine-learning–enabled large-scale kinetic Monte Carlo simulations

SignificancePhase separation is crucial to the functionalities of many correlated electron materials with notable examples including colossal magnetoresistance in manganites and high-Tc superconductivity in cuprates. However, the nonequilibrium phase-separation dynamics in such systems are poorly understood theoretically, partly because the required multiscale modeling is computationally very demanding. With the aid of machine-learning methods, we have achieved large-scale dynamical simulations in a representative correlated electron system. We observe an unusual relaxation process that is beyond the framework of classical phase-ordering theories. We also uncover a correlation-induced freezing behavior, which could be a generic feature of phase separation in correlated electron systems.