Hole-doped Cuprate Superconductors Research Articles

Universal correlation between H-linear magnetoresistance and T-linear resistivity in high-temperature superconductors

The signature feature of the ‘strange metal’ state of high-Tc cuprates—its linear-in-temperature resistivity—has a coefficient α1 that correlates with Tc, as expected were α1 derived from scattering off the same bosonic fluctuations that mediate pairing. Recently, an anomalous linear-in-field magnetoresistance (=γ1H) has also been observed, but only over a narrow doping range, leaving its relation to the strange metal state and to the superconductivity unclear. Here, we report in-plane magnetoresistance measurements on three hole-doped cuprate families spanning a wide range of temperatures, magnetic field strengths and doping. In contrast to expectations from Boltzmann transport theory, γ1 is found to correlate universally with α1. A phenomenological model incorporating real-space inhomogeneity is proposed to explain this correlation. Within this picture, superconductivity in hole-doped cuprates is governed not by the strength of quasiparticle interactions with a bosonic bath, but by the concentration of strange metallic carriers.

Computational demonstrations of density wave of Cooper pairs and paired-electron liquid in the quarter-filled band-A brief review.

There has been strong interest recently in the so-called Cooper pair density wave, subsequent to the proposition that such a state occurs in the hole-doped cuprate superconductors. As of now, there is no convincing demonstration of such a state in the cuprate theoretical literature. We present here a brief but complete review of our theoretical and computational work on the paired-electron crystal (PEC), which has also been experimentally seen in the insulating phase proximate to superconductivity (SC) in organic charge-transfer solid (CTS) superconductors. Within our theory, SC in the CTS does indeed evolve from the PEC. A crucial requirement for the finding of the PEC is that the proper carrier density of one charge carrier per two sites is taken into consideration at the outset. Following the discussion of CTS superconductors, we briefly discuss how the theory can be extended to understand the phase diagram of the cuprate superconductors that has remained mysterious after nearly four decades of the discovery of SC in this family.

Resonant inelastic X-ray scattering applications in quantum materials

The essence of quantum materials lies in the intricate coupling among charge, spin, orbital and lattice degrees of freedom. Although X-ray photoemission spectroscopy and inelastic neutron scattering have advantages in detecting fermionic single-particle spectral function and bosonic spin excitations in quantum materials, respectively, probing other bosonic collective excitations especially their coupling is not possible until the establishment of the advanced resonant inelastic X-ray scattering (RIXS). In the past decades, RIXS has flourished with continuously improved energy resolution which made a paradigm shift from measuring crystal-field splitting and the charge-transfer excitation, to probing collective excitations and the order parameters of all degrees of freedom. This review paper summarises the latest research progress of quantum materials studied by the soft X-ray RIXS. For instance, three-dimensional collective charge excitations, plasmons, were discovered experimentally by RIXS in both electron and hole doped cuprate superconductors. The collective orbital excitations and excitons were found in copper and nickel based quantum materials. For the newly discovered nickelate superconductors, RIXS has made substantial contributions to characterising their electronic and magnetic excitations and the related ordering phenomena critical for an in-depth understanding of the underlying superconducting mechanicsm. The RIXS is a unique tool in probing the higher-order spin excitations in quantum materials due to the strong spin-orbit coupling and the core-valence exchange interaction. The RIXS is also found to be superior in probing the Stoner magnetic excitations in magnetic metals and topological magnetic materials. Finally, the development of RIXS technology in Chinese large-scale research facilities is briefly prospected.

Differentiated roles of Lifshitz transition on thermodynamics and superconductivity in La2-xSrxCuO4

The effect of Lifshitz transition on thermodynamics and superconductivity in hole-doped cuprates has been heavily debated but remains an open question. In particular, an observed peak of electronic specific heat is proposed to originate from fluctuations of a putative quantum critical point p* (e.g., the termination of pseudogap at zero temperature), which is close to but distinguishable from the Lifshitz transition in overdoped La-based cuprates where the Fermi surface transforms from hole-like to electron-like. Here we report an in situ angle-resolved photoemission spectroscopy study of three-dimensional Fermi surfaces in La2-xSrxCuO4 thin films (x = 0.06 to 0.35). With accurate kz dispersion quantification, the said Lifshitz transition is determined to happen within a finite range around x = 0.21. Normal state electronic specific heat, calculated from spectroscopy-derived band parameters, reveals a doping-dependent profile with a maximum at x = 0.21 that agrees with previous thermodynamic microcalorimetry measurements. The account of the specific heat maximum by underlying band structures excludes the need for additionally dominant contribution from the quantum fluctuations at p*. A d-wave superconducting gap smoothly across the Lifshitz transition demonstrates the insensitivity of superconductivity to the dramatic density of states enhancement.

Continuously Doping BiM2Sr2CaCu2O8+δ into Electron-Doped Superconductor by CaH2 Annealing Method

As a typical hole-doped cuprate superconductor, Bi2Sr2CaCu2O8 + δ (Bi2212) carrier doping is mostly determined by its oxygen content. Traditional doping methods can regulate its doping level within the range of hole doping. Here we report the first application of CaH2 annealing method in regulating the doping level of Bi2212. By continuously controlling the anneal time, a series of differently doped samples can be obtained. The combined experimental results of x-ray diffraction, scanning transmission electron microscopy, resistance and Hall measurements demonstrate that the CaH2 induced topochemical reaction can effectively change the oxygen content of Bi2212 within a very wide range, even switching from hole doping to electron doping. We also found evidence of a low-T c superconducting phase in the electron doping side.

Acoustic plasmons and conducting carriers in hole-doped cuprate superconductors

The layered crystal structures of cuprates enable collective charge excitations fundamentally different from those of three-dimensional metals. Acoustic plasmons have been observed in electron-doped cuprates by resonant inelastic x-ray scattering (RIXS); in contrast, the characteristics of acoustic plasmons in hole-doped cuprates are under debate, despite extensive measurements. This contrast led us to investigate the charge excitations of hole-doped cuprate ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$. Here we present incident-energy-dependent RIXS measurements and calculations of collective charge response via the loss function to reconcile the issues above. Our results provide evidence for the acoustic plasmons of Zhang-Rice singlet (ZRS), which has a character of the Cu $3{d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ strongly hybridized with the O $2p$ orbitals; the metallic behavior is implied to result from the movement of ZRS rather than the simple hopping of O $2p$ holes.

Topological pseudogap in highly polarizable layered systems with 2D hole-like dispersion

Pseudogap in hole-doped cuprate superconductors is acknowledged as a possible key to understanding their ground normal state, however, existing pseudogap models have essential inconsistencies with experiments. In our approach pseudogap emerges due to impact of autolocalized carriers on stationary states of delocalized ones and topology of the 2D hole-like dispersion. Autolocalized carriers create potential which transforms Bloch quasiparticles into distributed wave packets (DWPs) with different momentums in areas with different potential. Topology of hole-like constant energy curves in 2D-conducting cuprates forbids DWPs with average momentums near antinode. Manifestation of permitted DWPs in ARPES spectra demonstrates all known pseudogap features including midpoint shift, giant broadening and Fermi momentum misalignment. Calculated doping dependence of the pseudogap width and onset temperature agrees with experiments. The obtained ground normal state of the hole-doped cuprates, in which all the doped holes are autolocalized until high doping is reached and near-antinodal electron DWPs are absent, explains Fermi surface reconstruction from small electron pocket to large hole-like Fermi surface observed in quantum oscillation measurements. Our results open a possibility of creating systems with artificial pseudogap and switchable density of states on the base of highly polarizable layered structures with 2D conductivity and hole-like dispersion.

Evolution of Charge-Lattice Dynamics across the Kuramoto Synchronization Phase Diagram of Quantum Tunneling Polarons in Cuprate Superconductors

Because of its sensitivity to the instantaneous structure factor, S(Q,t = 0), Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for probing the dynamic structure of condensed matter systems in which the charge and lattice dynamics are coupled. When applied to hole-doped cuprate superconductors, EXAFS has revealed the presence of internal quantum tunneling polarons (IQTPs). An IQTP arises in EXAFS as a two-site distribution for certain Cu–O pairs, which is also duplicated in inelastic scattering but not observed in standard diffraction measurements. The Cu–Sr pair distribution has been found to be highly anharmonic and strongly correlated to both the IQTPs and to superconductivity, as, for example, in YSr2Cu2.75Mo0.25O7.54(Tc=84 K). In order to describe such nontrivial, anharmonic charge-lattice dynamics, we have proposed a model Hamiltonian for a prototype six-atom cluster, in which two Cu-apical-O IQTPs are charge-transfer bridged through Cu atoms by an O atom in the CuO2 plane and are anharmonically coupled via a Sr atom. By applying an exact diagonalization procedure to this cluster, we have verified that our model indeed produces an intricate interplay between charge and lattice dynamics. Then, by using the Kuramoto model for the synchronization of coupled quantum oscillators, we have found a first-order phase transition for the IQTPs into a synchronized, phase-locked phase. Most importantly, we have shown that this transition results specifically from the anharmonicity. Finally, we have provided a phase diagram showing the onset of the phase-locking of IQTPs as a function of the charge-lattice and anharmonic couplings in our model. We have found that the charge, initially confined to the apical oxygens, is partially pumped into the CuO2 plane in the synchronized phase, which suggests a possible connection between the synchronized dynamic structure and high-temperature superconductivity (HTSC) in doped cuprates.

Superconducting Fluctuations in Overdoped Bi2Sr2CaCu2O8+δ

Fluctuating superconductivity - vestigial Cooper pairing in the resistive state of a material - is usually associated with low dimensionality, strong disorder or low carrier density. Here, we report single particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in heavily hole-doped cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ ($T_c$ = 66~K) despite the high carrier density. With a sign-problem free quantum Monte Carlo calculation, we show how a partially flat band at ($\pi$,0) can help enhance superconducting phase fluctuations. Finally, we discuss the implications of an anisotropic band structure on the phase-coherence-limited superconductivity in overdoped cuprates and other superconductors.

Anisotropic dressing of electrons in electron-doped cuprate superconductors

The recent experiments revealed a remarkable possibility for the absence of the disparity between the phase diagrams of the electron- and hole-doped cuprate superconductors, while such an aspect should be also reflected in the dressing of the electrons. Here the phase diagram of the electron-doped cuprate superconductors and the related exotic features of the anisotropic dressing of the electrons are studied based on the kinetic-energy driven superconductivity. It is shown that although the optimized Tc in the electron-doped side is much smaller than that in the hole-doped case, the electron- and hole-doped cuprate superconductors rather resemble each other in the doping range of the superconducting dome, indicating an absence of the disparity between the phase diagrams of the electron- and hole-doped cuprate superconductors. In particular, the anisotropic dressing of the electrons due to the strong electron's coupling to a strongly dispersive spin excitation leads to that the electron Fermi surface is truncated to form the disconnected Fermi arcs centered around the nodal region. Concomitantly, the dip in the peak-dip-hump structure of the quasiparticle excitation spectrum is directly associated with the corresponding peak in the quasiparticle scattering rate, while the dispersion kink is always accompanied by the corresponding inflection point in the total self-energy, as the dip in the peak-dip-hump structure and dispersion kink in the hole-doped counterparts. The theory also predicts that both the normal and anomalous self-energies exhibit the well-pronounced low-energy peak-structures.

Detection of Acoustic Plasmons in Hole-Doped Lanthanum and Bismuth Cuprate Superconductors Using Resonant Inelastic X-Ray Scattering.

High T_{c} superconductors show a rich variety of phases associated with their charge degrees of freedom. Valence charges can give rise to charge ordering or acoustic plasmons in these layered cuprate superconductors. While charge ordering has been observed for both hole- and electron-doped cuprates, acoustic plasmons have only been found in electron-doped materials. Here, we use resonant inelastic x-ray scattering to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors (La_{1.84}Sr_{0.16}CuO_{4} and Bi_{2}Sr_{1.6}La_{0.4}CuO_{6+δ}), crucially completing the picture. Interestingly, in contrast to the quasistatic charge ordering which manifests at both Cu and O sites, the observed acoustic plasmons are predominantly associated with the O sites, revealing a unique dichotomy in the behavior of valence charges in hole-doped cuprates.

Cuprate superconductors as viewed through a striped lens

Understanding the electron pairing in hole-doped cuprate superconductors has been a challenge, in particular because the "normal" state from which it evolves is unprecedented. Now, after three and a half decades of research, involving a wide range of experimental characterizations, it is possible to delineate a clear and consistent cuprate story. It starts with doping holes into a charge-transfer insulator, resulting in in-gap states. These states exhibit a pseudogap resulting from the competition between antiferromagnetic superexchange $J$ between nearest-neighbor Cu atoms (a real-space interaction) and the kinetic energy of the doped holes, which, in the absence of interactions, would lead to extended Bloch-wave states whose occupancy is characterized in reciprocal space. To develop some degree of coherence on cooling, the spin and charge correlations must self-organize in a cooperative fashion. A specific example of resulting emergent order is that of spin and charge stripes, as observed in La$_{2-x}$Ba$_x$CuO$_4$. While stripe order frustrates bulk superconductivity, it nevertheless develops pairing and superconducting order of an unusual character. The antiphase order of the spin stripes decouples them from the charge stripes, which can be viewed as hole-doped, two-leg, spin-$\frac12$ ladders. To achieve superconducting order, the pair correlations in neighboring ladders must develop phase order. In the presence of spin stripe order, antiphase Josephson coupling can lead to pair-density-wave superconductivity. Alternatively, in-phase superconductivity requires that the spin stripes have an energy gap, which empirically limits the coherent superconducting gap. Hence, superconducting order in the cuprates involves a compromise between the pairing scale, which is maximized at $x\sim\frac18$, and phase coherence, which is optimized at $x\sim0.2$.

Effect of the nonmonotonic d-wave superconducting gap on the electronic Raman scattering of electron-doped cuprate superconductors

ABSTRACT By considering a nonmonotonic d-wave superconducting (SC) gap effect in electron-doped cuprate superconductors, the energy and momentum dependence of the electronic Raman scattering is studied. The electronic Raman scattering of electron-doped cuprate superconductors has obvious differences with hole-doped case described by a pure d-wave SC gap, which can be attributed to the nonmonotonic d-wave SC gap in electron-doped cuprate superconductors. Three main different behaviours for the electronic Raman scattering spectra between electron-doped and hole-doped cuprate superconductors have been obtained, the intensity comparison of and spectra, the Raman peak positions as a function of energy for and spectra, and energy asymptotic behaviour of the low-energy spectrum. For electron-doped cuprate superconductors, the intensity of spectrum as a function of energy is larger than one, and the Raman peak position of spectrum appears at a higher energy than one, then the low-energy spectrum of as a function of energy increases linearly, not energy dependence. All these theoretical results of electron-doped cuprate superconductors are in qualitative agreement with the corresponding Raman scattering experimental data.

A unified form of low-energy nodal electronic interactions in hole-doped cuprate superconductors

Using angle resolved photoemission spectroscopy measurements of Bi2Sr2CaCu2O8+δ over a wide range of doping levels, we present a universal form for the non-Fermi liquid electronic interactions in the nodal direction in the exotic normal state phase. It is described by a continuously varying power law exponent versus energy and temperature (hence named a Power Law Liquid or PLL), which with doping varies smoothly from a quadratic Fermi Liquid in the overdoped regime, to a linear Marginal Fermi Liquid at optimal doping, to a non-quasiparticle non-Fermi Liquid in the underdoped regime. The coupling strength is essentially constant across all regimes and is consistent with Planckian dissipation. Using the extracted PLL parameters we reproduce the experimental optics and resistivity over a wide range of doping and normal-state temperature values, including the T* pseudogap temperature scale observed in the resistivity curves. This breaks the direct link to the pseudogapping of antinodal spectral weight observed at similar temperature scales and gives an alternative direction for searches of the microscopic mechanism.

Dynamical density matrix renormalization group study of spin and charge excitations in the four-leg t−t′−J ladder

The ground state of the t-t'-J ladder with four legs favors a striped charge distribution for the parameters corresponding to hole-doped cuprate superconductors. We investigate the dynamical spin and charge structure factors of the model by using the dynamical density matrix renormalization group (DMRG) and clarify the influence of the stripe on the structure factors. The dynamical charge structure factor along the momentum direction from q=(0,0) to (pi,0) clearly shows low-energy excitations corresponding to the stripe order in hole doping. On the other hand, the stripe order weakens in electron doping, resulting in fewer low-energy excitations in the charge channel. In the spin channel, we find incommensurate spin excitations near q=(pi,pi) forming an hourglass behavior in hole doping, while in electron doping we find clearly spin-wave-like dispersions starting from q=(pi,pi). Along the (0,0)-(pi,0) direction, the spin excitations are strongly influenced by the stripes in hole doping, resulting in two branches that form a discontinuous behavior in the dispersion. In contrast, the electron-doped systems show a downward shift in energy toward (pi,0). These behaviors along the (0,0)-(pi,0) direction are qualitatively similar to momentum-dependent spin excitations recently observed by resonant inelastic x-ray scattering experiments in hole- and electron-doped cuprate superconductors.

Suppression of the Hall number due to charge density wave order in high- Tc cuprates

Understanding the pseudogap phase in hole-doped high temperature cuprate superconductors remains a central challenge in condensed matter physics. From a host of recent experiments there is now compelling evidence of translational symmetry breaking charge density wave (CDW) order in a wide range of doping inside this phase. Two distinct types of incommensurate charge order -- bidirectional at zero or low magnetic fields and unidirectional at high magnetic fields close to the upper critical field $H_{c2}$ -- have been reported so far in approximately the same doping range between $p\simeq 0.08$ and $p\simeq 0.16$. In concurrent developments, recent high field Hall experiments have also revealed two indirect but striking signatures of Fermi surface reconstruction in the pseudogap phase, namely, a sign change of the Hall coefficient to negative values at low temperatures at intermediate range of hole doping and a rapid suppression of the positive Hall number without change in sign near optimal doping $p \sim 0.19$. We show that the assumption of a unidirectional incommensurate CDW (with or without a coexisting weak bidirectional order) at high magnetic fields near optimal doping and a coexistence of both types of orders of approximately equal magnitude at high magnetic fields at intermediate range of doping may help explain the striking behavior of low temperature Hall effect in the entire pseudogap phase.

Pseudogap and Fermi-Surface Topology in the Two-Dimensional Hubbard Model

One of the distinctive features of hole-doped cuprate superconductors is the onset of a `pseudogap' below a temperature $T^*$. Recent experiments suggest that there may be a connection between the existence of the pseudogap and the topology of the Fermi surface. Here, we address this issue by studying the two-dimensional Hubbard model with two distinct numerical methods. We find that the pseudogap only exists when the Fermi surface is hole-like and that, for a broad range of parameters, its opening is concomitant with a Fermi surface topology change from electron- to hole-like. We identify a common link between these observations: the pole-like feature of the electronic self-energy associated with the formation of the pseudogap is found to also control the degree of particle-hole asymmetry, and hence the Fermi surface topology transition. We interpret our results in the framework of an SU(2) gauge theory of fluctuating antiferromagnetism. We show that a mean-field treatment of this theory in a metallic state with U(1) topological order provides an explanation of this pole-like feature, and a good description of our numerical results. We discuss the relevance of our results to experiments on cuprates.

Zn induced in-gap electronic states in La214 probed by uniform magnetic susceptibility: relevance to the suppression of superconducting Tc

Substitution of isovalent non-magnetic defects, such as Zn, in the CuO2 plane strongly modifies the magnetic properties of strongly electron correlated hole doped cuprate superconductors. The reason for enhanced uniform magnetic susceptibility, χ, in Zn substituted cuprates is debatable. Generally the defect induced magnetic behavior has been analyzed mainly in terms of two somewhat contrasting scenarios. The first one is due to independent localized moments appearing in the vicinity of Zn arising because of the strong electronic/magnetic correlations present in the host compound and the second one is due to transfer of quasiparticle (QP) spectral weight and creation of weakly localized low-energy electronic states associated with each Zn atom in place of an in-plane Cu. If the second scenario is correct, one should expect a direct correspondence between Zn induced suppression of the superconducting transition temperature, Tc, and the extent of the enhanced magnetic susceptibility at low temperature. In this case, the low-T enhancement of χ would be due to weakly localized QP states at low energy and these electronic states will be precluded from taking part in Cooper pairing. We explore this second possibility by analyzing the χ(T) data for La2−xSrxCu1−yZnyO4 with different hole contents, p (=x), and Zn concentrations (y) in this paper. The results of our analysis support this scenario.

External current as a coupler between the spin-vortex-induced loop current qubits

The spin-vortex-induced loop current (SVILC) is a nano-sized loop current predicted to exist in the CuO2 plane in the bulk of hole-doped cuprate superconductors. It is a persistent loop current protected by the topological winding number associated with the wave function. It exists around a spin-vortex created by the itinerant electrons with a doped hole at its center. The direction of each SVILC can be either clockwise (winding number −1) or counterclockwise (winding number +1); and the currentless winding number zero is forbidden by the single-valued requirement of the wave function with respect to the electron coordinates. Recently, it has been demonstrated, theoretically, that this degree-of-freedom can be used for qubits. The gate-operation time by the Rabi oscillation using an electromagnetic field with electric field intensity 105 V m–1 is estimated to be several nanoseconds. This is comparable or shorter than the existing superconducting qubits. Since SVILCs do not require Cooper pairs, the SVILC qubit is free from the relaxation caused by broken Cooper pair electrons that is speculated to limit the qubit coherence time in the existing superconducting qubits. Thus, the coherence time for the SVILC qubit may exceed the value achieved by the superconducting qubit (about 100 μs). Further, since the stabilization temperature of SVILCs is expected to be the superconducting transition temperature of the cuprates, a much higher operation temperature may be possible for the SVILC qubits compared to the existing superconducting qubits, which requires the operation temperature of about 10 mK. In the present work, we show, theoretically, that coupling of two SVILC qubits can be achieved by external current feeding. This enables the construction of nano-sized qubit-couplers, and may provide a scalability that is needed in the construction of a fully fault-tolerant quantum computer.

Intertwining Topological Order and Broken Symmetry in a Theory of Fluctuating Spin-Density Waves.

The pseudogap metal phase of the hole-doped cuprate superconductors has two seemingly unrelated characteristics: a gap in the electronic spectrum in the "antinodal" region of the square lattice Brillouin zone and discrete broken symmetries. We present a SU(2) gauge theory of quantum fluctuations of magnetically ordered states which appear in a classical theory of square lattice antiferromagnets, in a spin-density wave mean field theory of the square lattice Hubbard model, and in a CP^{1} theory of spinons. This theory leads to metals with an antinodal gap and topological order which intertwines with the observed broken symmetries.