Recent development in the physics of high-temperature cuprate superconductivity is reviewed, with special emphasis on the phenomena of unconventional and non-universal low-energy excitations of hole- and electron-type cuprate superconductors and the possible physical origin. A phenomenology based on coexisting competing orders with cuprate superconductivity in the ground state appears to provide consistent account for a wide range of experimental findings, including the presence (absence) of pseudogaps and Fermi arcs above the superconducting transition $T_c$ in hole-type (electron-type) cuprate superconductors and the novel conductance modulations below $T_c$, particularly in the vortex state. Moreover, the competing order scenario is compatible with the possibility of pre-formed Cooper pairs and significant phase fluctuations in cuprate superconductors. The physical implications of the unified phenomenology and remaining open issues for the microscopic mechanism of cuprate superconductivity are discussed.
Giant and nil proximity effects and unconventional symmetry of cuprate superconductors are explained as a result of the strong Froehlich interaction of holes with c-axis polarised optical phonons acting together with an anisotropic nonlocal deformation potential.
We begin with an overview of the experimental results for the temperature and doping dependences of the optical-conductivity spectral weight in cuprate superconductors across the whole phase diagram. Then we discuss recent attempts to explain the observed behavior of the spectral weight using reduced and full models with unconventional $d_{x^2-y^2}$ charge-density waves.
The proximity effect in a model manganite-cuprate system is investigated theoretically. We consider a situation in which spin-polarized electrons in manganite layers antiferromagnetically couple with electrons in cuprate layers as observed experimentally. The effect of the interfacial magnetic coupling is found to be much stronger than the injection of spin-polarized electrons into the cuprate region. As a result, the superconducting transition temperature depends on the thickness of the cuprate layer significantly. Since the magnetic coupling creates {\em negative} spin polarization, an appli…
It has gone almost unquestioned that superexchange in the t-J (or Hubbard) model, and not phonons, is responsible for the unconventional ("d-wave") pairing symmetry of cuprate superconductors. However a number of advanced numerical studies have not found superconductivity in the Hubbard model. On the other hand compelling experimental evidence for a strong electron-phonon interaction (EPI) has currently arrived. Here I briefly review some phonon-mediated unconventional pairing mechanisms. In particular the anisotropy of sound velocity makes the phonon-mediated attraction of electrons non-local…
There is compelling evidence for a strong electron-phonon interaction (EPI) in cuprate superconductors from the isotope effects on the supercarrier mass, high resolution angle resolved photoemission spectroscopies (ARPES), a number of optical and neutron-scattering measurements in accordance with our prediction of high-temperature superconductivity in polaronic liquids. A number of observations point to the possibility that high-Tc cuprate superconductors may not be conventional Bardeen-Cooper-Schrieffer (BCS) superconductors, but rather derive from the Bose-Einstein condensation (BEC) of real…
Taking into account the first localization corrections in the electron-impurity self-energy we study the effect of non-magnetic impurities on unconventional superconductivity (SC) mediated by small-q electron-phonon scattering. We show that when van Hove singularities are close to the Fermi level making the electronic system anisotropic as in the high-$T_c$ oxides, both the d-wave and s-wave states are sensitive to non-magnetic impurities and beyond a critical impurity concentration SC disappears in {\it both gap symmetry channels}. Impurity doping may induce a first order transition from d-wa…
To understand the origin of unconventional charge-density-wave (CDW) states in cuprate superconductors, we establish the self-consistent CDW equation, and analyze the CDW instabilities based on the realistic Hubbard model, without assuming any $q$-dependence and the form factor. Many higher-order many-body processes, which are called the vertex corrections, are systematically generated by solving the CDW equation. When the spin fluctuations are strong, the uniform $q=0$ nematic CDW with $d$-form factor shows the leading instability. The axial nematic CDW instability at $q = Q_a = (δ,0)$ ($δ\ap…
We construct a 2-leg ladder model of an Fe-pnictide superconductor and discuss its properties and relationship with the familiar 2-leg cuprate model. Our results suggest that the underlying pairing mechanism for the Fe-pnictide superconductors is similar to that for the cuprates.
This article presents our perspective on STM measurements by Hoffman et al. (cond-mat/0201348) of the vortex lattice in BSCCO. We discuss implications of these measurements for various theories of the cuprate superconductors.
At the nematic quantum critical point that exists in the $d_{x^2-y^2}$-wave superconducting dome of cuprates, the massless nodal fermions interact strongly with the quantum critical fluctuation of nematic order. We study this problem by means of renormalization group approach and show that, the fermion damping rate $\left|\mathrm{Im}Σ^R(ω)\right|$ vanishes more rapidly than the energy $ω$ and the quasiparticle residue $Z_f\rightarrow 0$ in the limit $ω\rightarrow 0$. The nodal fermions thus constitute an unconventional non-Fermi liquid that represents an even weaker violation of Fermi liquid t…
We develop a theory of normal-metal - superconductor (NS) and superconductor - superconductor (SS) tunnelling in bosonic superconductors with strong attractive correlations taking into account coherence effects in single-particle excitation spectrum and disorder. The theory accounts for the existence of two energy scales, their temperature and doping dependencies, asymmetry and inhomogeneity of tunnelling spectra of underdoped cuprate superconductors.
The nodal $d_{x^2-y^2}$ superconducting gap is a hallmark of the cuprate high T$_c$ superconductors. Surprisingly recent angle-resolved photoemission spectroscopy of deeply underdoped cuprates revealed a nodeless energy gap which is adhered to the Fermi surface. Importantly this phenomenon is observed for compounds across several different cuprate families. In this letter we propose an exciting possibility, namely the fully gapped state is a topological superconductor.
High-Tc superconductivity in layered cuprates is described in a BCS-BEC formalism with linearly-dispersive s- and d-wave Cooper pairs moving in quasi-2D finite-width layers about the CuO_2 planes. This yields a closed formula for Tc determined by the layer width, the Debye frequency, the pairing energy, and the in-plane penetration depth. The new formula reasonably reproduces empirical values of superconducting Tc's for seven different compounds among the LSCO, YBCO, BSCCO and TBCCO layered cuprates.
Within the kinetic energy driven superconducting mechanism, we study the interplay between superconductivity and the nodal and antinodal superconducting quasiparticle coherences in cuprate superconductors, and find the s-wave superconducting transition temperature is heavily suppressed by the antinodal superconducting quasiparticle coherence, while the d-wave superconducting transition temperature is enhanced, therefore the antinodal superconducting quasiparticle coherence plays a more crucial role in superconductivity of cuprate superconductors.
We propose a unified description of cuprate and iron-based superconductivity. Consistency with magnetic structure inferred from neutron scattering implies significant constraints on the symmetry of the pairing gap for the iron-based superconductors. We find that this unification requires the orbital pairing formfactors for the iron arsenides to differ fundamentally from those for cuprates at the microscopic level.
Based on an unconventional Fermi liquid model, we present several results on the optimally doped and overdoped cuprate superconductors. For the normal state, we provide an analytic demonstration, backed by self-consistent Baym-Kadanoff (BK) numerical calculations, of the linear in $T$ resistivity and linear in 1/$ε$ optical conductivity, provided the interacting Fermi liquid has strong peaks in its density of states (van-Hove singularities in 2 dimensions) near the chemical potential $μ$. Moreover, we find that the interactions tend to pin these strong density of states peaks close to $μ$. We …
We report a microscopic model wherein the unconventional superconductivity emerges from an incoherent `Cooper-pair glass' state. Driven by the pair-pair interaction, a new type of quasi-Bose phase transition is at work. The interaction leads to the unconventional coupling of the quasiparticles to excited pair states, or `super-quasiparticles', with a non-retarded energy-dependent gap. The model describes quantitatively the quasiparticle excitation spectra of both cuprates and pnictides, including the universal `peak-dip-hump' signatures, and for the pseudogap phase above $T_c$. The results sho…
This ``Perspective'' briefly reviews recent work showing that a class of organic superconductors have important similarities to the cuprate superconductors: (i) There is competition betweeen superconductivity and antiferromagnetism. (ii) Uncoventional metallic behavior is observed near the metal-insulator transition. A more detailed review and discussion of the appropriate strongly correlated electron model can be found in cond-mat/9802198.
We derive the Ginzburg-Landau theory of unconventional singlet superconductors in the presence of a Zeeman field and impurities, in order to examine the resulting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. We show that the behavior of the FFLO phases in unconventional superconductors in the presence of impurities is qualitatively different from that found for s-wave superconductors.
We suggest a model for electronic structure of cuprate superconductors that makes it possible to describe evolution of this structure with the doping and provides a new explanation for a number of typical features of cuprates, including the pseudogap and the Fermi arcs. According to this model, the unique electronic structure of cuprates is favorable for the formation of two-atomic negative-U centers (NUCs) and realization of a peculiar mechanism of the electron-electron interaction.
In this Letter, we develop a microscopic theory to describe the close proximity between the insulating antiferromagnetic (AF) order and the d-wave superconducting (dSC) order in cuprates. We show that the cuprate ground states form a configuration of coherent pairing states consisting of extended singlet Cooper pairs and triplet $π$ pairs, which can simultaneously describe AF and dSC orders.
The bulge in the doping dependence of the basal plane area of cuprate superconductors is shown to be an effect of the particular inhomogenous electronic structure created by the dense packing of paired self-protected singlets (PSPS) in CuO_2 lattices.
Present-day angle-resolved photoemission spectroscopy (ARPES) has offered a tremendous advance in the understanding of electron energy spectra in cuprate superconductors and some related compounds. However, in high magnetic field, magnetic quantum oscillations at low temperatures indicate the existence of small electron (hole) Fermi pockets seemingly missing in ARPES of hole (electron) doped cuprates. Here ARPES and quantum oscillations are reconciled in the framework of an impurity band in the charge-transfer Mott-Hubbard insulator.
A wave function is proposed for the "$4\times 4$" inhomogeneous structures observed on cuprate superconductors. It is based on the Gutzwiller-RVB technique proposed in recent papers, and consists of a Wigner solid of hole pairs embedded in a sea of d-wave spin singlet pairs. Arguments are given that the nodal quasiparticles may remain unscattered and even superconducting on such a structure.
We report a scaling relation between $ρ_s(0)$ and the product of the pseudogap temperature $T^{*}$, $σ_{\rm DC}$ and $T_c$, with $T^{*}$ rescaled by the maximum transition temperature $T_c^{\max}$, which holds universally in the entire doping range for the hole-doped cuprates.
In a recent letter, Alexandrov and Zavaritsky propose a model to explain the anomalous Nernst signal observed in the normal state of hole-doped cuprates. The aim of this comment is to recall that one of the main assumptions of the authors regarding the experimental data is false.
The recently discovered cuprate superconductor Ba$_2$CuO$_{3+δ}$ exhibits a high $T_c\simeq73$K at $δ\simeq0.2$. The polycrystal grown under high pressure has a structure similar to La$_2$CuO$_4$, but with dramatically different lattice parameters due to the CuO$_6$ octahedron compression. The crystal field in the compressed Ba$_2$CuO$_4$ leads to an inverted Cu $3d$ $e_g$ complex with the $d_{x^2-y^2}$ orbital sitting below the $d_{3z^2-r^2}$ and an electronic structure highly unusual compared to the conventional cuprates. We construct a two-orbital Hubbard model for the Cu $d^9$ state at hol…
The recent development of x-ray scattering techniques revealed the charge-excitation spectrum in high-$T_c$ cuprate superconductors. While the presence of a dispersive signal in the high-energy charge-excitation spectrum is well accepted in the electron-doped cuprates, its interpretation and universality are controversial. Since charge fluctuations are observed ubiquitously in cuprate superconductors, the understanding of its origin is a pivotal issue. Here, we employ the layered $t$-$J$ model with the long-range Coulomb interaction and show that an acoustic-like plasmon mode with a gap at in-…
We review various isotope effects in the high-T_c cuprate superconductors to assess the role of the electron-phonon interaction in the basic physics of these materials. Of particular interest are the unconventional isotope effects on the supercarrier mass, on the charge-stripe formation temperature, on the pseudogap formation temperature, on the EPR linewidth, on the spin-glass freezing temperature, and on the antiferromagnetic ordering temperature. The observed unconventional isotope effects strongly suggest that lattice vibrations play an important role in the microscopic pairing mechanism o…
We present an explanation of the unusual peak/dip/hump features observed in photoemission experiments on Bi2212 at $T \ll T_c$. We argue that these features arise from the interaction of the fermionic quasi-particles with overdamped spin fluctuations. We show that the strong spin-fermion interaction combined with the feedback effect on the spin damping due to superconductivity yields a Fermi-liquid form of the fermionic spectral function for $ω< 2 Δ$ where $Δ$ is the maximum value of the superconducting gap, and a non-Fermi-liquid form for $ω> 2 Δ$. In the Fermi-liquid regime, the spectral fun…
We report a transport study of nonequilibrium quasiparticles in a high-Tc cuprate superconductor using the transient grating technique. Low-intensity laser excitation (at photon energy 1.5 eV) was used to introduce a spatially periodic density of quasiparticles into a high-quality untwinned single crystal of YBa2Cu3O6.5. Probing the evolution of the initial density through space and time yielded the quasiparticle diffusion coefficient, and both inelastic and elastic scattering rates. The technique reported here is potentially applicable to precision measurement of quasiparticle dynamics, not o…
A Gutzwiller-type variational wave function is proposed for the neutron resonance mode in the cuprate superconductors. An efficient re-weighting technique is devised to perform variational Monte Carlo simulation on the proposed wave function which is composed of linearly superposed Gutzwiller projected Slater determinants. The calculation, which involves no free parameter, predicts qualitatively correct behavior for both the energy and the spectral weight of the resonance mode as functions of doping.
The Josephson coupling between optimally cuprate superconductors separated by a spacer with a finite energy cooperon excitation which contributes to the Josephson coupling strength, is examined. For an underdoped cuprate barrier in its normal state, the YRZ model gives a good description of the temperature dependent enhanced Josephson coupling. A detailed examination of origin of the enhancement shows a significant contribution from the cooperon excitation which is comparable to that from nodal quasiparticles.
An electron-phonon interaction arising from the modulation of the superexchange interaction by phonons is studied within the theoretical framework of Kondo lattices. It is relevant in strongly correlated electron liquids in cuprate oxide superconductors, which lie in the vicinity of the Mott-Hubbard metal-insulator transition. It is enhanced by antiferromagnetic and superconducting fluctuations, which are developed mainly because of the superexchange interaction. When the enhancement of the electron-phonon interaction is large enough, it can explain the softening of phonons and kinks in the qu…
We present a minimal model for cuprate superconductors. At the unrestricted mean-field level, the model produces homogeneous superconductivity at large doping, striped superconductivity in the underdoped regime and various antiferromagnetic phases at low doping and for high temperatures. On the underdoped side, the superconductor is intrinsically inhomogeneous and global phase coherence is achieved through Josephson-like coupling of the superconducting stripes. The model is applied to calculate experimentally measurable ARPES spectra.
We argue that recently measured downward dispersion of the neutron resonance peak in cuprate superconductors is naturally explained if the resonance is viewed as a spin-1 collective mode in a d-wave superconductor. The reduction of the resonant frequency away from the antiferromagnetic wave vector is a direct consequence of the momentum dependence of the d-wave superconducting gap. When the magnetic correlation length becomes large, the dispersion should become magnon-like, i.e., curve upwards from (pi,pi).
The tunneling spectra of the electron-doped cuprate Pr_2-xCe_xCuO4 as a function of doping and temperature is reported. We find that the superconducting gap, delta, shows a BCS-like temperature dependence even for extremely low carrier concentrations (studied here for the first time). Moreover, delta follows the doping dependence of Tc, in strong contrast with tunneling studies of hole-doped cuprates. From our results we conclude that there is a single superconducting energy scale in the electron-doped cuprates.
Through variational Monte Carlo calculation on Gutzwiller projected wave functions, we study the quasiparticle(qp) weight for adding and removing an electron from a high temperature superconductor. We find the qp weight is particle-hole symmetric at sufficiently low energy. We propose to use the tunneling asymmetry as a tool to study the mechanism of electron incoherence in high temperature superconductors.
Neutron scattering experiments have played a crucial role in characterizing the spin and charge correlations in copper-oxide superconductors. While the data are often interpreted with respect to specific theories of the cuprates, an attempt is made here to distinguish those facts that can be extracted empirically, and the connections that can be made with minimal assumptions.
We present a theoretical framework for understanding the behavior of the normal and superconducting states of overdoped cuprate high temperature superconductors in the vicinity of the doping-tuned quantum superconductor-to-metal transition. The key ingredients on which we focus are d-wave pairing, a flat antinodal dispersion, and disorder. Even for homogeneous disorder, these lead to effectively granular superconducting correlations and a superconducting transition temperature determined in large part by the superfluid stiffness rather than the pairing scale.
We propose that an extension of the exciton concept to doped Mott insulators offers a fruitful insight into challenging issues of the copper oxide superconductors. In our extension, new fermionic excitations called cofermions emerge in conjunction to generalized excitons. The cofermions hybridize with conventional quasiparticles. Then a hybridization gap opens, and is identified as the pseudogap observed in the underdoped cuprates. The resultant Fermi-surface reconstruction naturally explains a number of unusual properties of the underdoped cuprates, such as the Fermi arc and/or pocket formati…
We calculate the Nernst signal in disordered conductors with the chemical potential near the mobility edge. The Nernst effect originates from interference of itinerant and localised-carrier contributions to the thermomagnetic transport. It reveals a strong temperature and magnetic field dependence, which describes quantitatively the anomalous Nernst signal in high-Tc cuprates.
Impurity nuclear spin relaxation is studied theoretically. A single impurity generates a bound state localized around the impurity atom in unconventional superconductors. With increasing impurity potential, the relaxation rate $T_1^{-1}$ is reduced by the impurity potential. However, it has a peak at low temperatures due to the impurity bound state. The peak disappears at non-impurity sites. The impurity site NMR measurement detecting a local electronic structure just on the impurity atom is very useful for identifying the unconventional pairing states.
Transport properties of high transition temperature (high-Tc) superconductors have been shown to have two distinct relaxation rates. We argue that this apparent inconsistence can be resolved with an effective carrier density n linear in temperature T. Experimental evidences both for and against this explanation are analyzed and we conclude that this offers a simple yet promising scenario. Above the pseudogap temperature T* the normal state of high-Tc cuprates is close to a Fermi liquid. It however assumes non-Fermi- liquid behaviors below T*.
We introduce a minimal model to describe the charge degree of freedom in cuprates with the on-site Hilbert space reduced to only the three valence states CuO$_4^{7-,6-,5-}$ (nominally Cu$^{1+,2+,3+}$) and make use of the S=1 pseudospin formalism. The formalism constitutes a powerful method to study complex phenomena in interacting quantum systems characterized by the coexistence and competition of various ordered states. Overall, such a framework provides a simple and systematic methodology to predict and discover new kinds of orders. In particular, the pseudospin formalism provides the most e…
We present a review of the vortex-Nernst effect in the 3 cuprate families La_{2-x}Sr_xCuO_4, Bi_2Sr_2CaCu_2O_8, and YBa_2Cu_3O_{y}, and discuss the scenario that the superconducting transition in the hole-doped cuprates corresponds to the destruction of long-range phase coherence rather than the vanishing of the order-parameter amplitude.
Normal state orbital diamagnetism of charged bosons quantitatively accounts for recent high-resolution magnetometery results near and above the resistive critical temperature Tc of superconducting cuprates. Our parameter-free descriptions of normal state diamagnetism, Tc, upper critical fields and specific heat anomalies unambiguously support the 3D Bose-Einstein condensation at Tc of preformed real-space pairs with zero off-diagonal order parameter above Tc, at variance with phase fluctuation (or vortex) scenarios of the "normal" state of cuprates.
The electronic structure of cuprate superconductors is studied within the kinetic energy driven superconducting mechanism in the presence of the out-of-plane impurities. With increasing the impurity concentration, although both superconducting coherence peaks around nodal and antinodal regions are suppressed, the position of the leading-edge mid-point of the electron spectrum around the nodal region remains at the same position, while it is shifted towards higher binding energies around the antinodal region, this leads to a strong deviation from the monotonic d-wave superconducting gap in the …
We describe a reversible, spatially-controlled doping method for cuprate films. The technique has been used to create superconductor-antiferromagnetic insulator-superconductor (S-AFI-S) junctions and optimally doped superconductor-underdoped superconductor-optimally doped superconductor (OS-US-OS) cuprate structures. We demonstrate how the S-AFI-S structure can be employed to reliably measure the transport properties of the antiferromagnetic insulator region at cryogenic temperatures using the superconductors as seamless electrical leads. We also discuss applied and fundamental issues which ma…
A d-wave superconductor, its phase coherence progressively destroyed by unbinding of vortex-antivortex pairs, suffers an instability related to chiral symmetry breaking in two-flavor QED$_3$. The chiral manifold exhibits large degeneracy spanned by physical states acting as inherent ``competitors'' of d-wave superconductivity. Two of these states are associated with antiferromagnetic insulator and ``stripe'' phases, known to be stable in the pseudogap regime of cuprates near half-filling. The theory also predicts additional, yet unobserved state: a d+ip phase-incoherent superconductor.
Charge and spin stripe order is a type of electronic crystal observed in certain layered cuprates associated with high-temperature superconductivity. Quantum-disordered stripes could be relevant for understanding the superconductivity. Here I discuss recent experimental characterizations of the stripe-ordered state in La(1.875)Ba(0.125)CuO(4), and compare them with properties of superconducting compositions.
A generic theory of the quasi-particle superconducting gap in underdoped cuprates is derived in the strong coupling limit, and found to describe extremely well the experimental "second gap" in \textit{absolute scale}. In drastic contrast to the standard theories of Bogoliubov quasi-particle excitations, the quasi-particle gap is shown to originate from anomalous kinetic process, completely unrelated to the pairing strength. Furthermore, the $k$-dependence of the gap deviates significantly from the pure $d_{x^2-y^2}$-wave of the order parameter. Our study reveals a new paradigm for the nature o…
Coexistence of antiferromagnetism and d-wave superconductivity within a CuO_2 plane was recently observed in a wide doping region for multilayer high-temperature cuprate superconductors. We find that the experimental phase diagram is well reproduced in the slave-boson mean-field scheme of the two-dimensional t-J model by including antiferromagnetic order. We argue that weak three dimensionality coming from a multilayer structure is sufficient to stabilize antiferromagnetic order and its coexistence with superconductivity.
We calculate scattering interference patterns for various electronic states proposed for the pseudogap regime of the cuprate superconductors. The scattering interference models all produce patterns whose wavelength changes as a function of energy, in contradiction to the energy-independent wavelength seen by scanning tunneling microscopy (STM) experiments in the pseudogap state. This suggests that the patterns seen in STM local density of states measurements are not due to scattering interference, but are rather the result of some form of ordering.
This paper summarizes experimental results presented at the international conference honoring Prof. C.N. Yang's 80th birthday. I show seven examples that illustrate how one can use angle-resolved photoemission spectroscopy to gain insights into the many-body physics responsible for the rich phase diagram of cuprate superconductors. I hope to give the reader a snapshot of the evolution of this experimental technique from a tool to study chemical bonds and band structure to an essential many-body spectroscopy for one of the most important physics problems of our time.
High Tc 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 (RIXS) to observe the presence of acoustic plasmons in two families of hole-doped cuprate superconductors [La2-xSrxCuO4 (LSCO) and Bi2Sr1.6La0.4CuO6+d (Bi2201)], crucially completing t…
We study the emergence of a magnetic resonance in the superconducting state of the electron-doped cuprate superconductors. We show that the recently observed resonance peak in the electron-doped superconductor Pr$_{0.88}$LaCe$_{0.12}$CuO$_{4-δ}$ is consistent with an overdamped spin exciton located near the particle-hole continuum. We present predictions for the magnetic-field dependence of the resonance mode as well as its temperature evolution in those parts of the phase diagram where $d_{x^2-y^2}$-wave superconductivity may coexist with an antiferromagnetic spin-density wave.
Following the identification of the pairing state, the major challenge in understanding the cuprate superconductors has been determining the evolution with doping and temperature of their anomalous normal state behavior. Key to this understanding is the experimentally determined magnetic phase diagram for the cuprates, which provides information on the protected magnetic properties of the normal state, generic behavior that is reliably the same one system to the next, regardless of details. I discuss the constraints this places on candidate quantum protectorates, and the status of microscopic …
