Narrow Results

Experimental studies of the pairing state of cuprate superconductors reveal asymmetric behaviors of the hole-doped (p-type) and electron-doped (n-type) cuprates. The pairing symmetry, pseudogap phenomenon, low-energy spin excitations and the spatial homogeneity of the superconducting order parameter appear to be non-universal among the cuprates, which may be attributed to competing orders. We propose that the non-universal pseudogap and nano-scale variations in the quasiparticle spectra may be the result of a charge nematic (CN) phase stabilized by disorder in highly two-dimensional (2D) p-type cuprates. The CN phase is accompanied by gapped spin excitations and competes with superconductivity (SC). In contrast, gapless spin excitations may be responsible for the absence of pseudogap and the presence of excess sub-gap spectral weight in the momentum-independent quasiparticle spectra of n-type cuprates. The physical implications and further verifications for these conjectures are discussed.

We show by means of the theory of order parameter phase fluctuations that the temperature of the "closing" (or "opening") of the gap (and pseudogap) in the electron spectra of superconductors with anisotropic order parameter actually takes place within a finite temperature range. Every Fourier-component of the order parameter has its own critical temperature.

The incommensurate magnetic response observed in normal-state cuprate perovskites is interpreted based on the projection operator formalism and the t–J model of Cu-O planes. In agreement with experiment the calculated dispersion of maxima in the susceptibility has the shape of two parabolas with upward and downward branches which converge at the antiferromagnetic wave vector. The maxima are located at the momenta (½, ½ ± δ), (½ ± δ, ½) and at (½ ± δ, ½ ± δ), (½ ± δ, ½ ∓ δ) in the lower and upper parabolas, respectively. The upper parabola reflects the dispersion of magnetic excitations of the localized Cu spins, while the lower parabola arises due to a dip in the spin-excitation damping at the antiferromagnetic wave vector. For moderate doping this dip stems from the weakness of the interaction between the spin excitations and holes near the hot spots. The frequency dependence of the susceptibility is shown to depend strongly on the hole bandwidth and damping and varies from the shape observed in YBa₂Cu₃O_7-y to that inherent in La_2-xSr_xCuO₄.

We use path-integral Monte Carlo (PIMC) to study the effects of adding a long-range repulsive Coulomb interaction to the usual Van der Waals interaction between two atoms of a submonolayer quantum film such as helium on graphite or a pure two-dimensional superfluid. Such interactions frustrate or compete with the natural tendency of the system for phase separation namely to form a macroscopic liquid or solid phase. We find that as a function of the relative strength of the long-range repulsion, surface coverage and temperature, the system undergoes a series of transformations, including a triangular Wigner-like crystal of clusters, a charge stripe-ordered phase and a fluid phase. The goal of these studies is to understand the role of quantum fluctuations when such competing interactions appear together with formation of preexisting electron pairs as might be the case in cuprate superconductors.

Muon spin rotation (μ⁺SR) measurements conducted on crystalline YBa₂Cu₃O₇ are consistent with s-wave pairing, not d-wave, suggesting that the superconducting hole condensate resides in the BaO layers, not in the cuprate-planes. The specific heat and thermal conductivity data are explained by the superconducting BaO layers alone, unlike the failed interpretation based on CuO₂-plane superconductivity. The layer charges of the CuO₂ planes are almost -2 |e|, indicating that those planes are primarily carriers of electrons, not holes. The cuprate-planes are not the dominant hole-carriers of high-T_C superconductivity, as demonstrated by doped YBa₂RuO₆, which has no such CuO₂ lanes, yet superconducts at ~ 93 K. Moreover the trio of related compounds, YSr₂RuO₆ (doped with Cu on Ru sites), undoped GdSr₂Cu₂RuO₈, and undoped Gd_2-zCe_zSr₂Cu₂RuO₁₀ all start superconducting near 49 K in their SrO layers, not in the cuprate planes of the two compounds that have such planes, because those planes are either antiferromagnetic or weakly ferromagnetic and so do not superconduct. In PrBa₂Cu₃O₇, a Pr-on-Ba-site (Pr_Ba) defect kills the superconductivity, but Pr-on-Pr-site (Pr_Pr) does not. Both defects are approximately equidistant from the intervening cuprate plane, suggesting that the cuprate plane does not carry significant superconductivity. In GdBa₂Cu₃O₇, Gd-on-a-Gd-site (Gd_Gd) does not break Cooper pairs, but Gd-on-a-Ba-site (Gd_Ba) does, indicating that the superconductivity is in the BaO layers, and not in the cuprate-planes. In HgBa₂Ca_n-1Cu_nO_2n+2, the BaO layers, not the cuprate-planes, gain positive charge as T_C, pressure, and the number of layers n increase. The reason that theories based on holes in the cuprate-planes have done so poorly is that those planes were incorrectly identified as the source of high-temperature superconductivity on the basis of a single datum by Cava et al., that was first contradicted by Jorgensen et al., and then endorsed by Jorgensen alone on the basis of the Cava datum, not his own. This error is the main reason why cuprate-plane superconductivity, which probably does not exist, has been so widely accepted.

In this paper, we review the low energy electronic structure of the kinetic energy driven d-wave cuprate superconductors. We give a general description of the charge-spin separation fermion-spin theory, where the constrained electron is decoupled as the gauge invariant dressed holon and spin. In particular, we show that under the decoupling scheme, the charge-spin separation fermion-spin representation is a natural representation of the constrained electron defined in a restricted Hilbert space without double electron occupancy. Based on the charge-spin separation fermion-spin theory, we have developed the kinetic energy driven superconducting mechanism, where the superconducting state is controlled by both superconducting gap parameter and quasiparticle coherence. Within this kinetic energy driven superconductivity, we have discussed the low energy electronic structure of the single layer and bilayer cuprate superconductors in both superconducting and normal states, and qualitatively reproduced all main features of the angle-resolved photoemission spectroscopy measurements on the single layer and bilayer cuprate superconductors. We show that the superconducting state in cuprate superconductors is the conventional Bardeen-Cooper-Schrieffer like with the d-wave symmetry, so that the basic Bardeen-Cooper-Schrieffer formalism with the d-wave gap function is still valid in discussions of the low energy electronic structure of cuprate superconductors, although the pairing mechanism is driven by the kinetic energy by exchanging spin excitations. We also show that the well-pronounced peak-dip-hump structure of the bilayer cuprate superconductors in the superconducting state and double-peak structure in the normal state are mainly caused by the bilayer splitting.

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 a 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.

New boundary condition for the order parameter in the Ginzburg-Landau theory is applied to the case of CuO₂ planes which are the main structural elements responsible for superconductivity in high-T_c superconductors. It was found that the order parameter in these superconductors is significantly depressed in the CuO₂ planes. As a result, this boundary condition to the GL equations is found to limit the critical temperature of high-T_c superconductors. Thus, in order to increase T_c of cuprate superconductors, the number of CuO₂ planes that are within a short distance of each other in unit cell or insulating properties of the layers located in the vicinity to the CuO₂ planes should be increased.

With particular reference to the role of the renormalization group (RG) approach and Ward identities (WI's), we start by recalling some old features of the one-dimensional Luttinger liquid as the prototype of non-Fermi-liquid behavior. Its dimensional crossover to the Landau normal Fermi liquid implies that a non-Fermi liquid, as, e.g., the normal phase of the cuprate high temperature superconductors, can be maintained in d>1 only in the presence of a sufficiently singular effective interaction among the charge carriers. This is the case when, nearby an instability, the interaction is mediated by critical fluctuations. We are then led to introduce the specific case of superconductivity in cuprates as an example of avoided quantum criticality. We will disentangle the fluctuations which act as mediators of singular electron–electron interaction, enlightening the possible order competing with superconductivity and a mechanism for the non-Fermi-liquid behavior of the metallic phase.

This paper is not meant to be a comprehensive review. Many important contributions will not be considered. We will also avoid using extensive technicalities and making full calculations for which we refer to the original papers and to the many good available reviews. We will here only follow one line of reasoning which guided our research activity in this field.

High-T_c 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 around the CuO₂ planes. This yields a closed formula for T_c involving the layer width, the Debye frequency, the pairing energy and the in-plane penetration depth. The new formula has no free parameters and reasonably reproduces empirical values of superconducting T_cs for 11 different layered superconductors over a wide doping regime including YBCO itself as well as other compounds like LSCO, BSCCO and TBCCO. In agreement with the London formalism, the formula also yields a fair description of the T_c dependence of the lower critical magnetic field in highly underdoped YBCO.

Superconductivity in cuprate superconductors occurs upon charge-carrier doping Mott insulators, where a central question is what mechanism causes the loss of electrical resistance below the superconducting (SC) transition temperature? In this paper, we attempt to summarize the basic idea of the kinetic-energy-driven SC mechanism in the description of superconductivity in cuprate superconductors. The mechanism of the kinetic-energy-driven superconductivity is purely electronic without phonons, where the charge-carrier pairing interaction in the particle–particle channel arises directly from the kinetic energy by the exchange of spin excitations in the higher powers of the doping concentration. This kinetic-energy-driven d-wave SC-state is controlled by both the SC gap and quasiparticle coherence, which leads to that the maximal SC transition temperature occurs around the optimal doping, and then decreases in both the underdoped and overdoped regimes. In particular, the same charge-carrier interaction mediated by spin excitations that induces the SC-state in the particle–particle channel also generates the normal-state pseudogap state in the particle–hole channel. The normal-state pseudogap crossover temperature is much larger than the SC transition temperature in the underdoped and optimally doped regimes, and then monotonically decreases upon the increase of doping, eventually disappearing together with superconductivity at the end of the SC dome. This kinetic-energy-driven SC mechanism also indicates that the strong electron correlation favors superconductivity, since the main ingredient is identified into a charge-carrier pairing mechanism not from the external degree of freedom such as the phonon but rather solely from the internal spin degree of freedom of the electron. The typical properties of cuprate superconductors discussed within the framework of the kinetic-energy-driven SC mechanism are also reviewed.

The sharp low energy kink (LEK) in quasiparticle (qp) spectra well below the superconducting energy gap observed in the angle-resolved photo-emission spectroscopy (ARPES) of the Bi-cuprates may be understood in terms of the forward scattering impurities located off the Cu–O planes. The relevance of the idea has been established by comparing the calculated normal self-energy from the off-plane impurity effects and the extracted one from the self-energy analysis of ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Sr}}}_2{\mathrm{\text{CaCu}}}_2{\mathrm{\text{O}}}_{8+\delta }$ (Bi2212) ARPES data in Hong et al. [Phys. Rev. Lett.113, 057001 (2014)]. In addition to the explanation of the LEK, this is a necessary step to analyze ARPES data, to reveal the spectrum of fluctuations promoting superconductivity. We also present the extracted anomalous self-energy from the self-energy analysis, which is its first experimental determination as far as we are aware of. The extracted anomalous self-energy and its implications are discussed in comparison with the calculated impurity self-energy term.

The dynamics of quasi-particle (QP) excitations with different symmetry is investigated in the superconducting (SC) and pseudogap (PG) states of the high-temperature superconductor ${\mathrm{\text{Bi}}}_2{\mathrm{\text{Sr}}}_2{\mathrm{\text{CaCu}}}_2{\mathrm{\text{O}}}_{8+d}$ (Bi2212) using a polarization-sensitive optical pump-probe measurement. The observation of distinct anisotropies for SC excitations and for PG excitations by the probe beam polarization and absence of any dependence on the pump beam polarization evidence the existence of a spontaneous spatial symmetry breaking in the PG state.

The recently discovered charge order is an intrinsic and universal property of cuprate superconductors, however, its microscopic origin remains debated. Here we review briefly the theoretical work about the nature of charge order in cuprate superconductors. In particular, we show that the electron self-energy obliterates the electron Fermi surface around the antinodal region, leaving behind disconnected Fermi arcs located around the nodal region. The charge-order state on the other hand is driven by the Fermi-arc instability, with a characteristic wavevector corresponding to the hot spots of the Fermi arcs rather than the antinodal nesting vector. Since the pseudogap emanates from the electron self-energy, the Fermi arc, charge order, and pseudogap in cuprate superconductors are intimately related each other.

The normal and pairing self-energies are the microscopic quantities which reflect and characterize the underlying interaction in superconductors. The momentum and frequency dependence of the self-energies, therefore, provides the experimental criteria which can single out the long sought-after pairing interaction among many proposed ideas. This line of research to pin down the pairing interaction for the cuprate superconductors has been carried out with some success by analyzing the momentum distribution curves (MDCs) of laser angle-resolved photo-emission spectroscopy (ARPES) data. Some progress and results are presented and compared with theoretical calculations based on leading proposals. Comments are made on the proposed scenarios from the comparisons.

Considering Born–Mayer–Huggins potential as a most suitable potential to study the dynamical properties of high-temperature superconductors (HTS), the many-body quantum dynamics to obtain phonon Green’s functions has been developed via a Hamiltonian that incorporates the contributions of harmonic electron and phonon fields, phonon field anharmonicities, defects and electron–phonon interactions without considering BCS structure. This enables one to develop the quasiparticle renormalized frequency dispersion in the representative high-temperature cuprate superconductor YBa₂Cu₃O${}_{7-\delta }$. The superconducting gap shows substantial changes with increased doping. The in-plane gap study revealed a $v$-shape gap with a nodal point along $k_x=\pm k_y$ direction for optimum doping ($\delta$ = 0.16) and the nodal point vanished in underdoped and overdoped regimes. The d${}_{x^2-y^2}$ pairing symmetry is observed at optimum doping with the presence of s or d${}_{xy}$ components ($<$ 3%) in underdoped and overdoped regimes.

To understand the interplay of d-wave superconductivity and antiferromagnetism in the cuprates, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. Free energy of the homogeneous (coexisting superconducting and antiferromagnetic) state calculated as a function of the band filling shows a region of phase separation. The phase separation caused by the intersite attractive force leads to novel insights into salient features of the pseudogap phase diagram. In particular, the upper crossover curve can be identified with the phase separation boundary. At zero temperature, the boundary constitutes a critical point. The inhomogeneity observed in the underdoped cuprates is a consequence of incomplete phase separation. The disorder (inhomogeneity) brings about the disparity between the high pseudogap temperature and the low bulk superconducting transition temperature.

We propose a charge crystal model that captures all the essential physics of the high temperature superconductivity (HTS) in the long wavelength limit. Based on the recent transport and the far-infrared (far-IR) experiments, we argue that the three-dimensional (3D) ordering of the pinned two-dimensional (2D) square electronic lattice (EL) in each CuO₂ plane is the building block of HTS. Incorporating the physical picture derived from the neutron scattering experiments, we demonstrate that our model presents a coherent picture of the HTS. We suggest that the charge crystal model serves as a model for the microscopic theory and, hence, offers the key to the mechanism for the HTS.

To understand the interplay of d-wave superconductivity and antiferromagnetism, we consider a two-dimensional extended Hubbard model with nearest neighbor attractive interaction. The Hamiltonian is solved in the mean field approximation on a finite lattice. In the impurity-free case, the minimum energy solutions show phase separation as predicted previously based on free energy argument. The phase separation tendency implies that the system can be easily rendered inhomogeneous by a small external perturbation. Explicit solutions of a model including weak impurity potentials are indeed inhomogeneous in the spin-density-wave and d-wave pairing order parameters. Relevance of the results to the inhomogeneous cuprate superconductors is discussed.

Since the discovery of cuprate superconductors, the mechanism of high temperature superconductivity is still a mystery. Among the investigation tools, the electronic Raman scattering is a powerful one to probe electronic excitations in different regions of the Fermi surface of cuprate superconductors by a simple choice of the incident and scattered polarization vectors. Thus the symmetry of the superconducting Cooper pairs can be indicated. In this article we review our investigations of electronic Raman scattering in cuprate superconductors based on the t–J model within the kinetic energy driven superconductivity. The theory of electronic Raman response in cuprate superconductors is presented together with an overview of the charge-spin separation fermion-spin theory to handle the t–J model. Some theoretical results of electronic Raman response are presented in comparison with the experimental results. Special emphasize is given to the doping and temperature dependent of electronic Raman spectra.