Pseudogap Region Research Articles

Pairing and superconductivity from weak to strong coupling in the attractive Hubbard model

The finite-temperature phase diagram of the attractive Hubbard model is studied by means of the dynamical mean-field theory. We first consider the normal phase of the model by explicitly frustrating the superconducting ordering. In this case, we obtain a first-order pairing transition between a metallic phase and a paired phase formed by strongly coupled incoherent pairs. The transition line ends in a finite temperature critical point, but a crossover between two qualitatively different solutions still occurs at higher temperature. Comparing the superconducting- and the normal-phase solutions, we find that the superconducting instability always occurs before the pairing transition in the normal phase, i.e. Tc > Tpairing. Nevertheless, the high-temperature phase diagram at T > Tc is still characterized by a crossover from a metallic phase to a preformed pair phase. We characterize this crossover by computing different observables that can be used to identify the pseudogap region, like the spin susceptibility, the specific heat and the single-particle spectral function.

Evidence for Vortices in the Pseudogap Region ofY1−xPrxBa2Cu3O7from Angular Magnetoresistivity Measurements

In-plane angular magnetoresistivity Deltarho(anis)(ab) measurements were made on Y(1-x)Pr(x)Ba(2)Cu(3)O(7-delta) single crystals in the pseudogap region. For x>/=0.2 single crystals, Deltarho(anis)(ab)(theta) displays a deviation from the typical quasiparticle contribution (proportional, sin((2)theta) for temperatures smaller than a certain value T(phi) in the pseudogap region. This deviation is consistent with a flux-flow type contribution to angular magnetoresistivity, indicating the presence of vortexlike excitations above the zero-field critical temperature in the pseudogap region.

Absence of thed-density-wave state from the two-dimensional Hubbard model

Using the Dynamical Cluster Approximation (DCA) we calculate the alternating circulating-current susceptibility and investigate the transition to the d-density wave (DDW) order in the two-dimensional Hubbard model. The 2 x 2 cluster used in the DCA calculation is the smallest that can capture d-wave order; therefore, due to the mean-field character of our calculation, we expect to overestimate d-wave transition temperatures. Despite this, we found no transition to the DDW state. In the pseudogap region the DDW susceptibility is enhanced, as predicted by the slave boson SU(2) theory, but it still is much smaller than the d-wave pairing susceptibility.

Normal state properties of quasi-2D superconductors due to spin fluctuations

Spin fluctuation effects are studied in quasi-2D superconductors, such as high critical temperature superconductors and organic 2D BEDT-TTF superconductors (with T c smaller than 13 K). We discuss the important similarities and differences between these two systems. We show that, due to nesting properties of the Fermi surface, the magnetic and the transport properties are different from the behaviours we should observe in usual metal, because of strong magnetic fluctuation effect. We distinguish different regions in the normal state with different dependences as a function of temperature for several properties, such as the resistivity, NMR relaxation rate and spin susceptibility. We show that the pseudogap region is strongly related to the existence of a pseudogap in the density of states at the Fermi level.

Isotope, pressure, and doping effects on the pseudogap in the LSCO-type compounds studied by neutron spectroscopy

Isotope, pressure, and doping effects on the pseudogap temperature T ∗ were investigated by neutron spectroscopic experiments of the relaxation rate of crystal-field excitations in La 1.96− x Sr x Ho 0.04CuO 4 ( x=0.11, 0.15, 0.20). With increasing doping, T ∗ is found to decrease from 80 K ( x=0.11) to 60 K ( x=0.15) and 50 K ( x=0.20). The application of hydrostatic pressure ( p=0.8 GPa) results in a downward shift of T ∗ by 5 K for the optimally doped compound. Upon oxygen isotope substitution ( 18O vs 16O), T ∗ is shifted upwards by 20, 10, and 5 K for x=0.11, x=0.15, and x=0.20, respectively. The large isotope and pressure effects indicate that lattice fluctuations are involved in the pseudogap phenomena. Our relaxation data are compatible with the unusual temperature dependence of the gap function in the pseudogap region, namely a breakup of the Fermi surface into disconnected arcs.

Magnetotransport properties of Y 1− xPr xBa 2Cu 3O 7− δ single crystals

Magnetotransport measurements of Y 1− x Pr x Ba 2Cu 3O 7− δ ( x=0, 0.13, 0.2, 0.32, and 0.42) single crystals reveal two regimes in the pseudogap region for the x⩾0.20 samples, with a crossover at a temperature T cr( x). For T c< T< T cr, there is a vortex-like response in magnetoresistivity. For T> T cr, the results are consistent with the picture in which the origin of the pseudogap is the nearly antiferromagnetic Fermi liquid renormalized by strong superconducting fluctuations.

Internal structure of preformed Cooper pairs

The question of the internal structure of preformed pairs in the pseudogap region of HT c superconductors is addressed. We calculate the propagator X for the operator Q ll ′ †=c l↑ †c l ′↓ † by using a Bethe–Salpeter approach. The “pair structure function” g P ( P , ρ) derived from X, represents the internal structure of a pair with center of mass momentum P and internal distance between the partners ρ . We calculate g P both for a point-like potential and s-wave symmetry of the order parameter and for a separable potential and d-wave symmetry of the order parameter.

Superconductivity in the pseudogap state in the hot-spot model: Ginzburg-Landau expansion

Peculiarities of the superconducting state (s and d pairing) are considered in the model of the pseudogap state induced by short-range order fluctuations of the dielectric (AFM (SDW) or CDW) type, which is based on the model of the Fermi surface with “hot spots.” A microscopic derivation of the Ginzburg-Landau expansion is given with allowance for all Feynman diagrams in perturbation theory in the electron interaction with short-range order fluctuations responsible for strong scattering in the vicinity of hot spots. The superconducting transition temperature is determined as a function of the effective pseudogap width and the correlation length of short-range order fluctuations. Similar dependences are derived for the main parameters of a superconductor in the vicinity of the superconducting transition temperature. It is shown, in particular, that the specific heat jump at the transition point is considerably suppressed upon a transition to the pseudogap region on the phase diagram.

The Pseudogap and the Superconducting Order Parameter in Inhomogeneous Bi2Sr2CaCu2O8+

Recent experiments on Bi2Sr2CaCu2O8+δ (Bi2212) have provided compelling evidence that the samples are inhomogeneous on a nanoscale, with spatially separated superconducting gap (SG) and nonsuperconducting, pseudogap (PG) regions that arise from hole–hole and particle–hole pairings, respectively. We compare and contrast the nonphase sensitive experiments that cannot distinguish these orderings from the phase-sensitive experiments that can. Although the wave vector dependence of the pseudogap is highly anisotropic, we conclude that in Bi2212, the c-axis quasiparticle tunneling is incoherent and that the c-axis supercurrent arises solely from a rather isotropic s-wave superconducting order parameter (OP) for T < Tc.

On the (anisotropic) uniform metallic ground states of fermions interacting through arbitrary two-body potentials in d dimensions

We demonstrate that the skeleton of the Fermi surface pertaining to a uniform metallic ground state (corresponding to fermions with spin index σ) is determined by the Hartree–Fock contribution to the dynamic self-energy . That is to say, in order for , it is necessary (but for anisotropic ground states in general not sufficient) that the following equation be satisfied: where stands for the underlying non-interacting energy dispersion and ϵF for the exact interacting Fermi energy. The Fermi surface consists of the set of k points which in addition to satisfying the above equation fulfil where1 The set of k points which satisfy the first of the above two equations but fail to satisfy the second constitute the pseudogap region of the putative Fermi surface of the interacting system. We consider the behaviour of the ground-state momentum distribution function for k in the vicinity of and show that, whereas for the uniform metallic ground states of the conventional single-band Hubbard Hamiltonian, described in terms of an on-site interaction, and (here and denote vectors infinitesimally close to , located respectively inside and outside the underlying Fermi sea), for interactions of non-zero range these inequalities can be violated (without thereby contravening the stability condition ). This aspect is borne out by the pertaining to the normal states of for instance liquid 3He (corresponding to a range of applied pressure) as determined by means of quantum Monte Carlo calculations. We further demonstrate that for Fermi-liquid metallic states of fermions interacting through interaction potentials of non-zero range (e.g. the Coulomb potential), the zero-temperature limit of does not need to be equal to ½ for ; this in strict contrast with the uniform Fermi-liquid metallic states of the single-band Hubbard Hamiltonian (if such states at all exist). This aspect should be taken into account while analysing the deduced from the angle-resolved photoemission data concerning real materials. We discuss, in the light of the findings of the present work, the growing experimental evidence with regard to the ‘frustration’ of the kinetic energy of the charge carriers in the normal states of the copper-oxide-based high-temperature superconducting compounds.

Thermodynamics and phase diagram of high temperature superconductors.

Thermodynamic quantities are derived for superconducting and pseudogap regimes by taking into account both amplitude and phase fluctuations of the pairing field. In the normal (pseudogap) state of the underdoped cuprates, two domains have to be distinguished: near the superconducting region, phase correlations are important up to temperature T(phi). Above T(phi), the pseudogap region is determined only by amplitudes, and phases are uncorrelated. Our calculations show excellent quantitative agreement with specific heat and magnetic susceptibility experiments on cuprates. We find that the mean field temperature T0 has a similar doping dependence as the pseudogap temperature T(*), whereas the pseudogap energy scale is given by the average amplitude above T(c).

Quantum Resistive Behaviors in Vortex Liquid Regimes at Finite Temperatures

Motivated by a {\it mean field-like} resistive behavior in magnetic fields commonly seen in various superconducting (SC) cuprates and organics with strong fluctuation, {\it quantum} SC fluctuation effects on resistive behaviors are reexamined by putting emphasis on their roles in the so-called {\it thermal} vortex liquid regime. By incorporating the quantum fluctuation and a vortex pinning effect in the GL fluctuation theory, it is found that the resistivity curve shows not a fan-shaped broadening but a sharp drop at a 3d vortex-glass transition point far below an apparent upper critical field H_{c2}^*(T) as a result of a quantm fluctuation enhanced by an adequately small condensation energy or by a strong field. Fittings to data of cuprate and organic superconductors are performed by including effects of SC pseudogap region. It is argued on the cuprate materials that, irrespective of the presence of fluctuations of competing non-SC orders, the in-plane coherence length of hole-doped cuprates decreases on approaching the underdoped limit and that the condensation energy density to be measured from the heat capacity data is maximum near the optimal doping. The case of disordered quasi 2d s-wave films showing the field-tuned superconductor-insulator transition (FSIT) behavior is also studied for comparison, and an agreement with available data is found.

Observations of electronic inhomogeneity in heavily Pb-dopedBi2Sr2CaCu2Oysingle crystals by scanning tunneling microscopy

Cleaved $\mathrm{ab}$ surfaces of heavily Pb-doped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{y}$ single crystals, including phase separation into Pb-poor $\ensuremath{\alpha}$ and Pb-rich $\ensuremath{\beta}$ phases, were probed by cryogenic scanning tunneling microscopy/spectroscopy at 4.3 K. We could resolve individual Pb atoms substituted into Bi sites, which tend to be concentrated on the crest of modulation in the $\ensuremath{\alpha}$ phase, but are almost randomly dispersed throughout the $\ensuremath{\beta}$ phase. The scanning tunneling spectroscopy results revealed a considerably wide range of gap values $\ensuremath{\Delta},$ originating from the presence of both superconducting and pseudogap regions on a nanometer scale. Furthermore, we found that oxygen annealing substantially increases gap inhomogeneity. This strongly suggests that disorder of excess oxygen, possibly coupled with structural deformation of ${\mathrm{CuO}}_{2}$ sheets, destroys superconducting coherence, resulting in the appearance of a pseudogap.

Symmetry considerations for detection of time-reversal breaking phases in cuprates by x-ray diffraction and absorption

Time-reversal and inversion breaking in the pseudogap region of the cuprate compounds have been proposed and detected by means of ARPES in the compound Bi-2212. Given the implication of the effect in the physics of the cuprate superconductors, it is important to check the conclusions through quite independent experimental techniques. We show how time-reversal and inversion breaking may be revealed in the Cuprates through resonant x-ray scattering and through non-reciprocal or magnetochiral dichroism.

Theory of Nernst coefficient in high-Tc cuprates: the role of vertex corrections

We study the the Nernst coefficient (ν) in hole-doped as well as electron-doped high-Tc cuprates, which takes a much enhanced value compared with conventional metals. Especially, ν in hole-doped cuprates increases drastically below the pseudo-gap temperature, which attracts great attention in that it reflects the fundamental feature of the electronic state in the pseudo-gap region. In this article, we study these transport phenomena in terms of the fluctuation-exchange+T-matrix approximation. We focus on the role of the vertex corrections (VCs) which are necessary to keep the conservation laws, and find that both ν and Δρ/ρ are strongly enhanced by the VCs due to the antiferromagnetic (AF) and the superconducting (SC) fluctuations. In conclusion, the pseudo-gap region in high-Tc cuprates is well described by the AF and SC fluctuation scenario.

Superconducting condensation energy in the pseudogap region of La2−xSrxCuO4

The superconducting condensation energy at T=0, U0, was examined from the measurements of the electronic specific heat Cel on La2−xSrxCuO4. We reconfirmed that U0 is markedly reduced in the pseudogap regime (x≲0.2). The doping-level (p) dependence of U0 as well as Tc can be explained in the pseudogap regime by introducing an effective energy gap Δeff=βpΔ0 (β=4.5) instead of the maximum gap Δ0 at T≪Tc.

Symmetry considerations for the detection of second-harmonic generation in cuprates in the pseudogap phase

A proposal to test the proposed time-reversal and inversion breaking phase in the Pseudogap region of the Cuprate compounds through the variation of Second-harmonic generation intensity with temperature and polarization and angle of incidence is presented.

A Hidden Order in the Cuprate Superconductors: The d-Density-Wave Phase

We study the electronic structure near impurities in the d-density-wave (DDW) state, a possible candidate phase for the pseudo-gap region of the high-temperature superconductors. We show that the density of states near a nonmagnetic impurity in the DDW state is qualitatively different from that in a superconductor with dx2-y2 symmetry. Thus the electronic structure near impuritiescan provide insight into the nature of the two phases recently observed by scanning tunneling microscopy experiments in the superconducting state of underdoped Bi-2212 compounds.

Nernst coefficient and magnetoresistance in high-T(c) superconductors: the role of superconducting fluctuations.

In high-T(c) cuprates, the Nernst coefficient (nu) as well as the magnetoresistance (Deltarho/rho) increases drastically below the pseudogap temperature, T(*), which attracts much attention as a key phenomenon in the pseudogap region. We study these transport phenomena in terms of the fluctuation-exchange+T-matrix approximation. In this present theory, the d-wave superconducting (SC) fluctuations, which are mediated by antiferromagnetic (AF) correlations, become dominant below T(*). We especially investigate the vertex corrections both for the charge current and the heat one to keep the conservation laws. As a result, the mysterious behaviors of nu and Deltarho/rho are naturally explained as the reflection of the enhancement of the SC fluctuation, without assuming thermally excited vortices. The present result suggests that the pseudogap phenomena are well described in terms of the Fermi liquid with AF and SC fluctuations.

Fluctuation effects in underdoped cuprate superconductors under a magnetic field

Fluctuation effects in underdoped cuprates under high fields are examined by trying to fit theoretical results to resistivity and Nernst data in vortex states. The superconducting (SC) fluctuation in underdoped cuprates includes not only the ordinary thermal contribution but also a large amount of quantum dynamical contributions. Together with this, the presence of a SC pseudogap region T_0-T_{c0} increasing with underdoping is found to be the origin of the Nernst coefficient becoming anomalously smaller and the in-plane coherence length {\it apparently} increasing with underdoping.