Quasiparticles in a strongly correlated liquid with the fermion condensate: applications to high-temperature superconductors

A model of a strongly correlated electron liquid based on fermion condensation (FC) is extended to high-temperature superconductors. Within our model, the appearance of FC presents a boundary separating the region of a strongly interacting electron liquid from the region of a strongly correlated electron liquid. We study the superconductivity of a strongly correlated liquid and show that, under certain conditions, the superconductivity vanishes at temperatures T > T _c ≈ T _node, with the superconducting gap being smoothly transformed into a pseudogap. As a result, the pseudogap occupies only a part of the Fermi surface. The gapped area shrinks with increasing the temperature and vanishes at T = _T*. The single-particle excitation width is also studied. The quasiparticle dispersion in systems with FC can be represented by two straight lines, characterized by the effective masses and, intersecting near the binding energy that is on the order of the superconducting gap. It is argued that this strong change of the quasiparticle dispersion upon binding can be enhanced in underdoped samples because of strengthening the FC influence. The FC phase transition in the presence of the superconductivity is examined, and it is shown that this phase transition can be considered as driven by the kinetic energy.     

Pseudogap phenomena in ultracold atomic Fermi gases

The pairing and superfluid phenomena in a two-component ultracold atomic Fermi gas is an analogue of Cooper pairing and superconductivity in an electron system, in particular, the high Tc superconductors. Owing to the various tunable parameters that have been made accessible experimentally in recent years, atomic Fermi gases can be explored as a prototype or quantum sinmlator of superconductors. It is hoped that, utilizing such an analogy, the study of atomic Fermi gases may shed light to the mysteries of high Tc superconductivity. One obstacle to the ultimate understand- ing of high Tc superconductivity, from day one of its discovery, is the anomalous yet widespread pseudogap phenomena, for which a consensus is yet to be reached within the physics comnnmity, after over 27 years of intensive research efforts. In this article, we shall review the progress in the study of pseudogap phenomena in atomic Fermi gases in terms of both theoretical understanding and experimental observations. We show that there is strong, unambiguous evidence for the existence of a pseudogap in strongly interacting Fermi gases. In this context, we shall present a pairing fuctuation theory of the pseudogap physics and show that it is indeed a strong candidate theory for high Tc superconductivity.     

Pseudogap and symmetry of superconducting order parameter in cuprates

The phase diagram, nature of the normal state pseudogap, type of the Fermi surface, and behavior of the superconducting gap in various cuprates are discussed in terms of a correlated state with valence bonds. The variational correlated state, which is a band analogue of the Anderson (RVB) states, is constructed using local unitary transformations. Formation of valence bonds causes attraction between holes in the d-channel and corresponding superconductivity compatible with antiferromagnetic spin order. Our calculations indicate that there is a fairly wide range of doping with antiferromagnetic order in isolated CuO₂ planes. The shape of the Fermi surface and phase transition curve are sensitive to the value and sign of the hopping interaction t′ between diagonal neighboring sites. In underdoped samples, the dielectrization of various sections of the Fermi boundary, depending on the sign of t′, gives rise to a pseudogap detected in photoemission spectra for various quasimomentum directions. In particular, in bismuth-and yttrium-based ceramics (t′>0), the transition from the normal state of overdoped samples to the pseudogap state of underdoped samples corresponds to the onset of dielectrization on the Brillouin zone boundary near k=(0,π) and transition from “large” to “small” Fermi surfaces. The hypothesis about s-wave superconductivity of La-and Nd-based ceramics has been revised: a situation is predicted when, notwithstanding the d-wave symmetry of the superconducting order parameter, the excitation energy on the Fermi surface does not vanish at all points of the phase space owing to the dielectrization of the Fermi boundary at k _x=± k _y. The model with orthorhombic distortions and two peaks on the curve of T _c versus doping is discussed in connection with experimental data for the yttrium-based ceramic. Zh. éksp. Teor. Fiz. 115, 649–674 (February 1999)     

Zeeman and orbital limiting magnetic fields in cuprates: The pseudogap connection

In cuprates, in a view where pairing correlations set in at the pseudogap energy scale T* and acquire global coherence at a lower temperature T_c, the regionT _c⪯ T ⪯ T* is a vast fluctuation regime.T _c andT* vary differently with doping and the question remains about the doping trends of the relevant magnetic field scales: the field H_c2 bounding the superconducting response and the pseudogap closing field H_pg. In-plane thermal (Nernst) and our interlayer (tunneling) transport experiments in Bi₂Sr₂CaCu₂O_8+y report hugely different limiting magnetic fields. Here, based on pairing (and the uncertainty principle) combined with the definitions of the Zeeman energy and the magnetic length, we show that both fields convert to the same pseudogap scaleT* upon transformation as orbital and Zeeman critical fields, respectively. The region of superconducting coherence is confined to the ‘dome’ that coincides with the usual unique upper critical field H_c2 on the strongly overdoped side. We argue that the distinctly different orbital and the Zeeman limiting fields can co-exist owing to charge and spin degrees of freedom separated to different parts of the strongly anisotropic Fermi surface.     

Microscopic theory of a strongly correlated two-dimensional electron gas

The rearrangement of the Fermi surface in a diluted two-dimensional electron gas beyond the topological quantum critical point has been examined within an approach based on the Landau theory of Fermi liquid and a nonperturbative functional method. The possibility of a transition of the first order in the coupling constant at zero temperature between the states with a three-sheet Fermi surface and a transition of the first order in temperature between these states at a fixed coupling constant has been shown. It has also been shown that a topological crossover, which is associated with the joining of two sheets of the Fermi surface and is characterized by the maxima of the density of states N(T) and ratio C(T)/T of the specific heat to the temperature, occurs at a very low temperature T _⋄ determined by the structure of a state with the three-sheet Fermi surface. A momentum region where the distribution n(p, T) depends slightly on the temperature, which is manifested in the maximum of the specific heat C(T) near T _*, appears through a crossover at temperatures T ∼ T _* > T _⋄. It has been shown that the flattening of the single-particle spectrum of the strongly correlated two-dimensional electron gas results in the crossover from the Fermi liquid behavior to a non-Fermi liquid one with the density of states N(T) ∝ T ^−α with the exponent α }~ 2/3.     

Theory of high-T c superconductivity based on the fermion-condensation quantum phase transition

A theory of high-temperature superconductivity based on the combination of the fermion-condensation quantum phase transition and the conventional theory of superconductivity is presented. This theory describes maximum values of the superconducting gap, which can be as big as Δ₁～0.1ε _F , with ε _F being the Fermi level. We show that the critical temperature 2T _c ?Δ₁. If the pseudogap exists above T _c , then 2T*?Δ₁ and T* is the temperature at which the pseudogap vanishes. A discontinuity in the specific heat at T _c is calculated. The transition from conventional superconductors to high-T _c ones as a function of the doping level is investigated. The single-particle excitations and their lineshape are also considered     

The vortex-like excitations detected by Nernst signals in high-Tc superconductors

The nature of the pseudogap state and its relation to the d-wave superconductivity in high-T _c superconductors is still an open issue. The vortex-like excitations detected by the Nernst effect measurements exist in a certain temperature range above superconducting transition temperature T _c, which strongly support that the pseudogap phase is characterized by finite pairing amplitude with strong phase fluctuations and imply that the phase transition at T _c is driven by the loss of long-range phase coherence. We first briefly introduce the electronic phase diagram and pseudogap state of high-T _c superconductors, and then review the results of Nernst effect for different high-T _c superconductors. Related theoretical models are also discussed.     

d-symmetry superconductivity due to valence bond correlations

It is shown that d-symmetry superconductivity due to valence bond correlations is possible. Valence bond correlations are compatible with antiferromagnetic spin order. In order to explictly construct a homogeneous state with the valence bond structure in the two-dimensional Hubbard model for an arbitrary doping, we have used the variational method based on unitary local transformation. Attraction between holes in the d-channel is due to modulation of hopping by the site population in course of the valence bond formation, and corresponding parameters have been calculated variationally. An important factor for the gap width is the increase in the density of states on the Fermi level due to antiferromagnetic splitting of the band. The gap width and its ratio to the T _c are 2Δ≃0.1t and 2Δ/kT _c≃4.5−4 for U/t≃8. The correspondence between the theoretical phase diagram and experimental data is discussed. The dependence of T _c on the doping δ=|n−1| and the Fermi surface shape are highly sensitive to the weak interaction t′ leading to diagonal hoppings. In the case of t′>0 and p-doping, the peak on the curve of T _c(δ) occurs at the doping δ _opt, when the energy of the flattest part of the lower Hubbard subband crosses the Fermi level at k∼(π,0). In underdoped samples with δ<δ _opt, the anisotropic pseudogap in the normal state corresponds to the energy difference |E(π,0)−μ| between this part of the spectrum and the Fermi level. Zh. éksp. Teor. Fiz. 114, 985–1005 (September 1998)     

Appearance of superconductivity in the tetragonal ceramic NdBa2Cu3O6.67 as a result of oxygen ordering under pressure

The appearance of superconductivity and the relaxation of T _c to the equilibrium value T _c ≈30 K in a period of five days were observed in the tetragonal ceramic NdBa₂Cu₃O_6.67 under a pressure of 1 GPa. The superconducting phase vanishes 1.3 h after the pressure is released. This behavior is explained by the charge redistribution occurring as a result of pressure-induced ordering of oxygen in the CuO_x planes. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 10, 784–787 (25 May 1996)     

Superconductivity in the exactly solvable model of pseudogap state: The absence of self-averaging

The features of the superconducting state are studied in the simple exactly solvable model of the pseudogap state induced by fluctuations of the short-range “dielectric” order in the model of the Fermi surface with “hot” spots. The analysis is carried out for arbitrary short-range correlation lengths ξ_corr. It is shown that the superconducting gap averaged over such fluctuations differs from zero in a wide temperature range above the temperature T _c of the uniform superconducting transition in the entire sample, which is a consequence of non-self-averaging of the superconducting order parameter over the random fluctuation field. In the temperature range T>T _c, superconductivity apparently exists in individual regions (drops). These effects become weaker with decreasing correlation length ξ_corr; in particular, the range of existence for drops becomes narrower and vanishes as ξ_corr → 0, but for finite values of ξ_corr, complete self-averaging does not take place.     

Magnetic field dependence ofT c and temperature dependence ofH c2 in layered superconductors with open normal state Fermi surface

A theoretical framework for treating the effects of magnetic fieldH on the pairing theory of superconductivity is considered, where the field is taken in an arbitrary direction with respect to crystal axes. This is applicable to closed, as well as open normal state Fermi surface (FS), including simple layered metals. The orbital effects of the magnetic field are treated semiclassically while retaining the full anisotropic paramagnetic contribution. Explicit calculations are presented in the limits |H| → |H _c2(T)|,T ∼ 0 andT →T _c(|H|), |H| ∼ 0. Effects of weak nonmagnetic impurity scattering, without vertex corrections, have also been taken into account in a phenomenological way. The final results for the case of open FS and layered materials are found to differ considerably from those of the closed FS. For example, an important parameter,h(T=0)=|H_c2(0)|/[-Tδ|H _c2 T|δT]_T{s0} for the case of a FS open ink _z-direction with thek _z-bandwidth, 4t ₃, very small compared to the Fermi energy,E _F, is close to 0.5906, compared to 0.7273 for the closed FS, in the clean limit. Analytical results are given for the magnetic field dependence ofT _c and the temperature dependence of H _c2 for a model of layered superconductors with widely open FS. For a set of band structure parameters for YBa₂Cu₃O₇ used elsewhere, we find reasonable values for the upper critical fieldH _c2(0), the slope (dH _c2/dT)_{T c0}, anisotropic coherence lengths ζ_i(T=0),i=x, y, z, and (dT _c/d|H|)_{|H| → 0}.     

Pseudogap and precursor superconductivity in underdoped cuprate high temperature superconductors: A far-infrared ellipsometry study

With the technique of infrared ellipsometry we performed a detailed study of the temperature- and doping dependence of the c-axis response of a series of YBa₂Cu₃O_7−δ single crystals. In particular, we explored the anomalous electronic properties at temperatures above the macroscopic superconducting transition temperature, T _c, whose conflicting explanations range from a precursor superconducting state to electronic correlations that compete with superconductivity. We show that the c-axis spectra provide evidence that both kinds of correlations are present and that their contributions can be disentangled based on an analysis with a so-called multilayer-model. We find that the onset temperature, T ^*, and the energy scale, Δ_PG, of the competing pseudogap increase rapidly towards the underdoped side whereas they vanish on the overdoped side. In addition, we provide evidence that in a strongly underdoped sample the precursor superconducting correlations develop below an onset temperature, T ^ons, that is considerably lower than T ^* but still much higher than T _c.     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.     

Disordering effects in superconductors with anisotropic pairing: From Cooper pairs to compact bosons

In the weak-coupling BCS-theory approximation, normal impurities do not influence the superconducting transition temperature T _c in the case of isotropic s pairing. In the case of d pairing they result in a rapid destruction of the superconducting state. This is at variance with many experiments on the disordering of high-T _c superconductors, assuming that d pairing is realized in them. As the interelectronic attraction in a Cooper pair increases, the system transforms continuously from a BCS-type superconductor with “loose” pairs to a picture of superconductivity of “compact,” strongly coupled bosons. Near such a transition substantial deviations can be expected from the universal disorder dependence of T _c , as determined by the Abrikosov-Gor’kov equation, and T _c becomes more stable against disordering. Since high-T _c super-conducting systems fall into the transitional region from BCS-type pairs to compact bosons, these results can explain their relative stability against disordering. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 3, 258–262 (10 February 1997)     

Phase fluctuations and pseudogap phenomena

This article reviews the current status of precursor superconducting phase fluctuations as a possible mechanism for pseudogap formation in high-temperature superconductors. In particular we compare this approach which relies on the two-dimensional nature of the superconductivity to the often used T-matrix approach. Starting from simple pairing Hamiltonians we present a broad pedagogical introduction to the BCS–Bose crossover problem. The finite temperature extension of these models naturally leads to a discussion of the Berezinskii–Kosterlitz–Thouless superconducting transition and the related phase diagram including the effects of quantum phase fluctuations and impurities. We stress the differences between simple Bose–BCS crossover theories and the current approach where one can have a large pseudogap region even at high carrier density where the Fermi surface is well-defined. Green's function and its associated spectral function, which explicitly show non-Fermi liquid behavior, is constructed in the presence of vortices. Finally different mechanisms including quasi-particle–vortex and vortex–vortex interactions for the filling of the gap above T_c are considered.     

Equations of two-fluid hydrodynamics in the Hubbard model

A set of equations is obtained using stationary and nonstationary superconductivity theories in terms of the Hubbard model. The equations near T _c and for a weak magnetic field have the general form of superconductivity equations with a strongly anisotropic Fermi surface. Calculations are performed using a kinetic equation for quasiparticles. The low-temperature collective excitations in a superconductor are studied. An explicit relationship for the temperature dependence of second sound is obtained.     

The vortex-like excitations detected by Nernst signals in high-T c superconductors

The nature of the pseudogap state and its relation to the d-wave superconductivity in high-T _c superconductors is still an open issue. The vortex-like excitations detected by the Nernst effect measurements exist in a certain temperature range above superconducting transition temperature T _c, which strongly support that the pseudogap phase is characterized by finite pairing amplitude with strong phase fluctuations and imply that the phase transition at T _c is driven by the loss of long-range phase coherence. We first briefly introduce the electronic phase diagram and pseudogap state of high-T _c superconductors, and then review the results of Nernst effect for different high-T _c superconductors. Related theoretical models are also discussed.     

Origin of “Hot Spots” in the pseudogap regime of Nd1.85Ce0.15CuO4: An LDA + DMFT + Σk study

The material-specific electronic band structure of the electron-doped high- T _c cuprate Nd_1.85Ce_0.15CuO₄ (NCCO) is calculated in the pseudogap regime using the recently developed generalized LDA + DMFT + Σ _k scheme. The LDA/DFT (density-functional theory within local density approximation) provides model parameters (hopping integral values and local Coulomb interaction strength) for the one-band Hubbard model, which is solved by the DMFT (dynamical mean-field theory). To take pseudogap fluctuations into account, the LDA + DMFT is supplied with an “external” k-dependent self-energy Σ _k that describes interaction of correlated conducting electrons with nonlocal Heisenberg-like antiferromagnetic (AFM) spin fluctuations responsible for the pseudogap formation. Within this LDA + DMFT + Σ _k approach, we demonstrate the formation of pronounced hot spots on the Fermi surface (FS) map in NCCO, opposite to our recent calculations for Bi₂Sr₂CaCu₂O_{8 − δ} (Bi2212), which have produced a rather extended region of the FS “destruction.” There are several physical reasons for this fact: (i) the hot spots in NCCO are located closer to the Brillouin zone center; (ii) the correlation length ξ of AFM fluctuations is longer for NCCO; (iii) the pseudogap potential Δ is stronger than in Bi2212. Comparison of our theoretical data with recent bulk-sensitive high-energy angle-resolved photoemission (ARPES) data for NCCO provides good semiquantitative agreement. Based on that comparison, an alternative explanation of the van Hove singularity at −0.3 eV is proposed. Optical conductivity for both Bi2212 and NCCO is also calculated within the LDA + DMFT + Δ _k scheme and is compared with experimental results, demonstrating satisfactory agreement. The text was submitted by the authors in English.     

Characteristic features of d pairing in bilayer cuprates under conditions of Peierls instability of the normal phase

A system of self-consistent integral equations for the superconducting gap is formulated and solved taking account of the instability of the normal phase of bilayer cuprates against charge-density waves. The critical parameters are calculated as a function of the wave vector, temperature, and doping index. It is found that the region in which superconductivity coexists with d-type charge-density waves depends strongly on the doping index. The effective energy-gap parameter, determined as the interval between the peaks of the density of states, can have a local minimum at temperatures T<T _c . Pis’ma Zh. éksp. Teor. Fiz. 68, No. 7, 583–587 (10 October 1998)