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Physical review. B, Condensed matter

Thermodynamics of local-pair superconductors with anisotropic lattice structures

R. Micnas, S. Robaszkiewicz

Published May 1, 1992• 39 citations
Publisher

Abstract

The effective-pseudospin model of the local-electron-pair superconductor, being equivalent to a hard-core charged Bose gas on a lattice, is analyzed for the case of anisotropic lattice structures and arbitrary electron concentration with the use of self-consistent random-phase approximation. The evolution of the ground-state phase diagrams, the low-temperature thermodynamic properties, and the superconducting critical temperature (${\mathit{T}}_{\mathit{c}}$), as a function of the lattice anisotropy and electron concentration (n), are determined. We also discuss the superfluid properties within the framework of the Landau quasiparticle model. In the quasi-two-dimensional case and for low concentrations, the changeover from ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}${\mathit{n}}^{2/3}$ to ${\mathit{T}}_{\mathit{c}}$\ensuremath{\sim}n is found to occur for ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/${\mathit{J}}_{\mathrm{\ensuremath{\parallel}}}$\ensuremath{\sim}${10}^{\mathrm{\ensuremath{-}}2}$, with ${\mathit{J}}_{\mathrm{\ensuremath{\parallel}}}$ and ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$ being the intraplanar and interplanar pair hopping amplitude parameters, respectively. It turns out that the increasing lattice anisotropy (i.e., reduction of interplanar or interchain couplings) extends the range of stability of the homogeneous superconducting phase and suppresses the charge-density-wave state. The results for the ground-state superconducting order parameter are in good agreement with recent Monte Carlo and exact-diagonalization studies for the two-dimensional square lattice. The relationship between the pseudospin and bosonic descriptions of local-electron-pair superconductor in the dilute limit is also further analyzed.

DOI
10.1103/physrevb.45.9900

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The effective-pseudospin model of the local-electron-pair superconductor, being equivalent to a hard-core charged Bose gas on a lattice, is analyzed for the case of anisotropic lattice structures and arbitrary electron concentration with the use of self-consistent random-phase approximation. The evolution of the ground-state phase diagrams, the low-temperature thermodynamic properties, and the superconducting critical temperature (Tc{\mathit{T}}_{\mathit{c}}Tc​), as a function of the lattice anisotropy and electron concentration (n), are determined. We also discuss the superfluid properties within the framework of the Landau quasiparticle model. In the quasi-two-dimensional case and for low concentrations, the changeover from Tc{\mathit{T}}_{\mathit{c}}Tc​\ensuremath{\sim}n2/3{\mathit{n}}^{2/3}n2/3 to Tc{\mathit{T}}_{\mathit{c}}Tc​\ensuremath{\sim}n is found to occur for J\ensuremath⊥{\mathit{J}}_{\mathrm{\ensuremath{\perp}}}J\ensuremath⊥​/J\ensuremath∥{\mathit{J}}_{\mathrm{\ensuremath{\parallel}}}J\ensuremath∥​\ensuremath{\sim}10\ensuremath−2{10}^{\mathrm{\ensuremath{-}}2}10\ensuremath−2, with J\ensuremath∥{\mathit{J}}_{\mathrm{\ensuremath{\parallel}}}J\ensuremath∥​ and J\ensuremath⊥{\mathit{J}}_{\mathrm{\ensuremath{\perp}}}J\ensuremath⊥​ being the intraplanar and interplanar pair hopping amplitude parameters, respectively. It turns out that the increasing lattice anisotropy (i.e., reduction of interplanar or interchain couplings) extends the range of stability of the homogeneous superconducting phase and suppresses the charge-density-wave state. The results for the ground-state superconducting order parameter are in good agreement with recent Monte Carlo and exact-diagonalization studies for the two-dimensional square lattice. The relationship between the pseudospin and bosonic descriptions of local-electron-pair superconductor in the dilute limit is also further analyzed.
We have studied the extended Hubbard model with pair hopping in the atomic limit for arbitrary electron density and chemical potential. The Hamiltonian considered consists of (i) the effective on-site interaction U and (ii) the intersite charge exchange interactions I, determining the hopping of electron pairs between nearest-neighbour sites. The model can be treated as a simple effective model of a superconductor with very short coherence length in which electrons are localized and only electron pairs have a possibility of transferring. The phase diagrams and thermodynamic properties of this model have been determined within the variational approach, which treats the on-site interaction term exactly and the intersite interactions within the mean-field approximation. We have also obtained rigorous results for a linear chain (d = 1) in the ground state. Moreover, at T = 0 some results derived within the random phase approximation (and the spin-wave approximation) for d = 2 and 3 lattices and within the low-density expansions for d = 3 lattices are presented. Our investigation of the general case (as a function of the electron concentration n and as a function of the chemical potential μ) shows that, depending on the values of interaction parameters, the system can exhibit not only the homogeneous phases, superconducting (SS) and nonordered (NO), but also the phase separated states (PS: SS-NO). The system considered exhibits interesting multicritical behaviour including tricritical points.
We study thermodynamic and electromagnetic properties of the local electron pair system being equivalent to that of hard-core charged bosons on a lattice. The theory of the response kernel is given and static electromagnetic properties of the model are analyzed in the superfluid phase in the random-phase approximation. The effects of quantum fluctuations on the superfluid density are analyzed in detail for cubic lattices. A generic feature of the London penetration depths ratio [\ensuremath{\lambda}(0)/\ensuremath{\lambda}(T)]2{]}^{2}]2 in the considered system is the T4{\mathit{T}}^{4}T4 behavior in the T\ensuremath{\rightarrow}0 limit and the 3D XY critical point behavior near Tc{\mathit{T}}_{\mathit{c}}Tc​ (for the screened long-range intersite interaction). In the low-density limit, a consistent description of superfluid characteristics is obtained with the use of the exact scattering length. The effects of long-range Coulomb interaction on the excitation spectrum and finite temperature properties of the superconducting phase are also discussed. Finally, we briefly comment on the relevance of our results to the recent experimental data concerning the London penetration depth and the universal critical behavior in high-Tc{\mathit{T}}_{\mathit{c}}Tc​ superconductors.
Recent experimental findings concerning the temperature-dependence of the penetration depth and strong empirical evidence for a universal 3D X – Y critical behaviour in several classes of high- T c superconductors suggest that Bose condensation of ‘weakly charged’ bosons can be a driving mechanism for the phase transition in extreme type II superconductors. We explore the occurence of analogous behaviour in a simple model of local electron pairs, which is that of hard-core charged bosons on a lattice. We examine the electromagnetic properties of the model in the superfiuid phase as a function of boson concentration and density–density interaction. In the low-density limit, with the use of the exact scattering length, we present new results for the ground state characteristics. The relevance of the obtained results to interpretation of experimental data on high- T c oxides is discussed. Introduction Some recent experimental results concerning temperature-dependence of the London penetration depth and empirical evidence for a universal 3D X – Y critical behaviour in several families of high- T c superconductors indicate that Bose condensation can be a driving mechanism for the phase transition in these extreme type II superconductors [1–3]. Motivated by these experimentally established universal trends, we examine the electromagnetic properties of the effective pseudo-spin model of the local pair superconductor, equivalent to a hard-core charged Bose gas on a lattice, for the case of arbitrary electron concentration n . From linear response theory, the current response is obtained and expressions for the paramagnetic and diamagnetic kernels are evaluated in the RPA (random phase approximation) and SWA (spin-wave approximation).
We study the superfluid properties of short-coherence-length superconductors described by the extended Hubbard model with on-site repulsive and intersite attractive interaction. We have analysed the superfluid stiffness and thermodynamic properties of the model versus electron concentration and pairing interaction on a two-dimensional square lattice with nearest- and next-nearest-neighbour hopping. The effects of phase fluctuations on anisotropic superconductivity of extended s-and d x 2 − y 2 -wave type were examined within the Kosterlitz–Thouless (KT) scenario. The KT critical temperatures were determined and compared with those from the BCS–Hartree–Fock approximation. The Uemura-type plots, i.e. the critical temperature versus zero-temperature phase stiffness, were obtained for both extended s- and d-wave pairings. The states with mixed (s ∗ and d x 2 − y 2 ) symmetry, and in particular the time-reversal breaking state of s + id symmetry, were analysed and the phase diagrams taking into account these states are presented. We also briefly discuss the crossover from BCS to local pair superconductivity for the d x 2 − y 2 -wave pairing. A comparison of the theoretical results with the experimental data, in particular those of T c versus λ −2 (0), for high- T c cuprate superconductors is made.
The phase diagrams and superconducting properties of the extended Hubbard model with pair hopping interaction, i.e., the Penson-Kolb-Hubbard model are studied. The analysis of the model is performed for d-dimensional hypercubic lattices, including d=1d=1d=1 and $d=\ensuremath{\infty},$ by means of the (broken symmetry) Hartree-Fock approximations and, for $d=\ensuremath{\infty},$ by the slave-boson mean-field method. For d=1,d=1,d=1, at half filling the phase diagram is shown to consist of nine different phases including two superconducting states with center-of-mass momentum q=0q=0q=0 and q=Qq=Qq=Q $(\ensuremath{\eta}$ pairing), site and bond-located antiferromagnetic and charge-density wave states as well as three mixed phases with coexisting site and bond orderings. The stability range of the bond-type orderings shrinks with increasing lattice dimensionality d and for $d=\ensuremath{\infty}$ the corresponding diagram consists of four phases only, involving exclusively site-located orderings. Comparing the pair hopping model with the attractive Hubbard model we found in both cases gradual evolution from the BCS-like limit to the tightly bound pairs regime and a monotonic increase of the gap in the excitation spectrum with increasing coupling. However, the dynamics of electron pairs in both models is qualitatively different, which results in different dependences of condensation energies and critical temperatures on interaction parameters as well as in different electrodynamic properties, especially in a strong coupling regime.
The two component model of coexisting local electron pairs and itinerant fermions coupled via charge exchange mechanism, which mutually induces superconductivity in both subsystems, is discussed. The cases of isotropic s-wave and anisotropic pairing of extended s and d x 2 −y 2-wave symmetries are analyzed for a 2D square lattice within the BCS-mean field approximation and the Kosterlitz-Thouless theory. We determined the phase diagrams and superconducting characteristics as a function of the position of the local pair (LP) level and the total electron concentration. The model exhibits several types of interesting crossovers from BCS like behavior to that of LP’s. Some of our results are discussed in connection with a two-component scenario of preformed pairs and unpaired electrons for exotic superconductors. Key words: Boson-Fermion model, Phase fluctuations A system of interacting charged bosons (bound electron pairs) and electrons can show features which are intermediate between those of local pair superconductors and those of classical BCS systems. Such a two component (bosonfermion) model is of relevance for high temperature superconductors (HTS) and other exotic superconductors [1,2,3,4,5,6,7,8,9,10]. Recently, we have studied a generalization of this model to the case of anisotropic pairing [9,10]. Here, we shortly outline the study and present further results concerning the phase diagrams and superconducting properties of such a system in the case of isotropic s-wave pairing as well as for anisotropic pairings of d- and extended s-wave symmetries, for a 2D square lattice.