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Physical review. B, Condensed matter

Thermodynamic and electromagnetic properties of hard-core charged bosons on a lattice

R. Micnas, S. Robaszkiewicz, T. Kostyrko

Published Sep 1, 1995• 36 citations
Publisher

Abstract

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)${]}^{2}$ in the considered system is the ${\mathit{T}}^{4}$ behavior in the T\ensuremath{\rightarrow}0 limit and the 3D XY critical point behavior near ${\mathit{T}}_{\mathit{c}}$ (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-${\mathit{T}}_{\mathit{c}}$ superconductors.

DOI
10.1103/physrevb.52.6863

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Physical review. B, Condensed matter•Nov 1, 1996•27 citations
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).
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 ${\mathit{J}}_{\mathrm{\ensuremath{\perp}}}$/${\mathit{J}}_{\mathrm{\ensuremath{\parallel}}}$\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.
We study thermodynamic and electromagnetic properties of the Penson-Kolb model, i.e., the tight-binding model with the pair-hopping interaction J, and analyze the effects of phase fluctuations on the s-wave superconductivity in this system. The evolution of the critical fields, the coherence length, the Ginzburg ratio, and the London penetration depth \ensuremath{\lambda} with particle concentration n and pairing strength is determined at T=0T=0T=0 for d-dimensional hypercubic lattices d=2d=2d=2 (SQ) and d=3d=3d=3 (SC). Within the Kosterlitz-Thouless scenario the critical temperatures Tc{T}_{c}Tc​ are calculated for d=2d=2d=2 SQ lattice and compared with the ones from BCS-HFA Tp.{T}_{p}.Tp​. The results show a substantial enhancement of the gap to critical temperature ratio due to the phase fluctuations as well as a separation of the energy scales for the pair formation $(\ensuremath{\sim}{k}_{B}{T}_{p})$ and the phase coherence $(\ensuremath{\sim}{k}_{B}{T}_{c}).$ The Uemura type plots, i.e., the Tc{T}_{c}Tc​ vs ${\ensuremath{\lambda}}^{\ensuremath{-}2}(0)$ plots, are obtained both as a function of n and as a function of pairing strength. The results are compared with those found earlier for the attractive Hubbard model.
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.
In the paper, we study the thermodynamic and electromagnetic properties of the Penson–Kolb (PK) model, i.e., the tight-binding model for fermionic particles with the pair-hopping interaction J. We focus on the case of repulsive J (i.e., J<0), which can stabilize the eta-pairing superconductivity with Cooper-pair center-of-mass momentum q→=Q→, Q→=(π/a,π/a,…). Numerical calculations are performed for several d-dimensional hypercubic lattices: d=2 (the square lattice, SQ), d=3 (the simple cubic lattice) and d=∞ hypercubic lattice (for arbitrary particle concentration 0<n<2 and temperature T). The ground state J versus n phase diagrams and the crossover to the Bose–Einstein condensation regime are analyzed and the evolution of the superfluid characteristics are examined within the (broken symmetry) Hartree–Fock approximation (HFA). The critical fields, the coherence length, the London penetration depth, and the Ginzburg ratio are determined at T=0 and T>0 as a function of n and pairing strength. The analysis of the effects of the Fock term on the ground state phase boundaries and on selected PK model characteristics is performed as well as the influence of the phase fluctuations on the eta-pairing superconductivity is investigated. Within the Kosterlitz–Thouless scenario, the critical temperatures TKT are estimated for d=2 SQ lattice and compared with the critical temperature Tc obtained from HFA. We also determine the temperature Tm at which minimal gap between two quasiparticle bands vanishes in the eta-phase. Our results for repulsive J are contrasted with those found earlier for the PK model with attractive J (i.e., with J>0).
The superfluid characteristics of the attractive Hubbard model are analyzed for any coupling |U| and arbitrary electron concentration (0n2) by means of the slave-boson mean-field method and also by the perturbative treatment of the strong-coupling limit. The slave boson method takes into account correlations of electrons and yields a reliable description of the crossover from BCS-type superconductivity to local pair (composite bosons) superconductivity with increasing |U|. The results for the ground state (the free energy, the gap in the excitation spectrum) and the electromagnetic characteristics (the critical magnetic field, the London penetration depth, the coherence length) are compared with those obtained by the Hartree-Fock approximation and by the self-consistent second-order perturbation theory in the weak-coupling limit as well as with those obtained using perturbational approaches in the strong-coupling limit. We show that the slave-boson method, in contrast to the Hartree-Fock approximation, gives credible results for all investigated quantities in the whole interaction range, interpolating smoothly between the BCS and local pair regimes. A comparison of theoretical predictions for our simple model with experimental data for various families of short-coherence-length superconductors suggests that the best agreement can be obtained for intermediate values of the local attraction. \textcopyright{} 1996 The American Physical Society.