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.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.

Physical review. B, Condensed matterSep 1, 199536 citations

Mode-mode coupling approach to critical fluctuations in superconductors aboveT c

Klaus D. Usadel

The European Physical Journal BJul 1, 19730 citations

Electromagnetic properties of local pair superconductors

S. Robaszkiewicz, R. Micnas, T. Kostyrko

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).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).

Cambridge University Press eBooksSep 7, 19950 citations

Phase Fluctuations of s-Wave Superconductors on a Lattice

Wooram Kim, J. P. Ćarbotte

arXiv:cond-mat/0309261Journal of Low Temperature PhysicsApr 21, 20041 citation

Spatial fluctuations of the pairing potential in disordered superconductors

Grzegorz Litak A

arXiv:cond-mat/0108330Physica C SuperconductivityJun 1, 20020 citations

Theory of a Superfluid Fermi Liquid. I. General Formalism and Static Properties

A. J. Leggett

The microscopic theory of a superfluid Fermi liquid at finite temperature is developed for the case of a pure system with $S$ -wave pairing, and applied to the calculation of the static properties. As a function of $\ensuremath{\theta}\ensuremath{\equiv}\frac{T}{{T}_{c}}$ these properties are determined entirely by the Landau parameters ${F}_{0}$ , ${F}_{1}$ , ${Z}_{0}$ , etc., characterizing quasiparticle interactions in the normal phase. In particular the spin susceptibility $\ensuremath{\chi}$ and the density of the normal component ${\ensuremath{\rho}}_{n}$ are given by $\frac{\ensuremath{\chi}(\ensuremath{\theta})}{\ensuremath{\chi}(1)}=(1+\frac{1}{4}{Z}_{0})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{4}{Z}_{0}f(\ensuremath{\theta})]},$ $\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}}=(1+\frac{1}{3}{F}_{1})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{3}{F}_{1}f(\ensuremath{\theta})]},$ where the universal function $f(\ensuremath{\theta})\ensuremath{\equiv}\ensuremath{-}{[\ensuremath{\nu}(0)]}^{\ensuremath{-}1}{\ensuremath{\Sigma}}_{\mathrm{p}}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is the "effective density of states near the Fermi surface" relative to its value $\ensuremath{\nu}(0)$ in the normal phase. Thus the often-quoted expression ${\ensuremath{\rho}}_{n}=\frac{1}{3}{\ensuremath{\Sigma}}_{\mathrm{p}}{\mathrm{p}}^{2}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is valid for an interacting system only in the limit $T\ensuremath{\rightarrow}0$. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ is developed for arbitrary conditions (including the presence of impurities and pairing with $l\ensuremath{\ne}0$); it is found that under most circumstances explicit expressions for $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ may be obtained which involve only the Landau parameters and a suitably generalized effective density of states. The theory should apply to the possible superfluid phase of ${\mathrm{He}}^{3}$ and to most superconductors. It is suggested that the Knight shift in nontransition-metal superconductors should display some "Fermi-liquid" effects. The weak-field dc penetration depth $\ensuremath{\lambda}(T)$ is shown to be insensitive to such effects both in the Pippard limit and near ${T}_{c}$ ; however, in a London superconductor at lower temperatures the correction to $\ensuremath{\lambda}(T)$ should be observable and yield a direct estimate of ${F}_{1}$ .The microscopic theory of a superfluid Fermi liquid at finite temperature is developed for the case of a pure system with $S$-wave pairing, and applied to the calculation of the static properties. As a function of $\ensuremath{\theta}\ensuremath{\equiv}\frac{T}{{T}_{c}}$ these properties are determined entirely by the Landau parameters ${F}_{0}$, ${F}_{1}$, ${Z}_{0}$, etc., characterizing quasiparticle interactions in the normal phase. In particular the spin susceptibility $\ensuremath{\chi}$ and the density of the normal component ${\ensuremath{\rho}}_{n}$ are given by $\frac{\ensuremath{\chi}(\ensuremath{\theta})}{\ensuremath{\chi}(1)}=(1+\frac{1}{4}{Z}_{0})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{4}{Z}_{0}f(\ensuremath{\theta})]},$ $\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}}=(1+\frac{1}{3}{F}_{1})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{3}{F}_{1}f(\ensuremath{\theta})]},$ where the universal function $f(\ensuremath{\theta})\ensuremath{\equiv}\ensuremath{-}{[\ensuremath{\nu}(0)]}^{\ensuremath{-}1}{\ensuremath{\Sigma}}_{\mathrm{p}}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is the "effective density of states near the Fermi surface" relative to its value $\ensuremath{\nu}(0)$ in the normal phase. Thus the often-quoted expression ${\ensuremath{\rho}}_{n}=\frac{1}{3}{\ensuremath{\Sigma}}_{\mathrm{p}}{\mathrm{p}}^{2}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is valid for an interacting system only in the limit $T\ensuremath{\rightarrow}0$. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ is developed for arbitrary conditions (including the presence of impurities and pairing with $l\ensuremath{\ne}0$); it is found that under most circumstances explicit expressions for $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ may be obtained which involve only the Landau parameters and a suitably generalized effective density of states. The theory should apply to the possible superfluid phase of ${\mathrm{He}}^{3}$ and to most superconductors. It is suggested that the Knight shift in nontransition-metal superconductors should display some "Fermi-liquid" effects. The weak-field dc penetration depth $\ensuremath{\lambda}(T)$ is shown to be insensitive to such effects both in the Pippard limit and near ${T}_{c}$; however, in a London superconductor at lower temperatures the correction to $\ensuremath{\lambda}(T)$ should be observable and yield a direct estimate of ${F}_{1}$.

Physical ReviewDec 13, 1965284 citations

{]}^{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.

The microscopic theory of a superfluid Fermi liquid at finite temperature is developed for the case of a pure system with

S

-wave pairing, and applied to the calculation of the static properties. As a function of $\ensuremath{\theta}\ensuremath{\equiv}\frac{T}{{T}_{c}}$ these properties are determined entirely by the Landau parameters

{F}_{0}

{F}_{1}

{Z}_{0}

, etc., characterizing quasiparticle interactions in the normal phase. In particular the spin susceptibility $\ensuremath{\chi}$ and the density of the normal component ${\ensuremath{\rho}}_{n}$ are given by $\frac{\ensuremath{\chi}(\ensuremath{\theta})}{\ensuremath{\chi}(1)}=(1+\frac{1}{4}{Z}_{0})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{4}{Z}_{0}f(\ensuremath{\theta})]},$ $\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}}=(1+\frac{1}{3}{F}_{1})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{3}{F}_{1}f(\ensuremath{\theta})]},$ where the universal function $f(\ensuremath{\theta})\ensuremath{\equiv}\ensuremath{-}{[\ensuremath{\nu}(0)]}^{\ensuremath{-}1}{\ensuremath{\Sigma}}_{\mathrm{p}}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is the "effective density of states near the Fermi surface" relative to its value $\ensuremath{\nu}(0)$ in the normal phase. Thus the often-quoted expression ${\ensuremath{\rho}}_{n}=\frac{1}{3}{\ensuremath{\Sigma}}_{\mathrm{p}}{\mathrm{p}}^{2}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is valid for an interacting system only in the limit $T\ensuremath{\rightarrow}0$. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ is developed for arbitrary conditions (including the presence of impurities and pairing with $l\ensuremath{\ne}0$); it is found that under most circumstances explicit expressions for $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ may be obtained which involve only the Landau parameters and a suitably generalized effective density of states. The theory should apply to the possible superfluid phase of

{\mathrm{He}}^{3}

and to most superconductors. It is suggested that the Knight shift in nontransition-metal superconductors should display some "Fermi-liquid" effects. The weak-field dc penetration depth $\ensuremath{\lambda}(T)$ is shown to be insensitive to such effects both in the Pippard limit and near

{T}_{c}

; however, in a London superconductor at lower temperatures the correction to $\ensuremath{\lambda}(T)$ should be observable and yield a direct estimate of

{F}_{1}