arXiv:cond-mat/0010085 · Physical review. B, Condensed matter

Thermodynamics of the crossover from weak- to strong-coupling superconductivity

Egor S. Babaev

Published Apr 20, 2001• 15 citations

Abstract

In this paper we study an evolution of low-temperature thermodynamical quantities for an electron gas with a \ensuremath{\delta}-function attraction as the system crosses over from weak-coupling (BCS-type) to strong-coupling (Bose-type) superconductivity in three and two dimensions.

DOI: 10.1103/physrevb.63.184514

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arXiv:cond-mat/0010085 · Physical review. B, Condensed matter

Thermodynamics of the crossover from weak- to strong-coupling superconductivity

Egor S. Babaev

Published Apr 20, 2001• 15 citations

arXiv HTML PDF

Abstract

DOI: 10.1103/physrevb.63.184514

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\mathrm{XY}

models which serve to determine nonperturbatively the temperature of phase decoherence where superconductivity breaks down. We find the transition temperature

{T}_{c}

as a monotonous function of the coupling strength both in two and three dimensions, and give analytic formulas for the merging of temperature of phase decoherence with the temperature of pair formation in the weak-coupling limit.

{\mathit{k}}_{\mathit{F}}

${\ensuremath{\xi}}_{\mathrm{pair}}$\ensuremath{\gg}1) from the strong- (

{\mathit{k}}_{\mathit{F}}

${\ensuremath{\xi}}_{\mathrm{pair}}$\ensuremath{\ll}1) coupling limits (

{\mathit{k}}_{\mathit{F}}

being the Fermi wave vector) as well as to follow the crossover in between. It is shown that ${\ensuremath{\xi}}_{\mathrm{phase}}$ coincides with ${\ensuremath{\xi}}_{\mathrm{pair}}$ down to

{\mathit{k}}_{\mathit{F}}

${\ensuremath{\xi}}_{\mathrm{pair}}$\ensuremath{\simeq}10, ${\ensuremath{\xi}}_{\mathrm{pair}}$ in turn coinciding with the Pippard coherence length. In the strong-coupling limit we find instead that ${\ensuremath{\xi}}_{\mathrm{phase}}$\ensuremath{\gg}${\ensuremath{\xi}}_{\mathrm{pair}}$, with ${\ensuremath{\xi}}_{\mathrm{pair}}$ coinciding with the radius of the bound-electron pair. From the mapping onto an effective system of bosons in the strong-coupling limit we further relate ${\ensuremath{\xi}}_{\mathrm{pair}}$ with the ``range'' of the residual boson-boson interaction, which is physically the only significant length associated with the dynamics of the bosonic system. \textcopyright{} 1996 The American Physical Society.