On the Crossover from BCS Superconductivity to Bose Condensation

TL;DR

This paper investigates the transition from BCS superconductivity to Bose-Einstein condensation in the attractive Hubbard model, using various theoretical approaches to understand fluctuations, pairing, and differences between lattice and continuum systems.

Contribution

It develops a microscopic framework for analyzing the BCS-Bose crossover, incorporating fluctuations and comparing lattice and continuum models with different interaction types.

Findings

Identifies the role of Gaussian fluctuations in the crossover regime

Constructs Ginzburg-Landau functionals for different models

Analyzes effects of non-local pairing interactions

Abstract

We outline a microscopic approach to the superconducting fluctuations and pairing correlations in the attractive Hubbard model above Tc, using the functional integral method. A crossover from BCS superconductivity to Bose condensation of preformed pairs is studied by constructing the appropriate Ginzburg-Landau functionals. The differences between the lattice and the continuum models are discussed. The case of quasi-two-dimensional superconductors as well as the model with non-local pairing interaction are also examined. The effects of gaussian fluctuations of the order parameter are analyzed in the T-matrix approach, the self-consistent Hartree approach and finally within the Ginzburg-Landau theory. Simlarities with a paramagnon theory of itinerant-electron magnetism are pointed out.