Evolution of the dynamics of neutral superconductors between BCS and BEC regimes: the variational approach

Abstract

We use variational approach to analyze the evolution of the dynamics of a neutral s-wave superconductor between BCS and BEC regimes. We consider 2D case, when BCS–BEC crossover occurs already at weak coupling and is governed by the ratio of the two scales — the Fermi energy EF and the bound state energy for two fermions in a vacuum, E₀. BCS and BEC regimes correspond to EF >> E₀ and EF << E₀, respectively. We compute the spectrum of low-energy bosonic excitations and show that the velocity of phase fluctuations remains υF / √2 through BCS–BEC crossover. We also discuss the topological Aφ ̇ term in the effective action.