Theory of Superfluids with Population Imbalance: Finite Temperature and BCS-BEC Crossover Effects

TL;DR

This paper develops a comprehensive finite-temperature theory for fermionic superfluids with population imbalance, capturing BCS-BEC crossover effects and various condensate phases, including LOFF states, beyond zero-temperature mean field models.

Contribution

It introduces a general theoretical framework that includes pairing fluctuations at finite temperature, extending previous zero-temperature theories to encompass a wider range of physical phenomena.

Findings

Unified finite-temperature theory for imbalanced fermionic superfluids

Inclusion of pre-formed pairs and pseudogap effects

Derivation of ground state and finite temperature LOFF states

Abstract

In this paper we present a very general theoretical framework for addressing fermionic superfluids over the entire range of BCS to Bose Einstein condensation (BEC) crossover in the presence of population imbalance or spin polarization. Our emphasis is on providing a theory which reduces to the standard zero temperature mean field theories in the literature, but necessarily includes pairing fluctuation effects at non-zero temperature within a consistent framework. Physically, these effects are associated with the presence of pre-formed pairs (or a fermionic pseudogap) in the normal phase, and pair excitations of the condensate, in the superfluid phase. We show how this finite $T$ theory of fermionic pair condensates bears many similarities to the condensation of point bosons. In the process we examine three different types of condensate: the usual breached pair or Sarma phase and both the one and two plane wave Larkin- Ovchinnikov, Fulde-Ferrell (LOFF) states. The last of these has been discussed in the literature albeit only within a Landau-Ginzburg formalism, generally valid near $T_c$. Here we show how to arrive at the two plane wave LOFF state in the ground state as well as at general temperature $T$.