Population imbalanced lattice fermions near the BCS-BEC crossover: I.The breached pair and metastable FFLO phases

TL;DR

This study explores the phase diagram and properties of imbalanced lattice fermions near the BCS-BEC crossover, emphasizing the breached pair state and inhomogeneous magnetization effects using Monte Carlo simulations.

Contribution

It provides a detailed thermal phase diagram for the attractive Hubbard model under magnetic field, incorporating spatial fluctuations and revealing new inhomogeneous and non-monotonic phenomena.

Findings

Tc scales significantly below mean field estimates

Spontaneous inhomogeneity in magnetization observed

Non-monotonic temperature dependence of low energy density of states

Abstract

We study s-wave superconductivity in the two dimensional attractive Hubbard model in an applied magnetic field, assume the extreme Pauli limit, and examine the role of spatial fluctuations in the coupling regime corresponding to BCS-BEC crossover. We use a decomposition of the interaction in terms of an auxiliary pairing field, retain the static mode, and sample the pairing field via Monte Carlo. The method requires iterative solution of the Bogoliubov-de-Gennes (BdG) equations for amplitude and phase fluctuating configurations of the pairing field. We establish the full thermal phase diagram of this strong coupling problem, revealing $T_c$ scales an order of magnitude below the mean field estimate, highlight the spontaneous inhomogeneity in the field induced magnetization, and discover a strong non monotonicity in the temperature dependence of the low energy density of states. We compare our results to the experimental phase diagram of the imbalanced Fermi gas at unitarity. This paper focuses on the magnetized but homogeneous (breached pair) superconducting state, a companion paper deals with the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) regime.