Spin-Imbalanced Fermi Superfluidity in a Lieb Lattice Hubbard Model

TL;DR

This paper explores the rich phase diagram of a spin-imbalanced Hubbard model on a Lieb lattice, revealing multiple superfluid phases, including FFLO and Sarma states, driven by the flat band and multiorbital effects.

Contribution

It introduces a detailed mean-field analysis of superfluid phases in a Lieb lattice Hubbard model, highlighting the stabilization mechanisms of FFLO and Sarma phases due to flat band properties.

Findings

Identification of four distinct FFLO phases with different pair momentum characteristics.

Large stable region of Sarma phase with zero pair momentum.

Flat band facilitates density readjustment at zero energy cost.

Abstract

We obtain a phase diagram of the spin imbalanced Hubbard model on the Lieb lattice, which is known to feature a flat band in its single-particle spectrum. Using the BCS mean-field theory for multiband systems, we find a variety of superfluid phases with imbalance. In particular, we find four different types FFLO phases, i.e. superfluid phases with periodic spatial modulation. They differ by the magnitude and direction of the centre-of-mass momentum of Cooper pairs. We also see a large region of stable Sarma phase, where the density imbalance is associated with zero Cooper pair momentum. In the mechanism responsible for the formation of those phases, the crucial role is played by the flat band, wherein particles can readjust their density at zero energy cost. The multiorbital structure of the unit cell is found to stabilize the Sarma phase by allowing for a modulation of the order parameter within a unit cell. We also study the effect of finite temperature and a lattice with staggered hopping parameters on the behaviour of these phases.