d_{xy}-Density wave in fermion-fermion cold atom mixtures

TL;DR

This paper investigates density wave instabilities in a fermion-fermion cold atom mixture with $SU(2)\times SU(2)$ symmetry, revealing a transition from conventional to unconventional $d_{xy}$-wave density waves and superconductivity, driven by Fermi surface shape and phase-space effects.

Contribution

It introduces a novel $d_{xy}$-density wave phase in a Fermi-Fermi mixture and explains its emergence through a phase-space discrepancy mechanism using functional renormalization-group analysis.

Findings

$d_{xy}$-density wave appears away from half-filling.

Superconductivity dominates when both species are far from half-filling.

Phase-space discrepancy triggers the $d_{xy}$-density wave instability.

Abstract

We study density wave instabilities in a doubly-degenerate Fermi-Fermi mixture with $SU(2)\times SU(2)$ symmetry on a square lattice. For sufficiently large on-site inter-species repulsion, when the two species of fermions are both at half-filling, two conventional ($s$-wave) number density waves are formed with a $\pi$-phase difference between them to minimize the inter-species repulsion. Upon moving one species away from half-filling, an unconventional density wave with $d_{xy}$-wave symmetry emerges. When both species are away from the vicinity of half-filling, superconducting instabilities dominate. We present results of a functional renormalization-group calculation that maps out the phase diagram at weak couplings. Also, we provide a simple explanation for the emergence of the $d_{xy}$-density wave phase based on a four-patch model. We find a robust and general mechanism for $d_{xy}$-density-wave formation that is related to the shape and size of the Fermi surfaces. The density imbalance between the two species of fermions in the vicinity of half-filling leads to phase-space discrepancy for different inter-species Umklapp couplings. Using a phase space argument for leading corrections in the one-loop renormalization group approach to fermions, we show that the phase-space discrepancy in our system causes opposite flows for the two leading intra-species Umklapp couplings and that this triggers the $d_{xy}$-density-wave instability.