dxy-density wave in fermion-fermion cold-atom mixtures

Abstract

We study density wave instabilities in a doubly-degenerate Fermi-Fermi mixture with SU (2) × 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 π-phase difference between them to minimize the inter-species repulsion. Upon moving one species away from half-filling, an unconventional density wave with dxy-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 dxy-density wave phase based on a four-patch model. We find a robust and general mechanism for dxy-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 phasespace 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 dxy-density-wave instability.