Instabilities of a birefringent semi-metal

TL;DR

This paper investigates the stability and phase transitions of birefringent semi-metals with spinless fermions on a square lattice, analyzing effects of interactions, magnetic fields, and potential 3D extensions.

Contribution

It provides a mean field analysis of interaction-induced phases in birefringent semi-metals and derives Landau levels showing unique quantum Hall features.

Findings

Robustness of birefringent semi-metal phase under weak interactions

Transitions to density wave and quantum anomalous Hall phases

Additional quantum Hall plateaux due to birefringence

Abstract

Birefringent fermions arise as massless fermionic low energy excitations of a particular tight binding model for spinless fermions on a square lattice which have two "speeds of light" [M. P. Kennett, ${\it et \, al.}$, Phys. Rev. A ${\bf 83}$, 053636 (2011)]. We use mean field theory to study phases that can arise when there are nearest neighbour and next-nearest neighbour repulsive interactions in this model and demonstrate robustness of the birefringent semi-metal phase in the presence of weak interactions and identify transitions to staggered density and quantum anomalous Hall ordered phases. We consider the effect of coupling birefringent fermions to a magnetic field, and find analytic expressions for the corresponding Landau levels and demonstrate that their integer Quantum Hall effect displays additional plateaux beyond those observed for regular Dirac fermions, such as in graphene. We briefly discuss a tight-binding construction that leads to three dimensional birefringent fermions.