Topological Insulators and Nematic Phases from Spontaneous Symmetry Breaking in 2D Fermi Systems with a Quadratic Band Crossing

TL;DR

This paper studies the stability of quadratic band-crossing points in 2D fermionic systems, revealing their topological nature and how weak interactions lead to various ordered phases such as quantum Hall and nematic states.

Contribution

It demonstrates the topological stability of QBCPs under certain symmetries and shows their instability to weak interactions, leading to multiple ordered phases.

Findings

QBCPs are topologically stable with fourfold or sixfold symmetry.

Weak interactions induce phases like quantum anomalous Hall, quantum spin Hall, and nematic.

QBCPs are marginally unstable to arbitrarily weak short-range repulsive interactions.

Abstract

We investigate the stability of a quadratic band-crossing point (QBCP) in 2D fermionic systems. At the non-interacting level, we show that a QBCP exists and is topologically stable for a Berry flux $\pm 2\pi$, if the point symmetry group has either fourfold or sixfold rotational symmetries. This putative topologically stable free-fermion QBCP is marginally unstable to {\em arbitrarily weak} short-range repulsive interactions. We consider both spinless and spin-1/2 fermions. Four possible ordered states result: a quantum anomalous Hall phase, a quantum spin Hall phase, a nematic phase, and a nematic-spin-nematic phase.