Instabilities of quadratic band crossing points

TL;DR

This paper investigates how interactions induce various instabilities in two-dimensional quadratic band crossing point models, revealing that quantum spin Hall states can emerge at very low interaction strengths due to wavevector-dependent eigenvectors.

Contribution

It extends previous work by analyzing the impact of wavevector dependence on interaction-driven instabilities in quadratic band crossing models using a functional renormalization group approach.

Findings

QSH state occurs at arbitrarily small interactions

Instabilities toward spin nematic, quantum anomalous Hall, and QSH states

Wavevector dependence influences the nature of instabilities

Abstract

Using a functional renormalization group approach, we study interaction-driven instabilities in quadratic band crossing point two-orbital models in two dimensions, extending a previous study of Sun et al. [1]. The wavevector-dependence of the Bloch eigenvectors of the free Hamiltonian causes interesting instabilities toward spin nematic, quantum anomalous Hall and quantum spin Hall states. In contrast with other known examples of interaction-driven topological insulators, in the system studied here, the QSH state occurs at arbitrarily small interaction strength and for rather simple intra- and inter-orbital repulsions.