Renormalization group study of systems with quadratic band touching

TL;DR

This paper investigates Lifshitz transitions in 2D systems with quadratic band touching, analyzing interaction effects via RG and exact models, revealing marginal relevance of repulsive interactions and excitonic instabilities.

Contribution

It provides a combined RG and exact model analysis of Lifshitz transitions in quadratic band touching systems, highlighting interaction effects and phase instabilities.

Findings

Repulsive interactions are marginally relevant at the transition.

Attractive interactions are marginally irrelevant.

System shows instability towards excitonic condensate away from transition.

Abstract

Lifshitz transitions in two 2D systems with a single quadratic band touching point as the chemical potential is varied have been studied here. The effects of interactions have been studied using the renormalization group (RG) and it is found that at the transition a repulsive interaction is marginally relevant and an attractive interaction is marginally irrelevant. We corroborate the results obtained from the RG calculation by studying a microscopic model whose ground state and Green's functions can be obtained exactly. We find that away from the transition, the system displays an instability towards forming and excitonic condensate.