Correlated interaction effects in an anisotropic flat band fermion system

TL;DR

This paper investigates a novel anisotropic flat band fermion system with mixed linear and cubic dispersion, revealing Coulomb interaction effects that lead to an excitonic gap and a topologically nontrivial phase.

Contribution

It introduces a new anisotropic fermion system and analyzes Coulomb interaction effects using renormalization group and Dyson-Schwinger methods, discovering excitonic gap formation and topological phases.

Findings

Fermion velocity is restored along the cubic dispersion direction.

A critical Coulomb strength induces an excitonic gap.

The system becomes an excitonic Chern insulator with quantized Hall conductivity.

Abstract

An anisotropic flat band fermion system with a novel dispersion that is linear along one direction and cubic along another is proposed in Phys. Rev. X. 13, 021012 (2023). We study the effects of Coulomb interaction in this fermion system by renormalization group theory and Dyson-Schwinger gap equation. We perform renormalizaton group analysis and find that fermion velocity is always restored along the direction that the fermions take cubic dispersion originally. Accordingly, the system takes the similar behaviors to the two-dimensional Dirac fermion system with Coulomb interaction in the low energy regime. Based on Dyson-Schwinger gap equation method, we find that an excitonic gap is generated if the Coulomb strength is large enough, and the system becomes a novel excitonic Chern insulator with quantized anomalous Hall conductivity. Observable quantities of this system in free case, under weak and strong enough Coulomb interaction are all analyzed.