Interaction-driven topological and nematic phases on the Lieb lattice

TL;DR

This paper demonstrates how electron-electron interactions in a Lieb lattice can induce various topological and nematic phases from quadratic band crossing points, revealing new interaction-driven quantum states.

Contribution

It introduces a concrete model on the Lieb lattice showing how quadratic band crossing points lead to multiple interaction-driven topological and nematic phases.

Findings

BCP is marginally unstable against infinitesimal repulsions

Different interaction strengths lead to quantum anomalous/spin Hall phases

Charge nematic and nematic-spin-nematic phases also develop

Abstract

We show that topological states are often developed in two dimensional semimetals with quadratic band crossing points (BCPs) by electron-electron interactions. To illustrate this, we construct a concrete model with the BCP on an extended Lieb lattice and investigate the interaction-driven topological instabilities. We find that the BCP is marginally unstable against infinitesimal repulsions. Depending on the interaction strengths, topological quantum anomalous/spin Hall, charge nematic, and nematic-spin-nematic phases, develop separately. Possible physical realizations of quadratic BCPs are provided.