Interaction-driven topological and nematic phases on the Lieb lattice

Wei-Feng Tsai,Chen Fang,Hong Yao,Jiangping Hu

doi:10.1088/1367-2630/17/5/055016

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.

Highlights

The search for new topological states of matter has not stopped since the discovery of the quantum Hall state in the 1980s [1]
The model we have solved on the Lieb lattice demonstrates that the topological insulators’ (TI) (QAH/quantum spin Hall (QSH) state) can be induced by appropriate interactions through a spontaneously symmetry breaking mechanism, which dynamically generates spin–orbit couplings necessary for a topological insulator
(2) The system should have weak spin–orbit coupling [spin SU(2) symmetry is preserved] and next nearest-neighbor (NNN) repulsions need to be more significant than the other short-range repulsions

Summary

14 May 2015

We show that topological states are often developed in two-dimensional semimetals with quadratic author(s) and the title of the work, journal citation band crossing points (BCPs) by electron–electron interactions. 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

Introduction

The lattice model

Topological nature of the band touching

Interaction-driven instabilities

Discussion and conclusion