Coulomb instabilities of 3D higher-order topological insulators

TL;DR

This paper investigates the stability of 3D higher-order topological insulators under weak Coulomb interactions, revealing they are inherently unstable and undergo phase transitions to either topological insulators or normal insulators.

Contribution

It provides the first renormalization group analysis of Coulomb effects on 3D higher-order TIs, identifying the nature of their interaction-driven phase transitions.

Findings

Higher-order TIs are always unstable under Coulomb interactions.

Two types of phase transitions are identified: to TIs and to normal insulators.

Emergent symmetries and critical exponents characterize the transitions.

Abstract

Topological insulator (TI) is an exciting discovery because of its robustness against disorder and interactions. Recently, higher-order TIs have been attracting increasing attention, because they host 1D topologically-protected hinge states in 3D or 0D corner states in 2D. A significantly critical issue is whether the higher-order TIs also survive interactions, but it is still unexplored. We study the effects of weak Coulomb interaction on a 3D second-order TI, with the help of a renormalization group calculation. We find that the 3D higher-order TIs are always unstable, suffering from two types of topological phase transitions. One is from higher-order TI to TI, the other is to normal insulator (NI). The first type is accompanied by emergent time-reversal and inversion symmetries and has a dynamical critical exponent $\kappa=1$. The second type does not have the emergent symmetries and has non-universal dynamical critical exponents $\kappa<1$. Our results may inspire more inspections on the stability of higher-order topological states of matter and related novel quantum criticalities.