Comment on "Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator"

TL;DR

This paper critiques a previous claim that three-dimensional second-order topological insulators are unstable to Coulomb interactions, demonstrating instead that they are stable against weak Coulomb interactions when using the correct phase transition criterion.

Contribution

It corrects the previous analysis by showing the stability of 3D SOTIs against Coulomb interactions using the proper surface gap criterion.

Findings

SOTIs are stable against weak Coulomb interactions.

The previous claim of phase transition was based on an incorrect criterion.

Proper analysis shows no topological phase transition occurs under weak interactions.

Abstract

Based on renormalization-group (RG) calculations, a recent Letter by Zhao et al [Phys. Rev. Lett. 127, 176601 (2021)] claimed that three-dimensional second-order topological insulators (SOTIs) are always unstable to the Coulomb interaction and they will thus undergo topological phase transitions to either topological insulators (TIs) or normal insulators. While the calculations in this paper are correct, the conclusion about the topological phase transition from SOTI to TI is not true. The reason behind this false conclusion lies in that the authors use a wrong criterion to identify the phase transition. In this Comment we would like to remind that, to locate the possible transitions from SOTI to TI, an appropriate quantity is the sign-changing mass gap $m_\textrm{surf}$ for the surface states. By examining its behavior within RG approach, the stability of SOTI against weak Coulomb interactions is demonstrated.