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

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.