  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.
