Disorder-Induced Phase Transitions in Three-Dimensional Chiral Second-Order Topological Insulator

Topological insulators have been extended to higher-order versions that possess topological hinge or corner states in lower dimensions. However, their robustness against disorder is still unclear. Here, we theoretically investigate the phase transitions of three-dimensional (3D) chiral second-order topological insulator (SOTI) in the presence of disorders. Our results show that, by increasing disorder strength, the nonzero densities of states of side surface and bulk emerge at critical disorder strengths of $W_{S}$ and $W_{B}$, respectively. The spectral function indicates that the bulk gap is only closed at one of the $R_{4z}\mathcal{T}$-invariant points, i.e., $\Gamma_{3}$. The closing of side surface gap or bulk gap is ascribed to the significant decrease of the elastic mean free time of quasi-particles. Because of the localization of side surface states, we find that the 3D chiral SOTI is robust at an averaged quantized conductance of $2e^{2}/h$ with disorder strength up to $W_{B}$. When the disorder strength is beyond $W_{B}$, the 3D chiral SOTI is then successively driven into two phases, i.e., diffusive metallic phase and Anderson insulating phase. Furthermore, an averaged conductance plateau of $e^{2}/h$ emerges in the diffusive metallic phase.