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 a three-dimensional chiral second-order topological insulator in the presence of disorder. Our results show that, by increasing disorder strength, the nonzero densities of states of the side surface and bulk emerge at 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., ${\mathrm{\ensuremath{\Gamma}}}_{3}$. The closing of the side surface gap or bulk gap is ascribed to a significant decrease of the elastic mean free time of quasiparticles. Based on the scaling theory of localization length, we obtain two fixed points as two critical disorder strengths for any given Fermi energy, indicating that the three-dimensional chiral second-order topological insulator gradually enters the diffusive metallic phase and Anderson insulating phase, respectively. In the end, a global phase diagram is provided to clearly demonstrate the evolution of different phases.