Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators
C. Wang, X. R. Wang
Abstract
Disorder effects on three-dimensional second-order topological insulators (3DSOTIs) are investigated numerically and analytically. The study is based on a tight-binding Hamiltonian for noninteracting electrons on a cubic lattice with a reflection symmetry that supports a 3DSOTI in the absence of disorder. Interestingly, unlike the disorder effects on a topological trivial system that can only be either a diffusive metal (DM) or an Anderson insulator (AI), disorders can sequentially induce four phases of 3DSOTIs, three-dimensional first-order topological insulators (3DFOTIs), DMs, and AIs. At a weak disorder when the on-site random potential of strength W is below a low critical value W c1 at which the gap of surface states closes while the bulk sates are still gapped, the system is a disordered 3DSOTI characterized by a constant density of states and a quantized integer conductance of e 2 /h through its chiral hinge states. The gap of the bulk states closes at a higher critical disorder W c2 , and the system is a disordered 3DFOTI in a lower intermediate disorder between W c1 and W c2 in which electron conduction is through the topological surface states. The system becomes a DM in a higher intermediate disorder between W c2 and W c3 above which the states at the Fermi level are localized. It undergoes a normal three-dimensional metal-to-insulator transition at W c3 and becomes the conventional AI for W > W c3 . The self-consistent Born approximation allows one to see how the density of bulk states and the Dirac mass are modified by the on-site disorders.