Disorder-induced quantum phase transitions in three-dimensional second-order topological insulators

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.

Hermitian chiral boundary states in non-Hermitian topological insulators

“…Model (5) also supports Hermitian helical hinge states with valley-momentum locking when 0 < m < 1 − b [84]. T for Hermitian helical hinge states is quantized (to 2) for iκ 3 Γ 13 , irrelevant to the value of κ 3 , see Fig.…”

“…m and b are the masses that control the band inversions of bulk states and surface states, respectively. For 0 < b < 1 and 1 + b < m < 3 − b, the Hermitian part of model ( 5) is a reflection-symmetric 3DSOTI with the reflection plane of y = 0 [84]. If model ( 5) is in a cubic lattice of size L × √ 2L × √ 2L with OBCs on surfaces perpendicular to (100), (01 1), (011), chiral hinge states will appear at the hinges when two surfaces meet at the reflection plane, e.g., y = 0, z = ±L.…”

Topological Phase Transitions and Evolution of Boundary States Induced by Zeeman Fields in Second-Order Topological Insulators

“…On the other hand, bound states with different dimensions can coexist in the same system [36], which may result in novel responses absent in conventional topological phases. The higher-order topology also enriches the possibility of topological phase transitions [37][38][39][40][41][42]. With the advent of higherorder topology, topological phase transitions can happen not only between the different topological sectors of a topological phase following Z or Z 2 classification [43,44], but also between phases with different orders in topology [37].…”

Coulomb Instabilities of a Three-Dimensional Higher-Order Topological Insulator

“…This raises the concerns on the stability of higher-order topological insulators against, e.g. disorder [41][42][43]. More importantly, it is still unknown whether higher-order topological insulators can survive a more intrinsic presence in electronic systems, the Coulomb interaction [44][45][46][47][48][49][50][51][52][53][54][55].…”