Title: 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 Wc1 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 e2/h through its chiral hinge states. The gap of the bulk states closes at a higher critical disorder Wc2, and the system is a disordered 3DFOTI in a lower intermediate disorder between Wc1 and Wc2 in which electron conduction is through the topological surface states. The system becomes a DM in a higher intermediate disorder between Wc2 and Wc3 above which the states at the Fermi level are localized. It undergoes a normal three-dimensional metal-to-insulator transition at Wc3 and becomes the conventional AI for W>Wc3. 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.2 MoreReceived 30 May 2020Accepted 1 September 2020DOI:https://doi.org/10.1103/PhysRevResearch.2.033521Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasAnderson localizationEdge statesTopological phase transitionTopological phases of matterTechniquesAnderson impurity modelBloch wave theoryLandauer formulaTight-binding modelCondensed Matter, Materials & Applied Physics