Effect of Strong Disorder on 3-Dimensional Chiral Topological Insulators: Phase Diagrams, Maps of the Bulk Invariant and Existence of Topological Extended Bulk States

Abstract

The effect of strong disorder on chiral-symmetric 3-dimensional lattice models is investigated via analytical and numerical methods. The phase diagrams of the models are computed using the non-commutative winding number, as functions of disorder strength and model's parameters. The localized/delocalized characteristic of the quantum states is probed with level statistics analysis. Our study re-confirms the accurate quantization of the non-commutative winding number in the presence of strong disorder, and its effectiveness as a numerical tool. Extended bulk states are detected above and below the Fermi level, which are observed to undergo the so called "levitation and pair annihilation" process when the system is driven through a topological transition. This suggests that the bulk invariant is carried by these extended states, in stark contrast with the 1-dimensional case where the extended states are completely absent and the bulk invariant is carried by the localized states.

8 pages, 9 figures

References in corpus (9)

• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Anderson Insulator
• Entanglement Spectrum of a Disordered Topological Chern Insulator
• Topological Anderson Insulator in Three Dimensions
• The dependence of topological Anderson insulator on the type of disorder
• Lattice model of three-dimensional topological singlet superconductor with time-reversal symmetry
• The edge spectrum of Chern insulators with rough boundaries
• Manifestly gauge independent formulations of the Z2 invariants
• The noncommutative Kubo Formula: Applications to Transport in Disordered Topological Insulators with and without Magnetic Fields

Cited by in corpus (5)

• Disorder Effects in Topological States -- Brief Review of the Recent Developments
• Probing Chern number by opacity and topological phase transition by a nonlocal Chern marker
• Fragility of surface states in non-Wigner Dyson topological insulators
• Dynamics of transmission in disordered topological insulators
• Universal localization-delocalization transition in chiral-symmetric Floquet drives