Topological invariant in three-dimensional band insulators with disorder

Abstract

Topological insulators in three dimensions are characterized by a Z2-valued topological invariant, which consists of a strong index and three weak indices. In the presence of disorder, only the strong index survives. This paper studies the topological invariant in disordered three-dimensional system by viewing it as a super-cell of an infinite periodic system. As an application of this method we show that the strong index becomes non-trivial when strong enough disorder is introduced into a trivial insulator with spin-orbit coupling, realizing a strong topological Anderson insulator. We also numerically extract the gap range and determine the phase boundaries of this topological phase, which ?ts well with those obtained from self-consistent Born approximation (SCBA) and the transport calculations.

5 pages and 5 figures; minor changes and publishing version

References in corpus (5)

• Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
• Topological Insulators with Inversion Symmetry
• Discovery (theoretical prediction and experimental observation) of a large-gap topological-insulator class with spin-polarized single-Dirac-cone on the surface
• Topological Field Theory of Time-Reversal Invariant Insulators
• Topological Anderson Insulator

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• Z2 phase diagram of three-dimensional disordered topological insulator via scattering matrix approach
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• Evolutions of helical edge states in disordered HgTe/CdTe quantum wells
• Topological enhancement of non-normality in non-Hermitian skin effects
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• Topological Anderson insulators in an Ammann-Beenker quasicrystal and a snub-square crystal
• Dirac surface states in magnonic analogs of topological crystalline insulators
• A New Numerical Method for ${\mathbb{Z}}_2$ Topological Insulators with Strong Disorder
• Density of states at disorder-induced phase transitions in a multichannel Majorana wire
• Single-point spin Chern number in a supercell framework
• Impact of magnetic dopants on magnetic and topological phases in magnetic topological insulators