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Elementary models of three-dimensional topological insulators with chiral symmetry

Liu, Donghao, Matveeva, Polina, Gutman, Dmitri, Carr, Sam T. (2023) Elementary models of three-dimensional topological insulators with chiral symmetry. Physical Review B: Condensed Matter and Materials Physics, 108 . Article Number 035418. ISSN 0163-1829. (doi:10.1103/PhysRevB.108.035418) (KAR id:103114)


We construct a set of lattice models of non-interacting topological insulators with chiral symmetry in three dimensions. We build a model of the topological insulators in the class AIII by coupling lower dimensional models of ℤ classes. By coupling the two AIII models related by time-reversal symmetry we construct other chiral symmetric topological insulators that may also possess additional symmetries (the time-reversal and/or particle-hole).

There are two different chiral symmetry operators for the coupled model, that correspond to two distinct ways of defining the sublattices. The integer topological invariant (the winding number) in case of weak coupling can be either the sum or difference of indices of the basic building blocks, dependent on the preserved chiral symmetry operator. The value of the topological index in case of weak coupling is determined by the chiral symmetry only and does not depend on the presence of other symmetries. For ℤ topological classes AIII, DIII, and CI with chiral symmetry are topologically equivalent, it implies that a smooth transition between the classes can be achieved if it connects the topological sectors with the same winding number. We demonstrate this explicitly by proving that the gapless surface states remain robust in ℤ classes as long as the chiral symmetry is preserved, and the coupling does not close the gap in the bulk. By studying the surface states in ℤ2 topological classes, we show that class CII and AII are distinct, and can not be adiabatically connected.

Item Type: Article
DOI/Identification number: 10.1103/PhysRevB.108.035418
Uncontrolled keywords: quantum materials, topological insulator, theoretical physics
Subjects: Q Science > QC Physics > QC173.45 Condensed Matter
Divisions: Divisions > Division of Natural Sciences > Physics and Astronomy
Funders: University of Kent (
Depositing User: Sam Carr
Date Deposited: 04 Oct 2023 14:10 UTC
Last Modified: 11 Jan 2024 11:30 UTC
Resource URI: (The current URI for this page, for reference purposes)

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