TY - JOUR

T1 - Elementary models of three-dimensional topological insulators with chiral symmetry

AU - Liu, Donghao

AU - Matveeva, Polina

AU - Gutman, Dmitri

AU - Carr, Sam T.

N1 - Publisher Copyright:
© 2023 American Physical Society.

PY - 2023/7/15

Y1 - 2023/7/15

N2 - We construct a set of lattice models of noninteracting 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 cannot be adiabatically connected.

AB - We construct a set of lattice models of noninteracting 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 cannot be adiabatically connected.

UR - http://www.scopus.com/inward/record.url?scp=85166782659&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.108.035418

DO - 10.1103/PhysRevB.108.035418

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AN - SCOPUS:85166782659

SN - 2469-9950

VL - 108

JO - Physical Review B

JF - Physical Review B

IS - 3

M1 - 035418

ER -