Feature-energy duality of topological boundary states in multilayer quantum spin Hall insulator
arxiv(2023)
摘要
Gapless topological boundary states characterize nontrivial topological
phases arising from the bulk-boundary correspondence in symmetry-protected
topological materials, such as the emergence of helical edge states in a
two-dimensional ℤ_2 topological insulator. However, the
incorporation of symmetry-breaking perturbation terms in the Hamiltonian leads
to the gapping of these edge bands, resulting in missing these crucial
topological boundary states. In this work, we systematically investigate the
robustness of bulk-boundary correspondence in the quantum spin Hall insulator
via recently introduced feature spectrum topology. Our findings present a
comprehensive understanding of feature-energy duality, illustrating that the
aggregate number of gapless edge states in the energy-momentum (E-k) map
and the non-trivial edge states in the Ŝ_z feature spectrum equals the
spin Chern number of multilayer quantum spin Hall insulator. We identify a van
der Waals material bismuth bromide (Bi_4Br_4) as a promising candidate
through first-principles calculations. Our work not only unravels the
intricacies of bulk-boundary correspondence but also charts a course for
exploring quantum spin Hall insulators with high spin-Chern number.
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