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  • Letter
  • Open Access

Topological blocking at the Bi(111) surface due to surface relaxation

Kazuki Koie1,2, Rikako Yaguchi1, and Yuki Fuseya1,2

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Phys. Rev. B 111, L201303 – Published 15 May, 2025

DOI: https://doi.org/10.1103/PhysRevB.111.L201303

Abstract

The topological characteristics of Bi and its alloys with Sb have fueled intense debate since the prediction of three-dimensional topological insulators. However, a definitive resolution has not been reached to date. Here, we provide theoretical evidence that surface relaxation conceals the underlying bulk topology of pure Bi. Using density-functional-theory calculations for thin Bi(111) films (up to 17 bilayers), we first demonstrate a substantial interbilayer expansion near the surface. Motivated by this finding, we extend our analysis to thick Bi(111) films (up to 250 bilayers) incorporating relaxation layers, within the framework of a empirical tight-binding model with spin-orbit coupling. Our results reveal that these relaxation layers topologically block the emergence of a surface state and significantly suppress the one-particle spectrum of surface states at the M¯ point, thereby obscuring the experimental identification of Bi's topological properties. This phenomenon, which we term “topological blocking,” provides crucial insights into the long-standing difficulty of observing surface states of Bi(111) at the M¯ point. Furthermore, it establishes a framework for understanding and predicting the topological behavior in systems where surface relaxation disrupts the bulk-edge correspondence.

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Phys. Rev. B 111, L201303– Published 15 May, 2025
  • Received 26 November 2024
  • Revised 8 April 2025
  • Accepted 9 April 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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