Topology of Bi$_2$Se$_3$ nanosheets

• URL: http://arxiv.org/abs/2309.02792v5
• Date: Thu, 28 Mar 2024 10:14:12 GMT
• Title: Topology of Bi$_2$Se$_3$ nanosheets
• Authors: Lucas Maisel Licerán, Sebastiaan Koerhuis, Daniel Vanmaekelbergh, Henk Stoof,
• Abstract summary: Recently, quantum spin-Hall edge channels of two-dimensional colloidal nanocrystals of the topological insulator Bi$$Se$_3$ were observed directly. We reconsider the four-band effective model which has been traditionally employed in the past to describe thin nanosheets of this material. We find that the eight-band model not only captures most of the experimental observations, but also agrees with previous first-principles calculations of the $mathbbZ_2$ in inversion in thin films of varying thickness.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Recently, the quantum spin-Hall edge channels of two-dimensional colloidal nanocrystals of the topological insulator Bi$_2$Se$_3$ were observed directly. Motivated by this development, we reconsider the four-band effective model which has been traditionally employed in the past to describe thin nanosheets of this material. Derived from a three-dimensional $\boldsymbol{k} \boldsymbol{\cdot} \boldsymbol{p}$ model, it physically describes the top and bottom electronic surface states at the $\Gamma$ point that become gapped due to the material's small thickness. However, we find that the four-band model for the surface states alone, as derived directly from the three-dimensional theory, is inadequate for the description of thin films of a few quintuple layers and even yields an incorrect topological invariant within a significant range of thicknesses. To address this limitation we propose an eight-band model which, in addition to the surface states, also incorporates the set of bulk states closest to the Fermi level. We find that the eight-band model not only captures most of the experimental observations, but also agrees with previous first-principles calculations of the $\mathbb{Z}_{2}$ invariant in thin films of varying thickness. The band inversion around the $\Gamma$ point, which endows the surface-like bands with topology, is shown to be enabled by the presence of the additional bulk-like states without requiring any reparametrization of the resulting effective Hamiltonian.

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