We develop an accurate nanoelectronic modeling approach for realistic three-dimensional topological insulator nanostructures and investigate their low-energy surface-state spectrum. Starting from the commonly considered four-band k⋅p bulk model Hamiltonian for the Bi2Se3 family of topological insulators, we derive new parameter sets for Bi2Se3, Bi2Te3 and Sb2Te3. We consider a fitting strategy applied to \emph{ab initio} band structures around the Γ point that ensures a quantitatively accurate description of the low-energy bulk and surface states, while avoiding the appearance of unphysical low-energy states at higher momenta, something that is not guaranteed by the commonly considered perturbative approach. We analyze the effects that arise in the low-energy spectrum of topological surface states due to band anisotropy and electron-hole asymmetry, yielding Dirac surface states that naturally localize on different side facets. In the thin-film limit, when surface states hybridize through the bulk, we resort to a thin-film model and derive thickness-dependent model parameters from \emph{ab initio} calculations that show good agreement with experimentally resolved band structures, unlike the bulk model that neglects relevant many-body effects in this regime. Our versatile modeling approach offers a reliable starting point for accurate simulations of realistic topological material-based nanoelectronic devices.

This work is supported by the QuantERA grant MAGMA (by the German Research Foundation under grant 491798118, by the National Research Fund Luxembourg under Grant No. INTER/QUANTERA21/16447820/MAGMA, and by MCIN/AEI/10.13039/501100011033 and the European Union NextGenerationEU/PRTR under project PCI2022-132927), and by Germany’s Excellence Strategy – Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1 – 390534769. K.M. and P.R. acknowledge the financial support by the Bavarian Ministry of Economic Affairs, Regional Development and Energy within Bavaria’s High-Tech Agenda Project “Bausteine f¨ur das Quantencomputing auf Basis topologischer Materialien mit experimentellen und theoretischen Ans¨atzen” (Grant No. 07 02/686 58/1/21 1/22 2/23), and K.M. acknowledges the financial support by the Quantum Future project ‘MajoranaChips’ (Grant No. 13N15264) within the funding program Photonic Research Germany.

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