Low-energy modeling of three-dimensional topological insulator nanostructures

Abstract

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 $\mathrm{k}\cdot \mathrm{p}$ bulk model Hamiltonian for the Bi${}_2$Se${}_3$ family of topological insulators, we derive new parameter sets for Bi${}_2$Se${}_3$, Bi${}_2$Te${}_3$ and Sb${}_2$Te${}_3$. We consider a fitting strategy applied to \emph{ab initio} band structures around the $\Gamma$ 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.

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Cited by in corpus (5)

• Optimizing proximitized magnetic topological insulator nanoribbons for Majorana bound states
• Promoted current-induced spin polarization in inversion symmetry broken topological insulator thin films
• Efficient prediction of topological superlattice bands with spin-orbit coupling
• Electrostatic gating and the interference of chiral Majoranas in thin slabs of magnetic topological insulators
• Quasiparticle interference on the surface of Bi${}_2$Se${}_3$ terminated (PbSe)${}_5$(Bi${}_2$Se${}_3$)${}_6$