Low-energy modeling of three-dimensional topological insulator nanostructures

We develop an accurate nanoelectronic modeling approach for realistic three-dimensional topological in-
sulator nanostructures and investigate their low-energy surface-state spectrum. Starting from the commonly
considered four-band k · p bulk model Hamiltonian for the Bi2 Se3 family of topological insulators, we derive
new parameter sets for Bi2 Se3 , Bi2 Te3 , and Sb2 Te3 . We consider a fitting strategy applied to ab initio band
structures around the  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 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.