Band inversion transition in HgTe nanowire grown along the [001] direction

TL;DR

This paper models the electronic structure of HgTe nanowires grown along [001], revealing a topological phase transition characterized by a gap closing and reopening at finite wave vectors, influenced by anisotropic effects.

Contribution

It provides a detailed effective Hamiltonian for [001] HgTe nanowires, including anisotropic and bulk inversion asymmetry effects, and identifies the conditions for a topological transition.

Findings

Gap-closing-and-reopening transition at finite wave vectors

Anisotropic term causes anticrossing of subbands

Bulk inversion asymmetry does not induce spin splitting

Abstract

The low-energy effective Hamiltonian of a cylindrical HgTe nanowire grown along the [001] crystallographic direction is constructed by using the perturbation theory. Both the anisotropic term and the bulk inversion asymmetry term of the Kane model are taken into account. Although the anisotropic term has converted the crossing between the $E_{1}$ and $H_{1}$ subbands into an anticrossing at $k_{z}R\!=\!0$, the gap-closing-and-reopening transition in the subband structure can still occur at finite wave vectors $k_{z}R\!\approx\!\pm0.24$ for critical nanowire radius $R\!\approx\!3.45$ nm. The bulk inversion asymmetry does not contribute to the low-energy effective Hamiltonian, i.e., there is no spin splitting in the $E_{1}$, $H_{1}$, and $H_{2}$ subbands for a [001] oriented cylindrical nanowire.