Hyperfine interactions in two-dimensional HgTe topological insulators

TL;DR

This paper analyzes the hyperfine interactions in HgTe quantum wells, a key 2D topological insulator, providing detailed models and results that highlight anisotropy and the dominance of P-like state contributions in edge states.

Contribution

It offers a comprehensive benchmark of hyperfine interactions within the BHZ model for HgTe, including their forms, magnitudes, and dependence on sample orientation and state composition.

Findings

Hyperfine interactions are anisotropic and depend on edge orientation.

P-like state contributions can dominate over S-like states in certain conditions.

Provides benchmark results for hyperfine interactions in HgTe nanostructures.

Abstract

We study the hyperfine interaction between the nuclear spins and the electrons in a HgTe quantum well, which is the prime experimentally realized example of a two-dimensional topological insulator. The hyperfine interaction is a naturally present, internal source of broken time-reversal symmetry from the point of view of the electrons. The HgTe quantum well is described by the so-called Bernevig-Hughes-Zhang (BHZ) model. The basis states of the BHZ model are combinations of both S- and P-like symmetry states, which means that three kinds of hyperfine interactions play a role: (i) The Fermi contact interaction, (ii) the dipole-dipole like coupling and (iii) the electron orbital to nuclear-spin coupling. We provide benchmark results for the forms and magnitudes of these hyperfine interactions within the BHZ model, which give a good starting point for evaluating hyperfine interactions in any HgTe nanostructure. We apply our results to the helical edge states of a HgTe two-dimensional topological insulator and show how their total hyperfine interaction becomes anisotropic and dependent on the orientation of the sample edge within the plane. Moreover, for the helical edge states the hyperfine interactions due to the P-like states can dominate over the S-like contribution in certain circumstances.