Self-Consistent Model for Gate Control of Narrow-, Broken-, and Inverted-Gap (Topological) Heterostructures

TL;DR

This paper develops a self-consistent model using the full-band envelope-function approach to accurately predict the electronic properties of narrow-, broken-, and inverted-gap heterostructures, especially where traditional methods fail.

Contribution

It introduces a numerically stable, open-source implementation of the full-band envelope-function approach for modeling complex heterostructures, improving upon conventional methods.

Findings

Accurately models subband density evolution in HgTe quantum wells.

Demonstrates the failure of the wide-gap approach in certain topological systems.

Provides a tool for better understanding of narrow- and inverted-gap materials.

Abstract

Even small electrostatic potentials can dramatically influence the band structure of narrow-, broken-, and inverted-gap materials. A quantitative understanding often necessitates a self-consistent Hartree approach. The valence and conduction band states strongly hybridize and/or cross in these systems. This makes distinguishing between electrons and holes impossible and the assumption of a flat charge carrier distribution at the charge neutrality point hard to justify. Consequently the wide-gap approach often fails in these systems. An alternative is the full-band envelope-function approach by Andlauer and Vogl, which has been implemented into the open-source software package kdotpy (arXiv:2407.12651). We show that this approach and implementation gives numerically stable and quantitatively accurate results where the conventional method fails by modeling the experimental subband density evolution with top-gate voltage in thick (26 nm - 110 nm), topologically inverted HgTe quantum wells. We expect our openly-available implementation to greatly benefit the investigation of narrow-, broken-, and inverted-gap materials.