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

Even small electrostatic potentials can dramatically influence the band structure of narrow-, broken-, and inverted-gap (topological) materials. A quantitative understanding often necessitates a self-consistent Hartree approach. However, the conventional wide-gap approach often fails in these systems as it relies on a clear separation between electrons and holes, and on the assumption of a flat charge carrier distribution at the charge neutrality point. An alternative is the full-band envelope-function approach [Andlauer and Vogl, Phys. Rev. B 80, 035304 (2009)], which we have implemented into the open-source band structure calculation package kdotpy [Beugeling et al., SciPost Phys. Codebases, 47 (2025)]. By modeling the subband density evolution with top-gate voltage in magnetotransport experiments on thick (26 – 110nm) tensile strained HgTe quantum wells [Hofer et al., arXiv:2510.18778 (2025)], a realization of the semimetallic three-dimensional topological insulator (3DTI) phase of the material, we show that this approach and implementation gives numerically stable and quantitatively accurate results where the conventional wide-gap approach fails.