Self-Consistent Electrostatic Modeling of Gated Narrow-Gap Topological Insulators

Even small electrostatic potentials can dramatically influence the band structure of narrow-gap semiconductors. 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 results in failure of the standard effective-mass theory, which relies on a clear distinction between electrons and holes and assumes a flat charge carrier distribution at the charge neutrality point. We show that the alternative full-band envelope-function approach [Andlauer and Vogl Phys. Rev. B, 2009, 80, 035304], which we have implemented into the open-source band structure software package kdotpy [Beugeling et al. SciPost Phys. Codebases, 2025, 47], gives numerically stable and quantitatively accurate results where the conventional method fails. We find excellent agreement in modeling the experimental subband density evolution with top-gate voltage in thick (26 nm-107 nm), topologically inverted HgTe quantum wells. We expect our openly available implementation to greatly benefit the investigation of narrow-, broken-, and inverted-gap materials.