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

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Summary

A new full-band envelope-function approach accurately models semiconductor band structures where effective-mass theory fails. This method, implemented in kdotpy, is crucial for understanding narrow-gap materials.

Keywords:
Narrow-gap semiconductorsband structure modelingheterostructuresk·p theoryself-consistent Hartreetopological insulators

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Area of Science:

  • Condensed Matter Physics
  • Semiconductor Physics

Background:

  • Electrostatic potentials significantly alter narrow-gap semiconductor band structures.
  • Conventional effective-mass theory fails due to strong band hybridization and crossing.

Purpose of the Study:

  • To implement and validate a full-band envelope-function approach for semiconductor band structure calculations.
  • To provide a numerically stable and accurate alternative to conventional methods.

Main Methods:

  • Implementation of the full-band envelope-function approach into the kdotpy software package.
  • Self-consistent Hartree calculations for quantitative analysis.
  • Modeling experimental subband density evolution in HgTe quantum wells.

Main Results:

  • The full-band envelope-function approach yields numerically stable and accurate results.
  • Excellent agreement was found with experimental data for HgTe quantum wells.
  • The method succeeds where effective-mass theory fails.

Conclusions:

  • The developed full-band envelope-function approach is a reliable tool for narrow-, broken-, and inverted-gap materials.
  • The open-source implementation in kdotpy will advance research in these semiconductor systems.