First-principles effective-mass Hamiltonian for semiconductor nanostructures in a magnetic field

TL;DR

This paper derives a comprehensive multi-band effective-mass Hamiltonian for semiconductor nanostructures in magnetic fields, incorporating interface effects and nonlocal potential coupling from first principles.

Contribution

It introduces a novel derivation from first-principles that includes interface terms and magnetic coupling effects previously omitted in nanostructure modeling.

Findings

Includes interface terms in the Hamiltonian

Shows how nonlocal potential couples to magnetic field

Provides analytical expressions for magnetic dipole moments

Abstract

A multi-band effective-mass Hamiltonian is derived for lattice-matched semiconductor nanostructures in a slowly varying external magnetic field. The theory is derived from the first-principles magnetic-field coupling Hamiltonian of Pickard and Mauri, which is applicable to nonlocal norm-conserving pseudopotentials in the local density approximation to density functional theory. The pseudopotential of the nanostructure is treated as a perturbation of a bulk reference crystal, with linear and quadratic response terms included in k.p perturbation theory. The resulting Hamiltonian contains several interface terms that have not been included in previous work on nanostructures in a magnetic field. The derivation provides the first direct analytical expressions showing how the coupling of the nonlocal potential to the magnetic field influences the effective magnetic dipole moment of the electron.