Electron energy spectrum and density of states for non-symmetric heterostructures in an in-plane magnetic field

TL;DR

This paper investigates how in-plane magnetic fields affect the electron energy spectrum and density of states in non-symmetric heterostructures, considering spin-orbit interactions and boundary conditions, with numerical estimates for specific heterostructures.

Contribution

It introduces a comprehensive analysis of spin-splitting modifications in non-symmetric heterostructures under magnetic fields, accounting for boundary conditions and spin-orbit interactions.

Findings

Modified energy spectra reveal separation of spin-orbit contributions.

Numerical estimates demonstrate effects in doped heterojunctions.

Interplay between Zeeman and spin-orbit effects is significant.

Abstract

Modifications of spin-splitting dispersion relations and density of states for electrons in non-symmetric heterostructures under in-plane magnetic field are studied within the envelope function formalism. Spin-orbit interactions, caused by both a slow potential and the heterojunction potentials (which are described by the boundary conditions) are taken into account. The interplay between these contributions and the magnetic field contribution to the spin-splitting term in the Hamiltonian is essential when energy amount resulting from the Zeeman and spin-orbit coupling are of the same order. Such modifications of the energy spectra allow us to separate the spin-orbit splitting contributions due to a slow potential and due to the heterojunctions. Numerical estimates for selectively-doped heterojunction and quantum well with narrow-gap region of electron localization are performed.