Quantum states and optics in a {\it p}-type heterojunction with lateral surface quantum dot or antidot superlattice subjected to perpendicular magnetic field

TL;DR

This paper investigates quantum states and optical properties of holes in a p-type heterojunction with a lateral superlattice under a magnetic field, solving the Azbel'-Hofstadter problem for complex valence bands and analyzing optical transitions.

Contribution

It presents the first solution of the Azbel'-Hofstadter problem for holes in a complex valence band using the 4x4 Luttinger Hamiltonian and explores optical transition probabilities.

Findings

Distinct hole spectra compared to electron Hofstadter butterfly.

Spin-orbit interaction significantly affects wavefunctions and energy spectrum.

Parameters for experimental observation of split Landau levels are identified.

Abstract

The studies of quantum states and optics in a {\it p}-type heterojunction with lateral surface quantum dot (antidot) superlattice and in the presence of perpendicular magnetic field are performed. For the first time the Azbel'-- Hofstadter problem is solved for holes in a complicated valence band described by the $4 \times 4$ Luttinger Hamiltonian. The set of magnetic subbands is obtained for separate hole levels in a wide interval of magnetic field. We found remarkable differences between hole spectra and the Hofstadter "butterfly" for electrons. The influence of the spin-orbit interaction onto wavefunctions and energy spectrum has been investigated. The probabilities of optical transitions between quantum states in the valence band and donors located in the monolayer inside the heterojunction are calculated. The set of parameters (superlattice periods, amplitude of periodic potential, magnitude of magnetic field, etc.) required for experimental observation of splitted hole Landau levels is determined.