Magnetic field implementation in multiband k.p Hamiltonians of holes in semiconductor heterostructures

TL;DR

This paper introduces a new method for incorporating magnetic fields into multiband k·p Hamiltonians for holes in semiconductor heterostructures, improving the modeling of magnetic responses in quantum dot molecules.

Contribution

It presents a novel implementation of magnetic fields in k·p Hamiltonians using minimal coupling and envelope functions, enhancing previous models for better accuracy.

Findings

The proposed Hamiltonian outperforms the standard Luttinger model in describing magnetic responses.

Illustrative calculations demonstrate improved modeling of holes in InGaAs quantum dot molecules.

The method advances previous work by integrating magnetic fields more effectively into multiband models.

Abstract

We propose an implementation of external homogeneous magnetic fields in k$\cdot$p Hamiltonians for holes in heterostructures, in which we made use of the minimal coupling prior to introduce the envelope function approximation. Illustrative calculations for holes in InGaAs quantum dot molecules show that the proposed Hamiltonian outperforms standard Luttinger model [Physical Review 102, 1030 (1956)] describing the experimentally observed magnetic response. The present implementation culminates our previous proposal [Phys. Rev. B 82, 155307 (2010)].