Effective Hamiltonians for Ge/Si core/shell nanowires from higher order perturbation theory

TL;DR

This paper develops higher order perturbation theory models for holes in Ge/Si core/shell nanowires, revealing complex effects like orbital inversions, spin-orbit interactions, and tunable effective masses relevant for quantum device applications.

Contribution

It introduces transferable low-energy models up to fifth order that capture intricate phenomena such as effective mass divergence and symmetry effects in Ge/Si nanowires.

Findings

Orbital inversions occur in low-symmetry growth directions.

Effective mass can diverge, leading to flat bands.

Spin-orbit interactions are reduced due to symmetry effects.

Abstract

We theoretically explore the electronic structure of holes in cylindrical Germanium/Silicon core/shell nanowires using a perturbation theory approach. The approach yields a set of interpretable and transferable effective low-energy models for the lowest few sub-bands up to fifth order for experimentally relevant growth directions. In particular, we are able to resolve higher order cross terms e.g., the dependency of the effective mass on the magnetic field. Our study reveals orbital inversions of the lowest sub-bands for low-symmetry growth directions, leading to significant changes of the lower order effective coefficients. We demonstrate a reduction of the direct Rashba spin-orbit interaction due to competing symmetry effects for low-symmetry growth directions. Finally, we find that the effective mass of the confined holes can diverge yielding quasi flat bands interesting for correlated states. We show how one can tune the effective mass of a single spin band allowing one to tune the effective mass selectively to its divergent points.