Degenerate states of narrow semiconductor rings in the presence of spin orbit coupling: Role of time-reversal and large gauge transformations

TL;DR

This paper investigates the degeneracy of electron states in narrow semiconductor rings with spin-orbit coupling, revealing symmetry properties and the effects of magnetic flux, disorder, and Zeeman interaction.

Contribution

It demonstrates that eigenstates are doubly degenerate under certain conditions due to symmetry, even with disorder, and analyzes how Zeeman interaction affects these degeneracies.

Findings

Eigenstates are doubly degenerate with integer or half-integer flux.

Wavefunctions of degenerate pairs are related by symmetry operations.

Degeneracies are partially lifted by Zeeman interaction.

Abstract

The electron Hamiltonian of narrow semiconductor rings with the Rashba and Dresselhaus spin orbit terms is invariant under time-reversal operation followed by a large gauge transformation. We find that all the eigenstates are doubly degenerate when integer or half-integer quantum fluxes thread the quantum ring. The wavefunctions of a degenerate pair are related to each other by the symmetry operation. These results are valid even in the presence of a disorder potential. When the Zeeman term is present only some of these degenerate levels anticross.