# Analytical solution of narrow quantum rings with general Rashba and Dresselhaus spin-orbit couplings

## TL;DR

This paper provides an exact analytical solution for the energy levels and eigenstates of narrow semiconductor quantum rings with combined Rashba and Dresselhaus spin-orbit interactions, covering all coupling strengths.

## Contribution

It derives a general, exact solution for quantum rings with arbitrary Rashba and Dresselhaus couplings, unifying previous special cases without approximations.

## Key findings

- Eigenstates expressed as Mathieu functions and spinors
- Solution valid for any coupling strength combination
- Reduces to known solutions for special cases

## Abstract

We solve analytically the energy eigenvalue problem of narrow semiconductor quantum rings with a general spin-orbit term that includes as a special case the Rashba and Dresselhaus interactions acting simultaneously. The eigenstates and eigenenergies of the system are found for arbitrary values of the spin-orbit coupling constants without making use of approximations. The general eigenstates are expressed as products of a scalar Mathieu function and a spinor factor which is periodic or pseudo-periodic on the ring. Our general solution reduces to the previously found solutions for particular combinations of the Rashba and Dresselhaus couplings, like the well-studied cases of Rashba-only and of equal coupling constants.