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

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.

arXiv comment16 pages, 4 figures

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Cited by in corpus (3)

• Spin-texture topology in curved circuits driven by spin-orbit interactions
• A quantum-network approach to spin interferometry driven by Abelian and non-Abelian fields
• Magnetic switching of spin-scattering centers in Dresselhaus [110] circuits