Pauli Equation on a Curved Surface and Rashba Splitting on a Corrugated Surface

TL;DR

This paper derives the Pauli equation for a spin-1/2 particle on a curved surface under electromagnetic influence and demonstrates Rashba splitting in energy spectra of spherical and corrugated surfaces.

Contribution

It extends the Schrödinger equation on curved surfaces to include spin and relativistic effects, specifically deriving the Pauli equation with applications to Rashba splitting.

Findings

Energy spectra show Rashba splitting on curved surfaces.

Derived equations enable analysis of spin effects on curved geometries.

Applications to sphere and corrugated surface demonstrate practical relevance.

Abstract

The Schroedinger equation for a spinless charged particle on a curved surface under an electromagnetic field has been obtained by adopting a proper gauge which allows the separation of the on-surface and transverse dynamics. [Phys. Rev. Lett. 100 (2008) 230403] As its extension, I provide the Pauli equation for a charged spin-1/2 particle confined to a curved surface under an electromagnetic field. Energy spectra of a sphere and a corrugated surface to which a particle is confined are given as simple applications of the equation. The energy levels obtained exhibit splittings due to the relativistic effect known as the Rashba effect.