Mesoscopic rings with Spin-Orbit interactions

TL;DR

This paper provides a comprehensive, didactic overview of charge and spin equilibrium currents in mesoscopic rings with Spin-Orbit interaction, emphasizing Hamiltonian construction, eigenvalue calculation, and the SU(2) gauge structure.

Contribution

It offers a detailed, pedagogical derivation of spin and charge currents in mesoscopic rings with Spin-Orbit coupling, highlighting the correct Hamiltonian formulation and gauge structure.

Findings

Correct Hamiltonian construction in polar coordinates

Explicit calculation of eigenvalues and eigenfunctions

Analysis of ground state symmetries and spin currents

Abstract

A didactic description of charge and spin equilibrium currents on mesoscopic rings in the presence of Spin-Orbit interaction is presented. Emphasis is made on the non trivial construction of the correct Hamiltonian in polar coordinates, the calculation of eigenvalues and eigenfunctions and the symmetries of the ground state properties. Spin currents are derived following an intuitive definition and then a more thorough derivation is built upon the canonical Lagrangian formulation that emphasizes the SU(2) gauge structure of the transport problem of spin 1/2 fermions in spin-orbit active media. The quantization conditions that follow from the constraint of single-valued Pauli spinors are also discussed. The targeted students are those of a graduate Condensed Matter Physics course.