Aharonov-Bohm Physics with Spin I: Geometric Phases in One-dimensional Ballistic Rings

TL;DR

This paper analytically investigates spin-dependent conductance in one-dimensional ballistic rings under inhomogeneous magnetic fields, revealing geometric phase effects and demonstrating control of electron polarization via Aharonov-Bohm flux.

Contribution

It provides a rigorous analytical framework for understanding geometric and Berry phases in non-adiabatic spin transport in ballistic rings, extending previous numerical studies.

Findings

Analytical expressions for magneto-conductance in ballistic rings.

Proof of spin-flip effect enabling polarization control.

Support for numerical results in two-dimensional rings.

Abstract

We analytically calculate the spin-dependent electronic conductance through a one-dimensional ballistic ring in the presence of an inhomogeneous magnetic field and identify signatures of geometric and Berry phases in the general non-adiabatic situation. For an in-plane magnetic field, we rigorously prove the spin-flip effect presented in Frustaglia et al., Phys. Rev. Lett. 87, 256602 (2001), which allows to control and switch the polarization of outgoing electrons by means of an Aharonov-Bohm flux, and derive analytical expressions for the energy-averaged magneto-conductance. Our results support numerical calculations for two-dimensional ballistic rings presented in the second paper (Frustaglia et al., submitted to Phys. Rev. B) of this series.