# Spin geometric-phases in hopping magnetoconductance

## TL;DR

This paper theoretically investigates how spin-related geometric phases influence charge and spin transport in Aharonov-Bohm interferometers with Rashba and Zeeman interactions, revealing non-traditional magnetoconductance behaviors.

## Contribution

It demonstrates the combined effects of Rashba and Zeeman interactions on magnetoconductance, showing a non-periodic, sine-dependent component and analyzing spin polarization directions and non-conserved spin currents.

## Key findings

- Magnetoconductance includes a sine term proportional to Zeeman field.
- The usual phase shift concept in Aharonov-Bohm oscillations does not apply.
- Spin currents are generally not conserved, leading to magnetization in terminals.

## Abstract

We identify theoretically the geometric phases of the electrons' spin that can be detected in measurements of charge and spin transport through Aharonov-Bohm interferometers threaded by a magnetic flux $\Phi$ (in units of the flux quantum) in which both the Rashba spin-orbit and Zeeman interactions are active. We show that the combined effect of these two interactions is to produce a $\sin(\Phi)$ [in addition to the usual $\cos(\Phi)$] dependence of the magnetoconductance, whose amplitude is proportional to the Zeeman field. Therefore the magnetoconductance, though an even function of the magnetic field is not a periodic function of it, and the widely-used concept of a phase shift in the Aharonov-Bohm oscillations, as indicated in previous work, is not applicable. We find the directions of the spin-polarizations in the system, and show that in general the spin currents are not conserved, implying the generation of magnetization in the terminals attached to the interferometer.