Interference in spin-orbit coupled transverse magnetic focusing; emergent phase due to in-plane magnetic fields

TL;DR

This paper investigates how combined Rashba and Zeeman interactions in 2D systems affect transverse magnetic focusing, revealing an emergent phase linear in in-plane magnetic fields that is unique to TMF and absent in Shubnikov de Haas oscillations.

Contribution

It predicts a novel in-plane magnetic field-dependent phase in TMF due to combined spin-orbit and Zeeman effects, distinct from classical trajectories.

Findings

Identifies an additional phase contribution linear in in-plane magnetic field.

Shows this phase is unique to TMF and not present in Shubnikov de Haas oscillations.

Proposes experimental signatures to detect this emergent phase.

Abstract

Spin-orbit (SO) interactions in two dimensional systems split the Fermi surface, and allow for the spatial separation of spin-states via transverse magnetic focusing (TMF). In this work, we consider the case of combined Rashba and Zeeman interactions, which leads to a Fermi surface without cylindrical symmetry. While the classical trajectories are effectively unchanged, we predict an additional contribution to the phase, linear in the applied in-plane magnetic field. We show that this term is unique to TMF, and vanishes for magnetic (Shubnikov de Haas) oscillations. Finally we propose some experimental signatures of this phase.