Interference in spin-orbit coupled transverse magnetic focusing: Emergent phase due to in-plane magnetic fields

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.