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 paper, 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.