Anisotropic magnetoresistance of two-dimensional Rashba systems with in-plane Zeeman field and point-like disorder

We study the dc conductivity of a two-dimensional Rashba system with an in-plane Zeeman field and delta-correlated scalar disorder. We show that, although the field deforms the two helicity Fermi contours and rotates the spin texture, it does not produce anisotropic magnetoresistance in the leading quasiclassical conductivity. The result follows from a geometric identity for the total area occupied by the two helicity sheets. A density Ward identity fixes the spin-vector part of the Born self-energy to the derivative of the total particle density with respect to the field. This derivative vanishes, because the total area enclosed by the two Rashba-Zeeman sheets is independent of the in-plane field. The Born self-energy is therefore scalar and field independent, and the quasiparticle lifetime stays isotropic. The same occupied-area identity controls transport: the leading impurity ladder reduces the current vertex to the parabolic velocity, and the diagonal intraband Kubo conductivity collapses onto the two-sheet occupied area and is field independent as well. Thus, point-like nonmagnetic impurities produce neither angular anisotropy nor field-magnitude dependence in the leading diagonal two-sheet quasiclassical conductivity. Any residual AMR from delta-correlated disorder must originate from corrections outside this sector.