Anisotropic magnetoresistance of 2D Rashba films with in-plane Zeeman field and short-range disorder

Abstract

We study the dc conductivity of a continuum two-dimensional Rashba film with an in-plane Zeeman field and delta-correlated scalar disorder. 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 mechanism is geometric. 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 area invariance controls transport: once the leading impurity ladder reduces the current vertex to the parabolic velocity, the diagonal intraband Kubo conductivity collapses onto the two-sheet occupied area and is field independent as well. The result settles the short-range-disorder quasiclassical problem: point-like nonmagnetic impurities do not produce AMR in this model. A nonzero AMR requires physics beyond this quasiclassical short-range-disorder mechanism.