Nonlinear Spin and Charge Transport in Bi (111) Thin Films: Influence of Spin-Canted Surface States

The Bi (111) surface is distinguished by its pronounced spin-orbit coupling and strongly anisotropic Fermi surface. While linear magnetoresistance has been extensively investigated, its nonlinear counterpart remains largely unexplored. In this work, we theoretically examine nonreciprocal and nonlinear spin and charge transport in Bi (111) thin films. Using an sp 3 tight-binding model (TBM), we model the film by stacking bilayers along the [111] direction and introduce a perpendicular potential gradient to capture surface inversion asymmetry. Magnetic effects are incorporated through a Zeeman term and Peierls substitution. By deriving retarded and advanced Green's functions from the TBM, we calculate the quadratic conductivity, accounting for both triangular and two-photon contributions. We reveal that nonlinear magnetoresistance depends intricately on the alignment of the electric field, magnetic field, and symmetry axis, stemming from the momentum-space spin distribution of electron and hole pockets. Furthermore, we discuss the connection between nonlinear magnetoresistance and the semi-Dirac dispersion near the high-symmetry M-points.