Formal integration of electron scattering processes via separation of dynamical and geometric contributions

By decoupling the geometric from the dynamical contributions in the scattering processes, we develop a method to compute the scattering matrix of electrons in a one-dimensional coherent conductor connected to two electrodes. In particular, we demonstrate that, in the high-energy regime, the transmission matrix converges to the Berry operator of the system. We showcase the method through several examples featuring different in-plane magnetic field profiles. Notably, our results reveal the possibility of achieving near-perfect spin-flip transmission, highlighting potential applications in spintronics.