Scattering matrix method for multimode electron transport through quantum wires under a local magnetic field modulation and spin-orbit interaction

A generalized scattering matrix method is presented for spin-dependent electron transport in a quantum waveguide under the modulations of local magnetic field and/or spin-orbit interaction (SOI). All the required Hamiltonian matrices are expressed in terms of a common basis spanned by the products of the transverse spatial eigenstates and the spin eigenstates of the leads. In the formulation we have included an additional SOI term caused by an in-plane electric potential modulation and have assumed a free choice of magnetic vector potential. Thus the method can easily be applied to two-dimensional electron gas systems with complex geometrical structure, SOI strength profile, distributions of electric potential and magnetic field, etc. The method is numerically stable and can be used to treat accurately spin-dependent, multisubband, electron scattering processes. As an application, the method has been implemented for a Rashba SOI wire subject to a local magnetic field generated by a single ferromagnetic metal stripe on top. In the absence of the magnetic field, the conductance of electrons passing through the SOI region shows a series of Fano-resonance type dips in the vicinity of the onsets of subbands (with the subband index n >= 2). When the local magnetic field is present, the degeneracy of SOI-induced bound states is removed, leading to splittings of these conductance dips. At two split conductance dips originated from the same degenerate dip, a remarkable difference is found in the spatial distribution of spin-projected probability and in the spatial distribution of local spin polarization. It is seen that for a Rashba wire a Hall-like spin accumulation appears at the conductance dips at zero magnetic field. However, in the presence of a local magnetic field a separation of opposite spins along the transport direction is observed in the Rashba wire. In contrast, the zitterbewegung oscillations can show up, when the conductance is at a plateau, and disappear, when the conductance is at a Fano-resonance type dip, regardless the presence of the local magnetic field.