Multimode electron transport through quantum waveguides with spin-orbit interaction modulation: Applications of the scattering matrix formalism

Abstract

We present a formulation of the scattering matrix method for spin-dependent electron transport in a quantum waveguide with spin-orbit interaction (SOI). All the required Hamiltonian matrices needed in the implementation of the formulation are represented in a basis of the transverse spatial eigenstates and the spin eigenstates of the leads. Thus the method has great flexibility and can be easily applied to systems with complex geometrical structure, potential distribution, and SOI strength profile. Also, the method is numerically stable and can be used to treat spin-dependent multisubband scattering processes accurately. We have applied the method to the spin-dependent electron transport in quasi-one-dimensional (Q1D) conductors, with a region of the Rashba SOI of uniform strength and with a region containing a Rashba SOI superlattice, made from a semiconductor heterostructure. The total conductance, spin-dependent conductances, and spin polarization of the system are calculated for a fully spin-polarized electron beam injected from a lead into the SOI region. For the Q1D conductor with a single region of the Rashba SOI, it is found that when the Fermi energy is set at a value, for which the total conductance is at a plateau, the spin-dependent conductances show regular oscillations with increasing SOI strength. This is approximately true even when the total conductance is at a high plateau and thus multiple subbands in the waveguide are open for conduction. However, when the Fermi energy is set at a value close to the onset of a subband (with the subband index $n\ensuremath{\geqslant}2$), the spin-polarized conductances plotted against the SOI strength and the SOI region length show sharp resonance features or complex fluctuations. These irregular conductance characteristics arise from SOI-induced strong coupling between subbands. For the Q1D conductor modulated by an array of strong Rashba SOI stripes, the total conductance shows regular superlattice behavior, while the spin-dependent conductances show complex behavior with regions of slow oscillations and regions of rapid oscillations. As in the Q1D conductor with a single SOI region, the slow oscillations are found in the energy regions where the total conductance is at plateaus. However, the rapid oscillations appear at energies close to the onsets of subbands with the subband index $n\ensuremath{\geqslant}2$. These oscillations originate from strong spin scattering by localized states formed in the SOI-modulated superlattice region.