Numerical methods for spin-dependent transport calculations and spin bound states analysis in Rashba waveguides

TL;DR

This paper develops numerical methods for quantum spin-dependent transport in Rashba waveguides, enabling analysis of bound states and transport properties in systems with complex geometries and potential profiles.

Contribution

It introduces hybrid mode-matching schemes for spin-dependent transport calculations, including eigenmode computation with quadratic eigenproblems and bound state analysis.

Findings

Effective numerical methods for variable geometry systems

Successful computation of Fano-Rashba bound states

Acceleration of calculations using sparse matrix techniques

Abstract

Numerical methods are developed in the quantum transport calculations for electron in the waveguides with spin-orbital (Rashba) interaction. The methods are based on a hybrid mode-matching scheme in which the wavefunctions are expressed as the superposition of eigenmodes in the lead regions and in the device region the wavefunction is expressed on the discrete basis. Two versions are presented for the lead without and with the Rashba interaction. In the latter case the eigenmodes are obtained from a quadratic eigenproblem calculation. These methods are suitable for the systems with variable geometries or arbitrary potential profiles. The computation can be effectively accelerated by the sparse matrix technique. We also investigate the Fano-Rashba bound states in the Rashba waveguides by some nonlinear eigenstate calculation. This calculation is based on a mode-matching method and self-consistent results are obtained in our calculations.