The influence of the discretized Rashba spin-orbit interaction on the Harper model

TL;DR

This paper investigates how discretized Rashba spin-orbit interaction modifies the energy spectrum of the Harper model, revealing significant spin-dependent effects and potential spin-filtering phenomena through analytical and numerical methods.

Contribution

It introduces a discretized spin-orbit interaction into the Harper model and analyzes its impact on energy bands and spin-dependent properties using transfer matrix methods.

Findings

Significant spin-dependent splitting of energy bands.

Manifestations of spin-filtering and spin correlations.

Alteration of the self-similar Harper spectrum.

Abstract

The movement of the electrons under the simultaneous influence of a scalar periodic potential and of a uniform transversal magnetic field is described by the well-known second order discrete Harper equation. This equation originates from a two-dimensional energy dispersion law under the minimal substitution. Here one deals with the Harper model under the additional influence of the discretized spin orbit interaction. Converting the spin-orbit interaction in terms of discrete derivatives opens the way for analytical and numerical studies. One finds coupled equations for the spin dependent wave functions, which leads to an appreciable alteration of the nested energy subbands characterizing the self-similar structure of the usual Harper spectrum. To this aim the transfer matrix method has been applied to selected spin-up and spin-down wavefunctions. Accordingly, very manifestations of spinfiltering and of spin correlations are accounted for. Our energy-bands calculations show that the splitting effect implemented by such wavefunctions is appreciable.