Harper-Hofstadter problem for 2D electron gas with ${\bf k}$-linear Rashba spin-orbit coupling

TL;DR

This paper investigates the energy spectrum and spin properties of a 2D electron gas with Rashba spin-orbit coupling in a magnetic field, revealing observable spectrum splitting effects due to strong spin-orbit interaction.

Contribution

It provides an analytical and numerical study of the Harper-Hofstadter problem incorporating Rashba spin-orbit coupling, highlighting experimentally observable spectrum splitting.

Findings

Energy spectrum exhibits butterfly-like structure.

Spin density and polarization are calculated.

Spectrum splitting due to Rashba coupling is observable.

Abstract

The Harper-Hofstadter problem for two-dimensional electron gas with Rashba spin-orbit coupling subject to periodic potential and perpendicular magnetic field is studied analytically and numerically. The butterfly-like energy spectrum, spinor wave functions as well as the spin density and average spin polarization are calculated for actual parameters of semiconductor structure. Our calculations show that in two-dimensional electron gas subject to periodic potential and uniform magnetic field the effects of energy spectrum splitting caused by large spin-orbit Rashba coupling can be observed experimentally.