Dirac-Weyl electrons in a periodic spin-orbit potential

TL;DR

This paper explores how spatially modulated spin-orbit interactions in graphene-like structures influence electronic band structures, deriving an analytic condition to estimate energy gaps and analyzing effects of lattice orientation.

Contribution

It introduces an analytic band condition for SU(2)xSU(2) super-structures with modulated spin-orbit interactions, providing new insights into gap formation and band structure dependence.

Findings

Derived an analytic band condition for modulated spin-orbit structures.

Estimated energy gap sizes due to avoided band crossings.

Analyzed band structure variations with lattice orientation.

Abstract

Graphene super-structures have been widely studied but the original structure of the SU(2) Hamiltonian was never modified. We study SU(2)xSU(2) super-structures arising from spatial modulation of spin-orbit interactions and derive an analytic band condition for a lattice vector along the direction of modulation of the spin-orbit interactions. The simple form of this band condition enables us to estimate the size of gaps due to avoided band crossings and gives insight into the dependence of the band structure on the width of the potential. We also investigate band structures for the case where the lattice momentum forms a finite angle with respect to the modulation direction of the spin-orbit interactions.