Periodic Structures with Rashba Interaction in Magnetic Field

TL;DR

This paper investigates the electronic and spin properties of particles in a periodic potential with Rashba spin-orbit interaction under magnetic fields, revealing band structures, symmetry breaking, and zero modes akin to graphene.

Contribution

It explicitly determines the band structures and Bloch spinors for such systems, analyzing symmetry breaking, polarization conservation, and zero-energy modes in various magnetic field regimes.

Findings

Explicit band structures and Bloch spinors derived.

Polarization symmetry broken in certain regimes.

Zero-energy modes similar to graphene's Dirac fermions identified.

Abstract

We analyze the behaviour of a system of particles living on a periodic crystal in the presence of a magnetic field B. This can be done by involving a periodic potential U(x) and the Rashba interaction of coupling constant k_{so}. By resorting the corresponding spectrum, we explicitly determine the band structures and the Bloch spinors. These allow us to discuss the system symmetries in terms of the polarizations where they are shown to be broken. The dynamical spin will be studied by calculating different quantities. In the limits: k_{so} and U(x)=0, we analyze again the system by deriving different results. Considering the strong $B$ case, we obtain an interesting result that is the conservation of the polarizations. Analyzing the critical point \lambda_{k,\sigma}=\pm\sq{1\over 2}, we show that the Hilbert space associated to the spectrum in z-direction has a zero mode energy similar to that of massless Dirac fermions in graphene. Finally, we give the resulting energy spectrum when B=0 and U(x) is arbitrary.