Rashba billiards

TL;DR

This paper analyzes the energy levels and spin properties of electrons in two-dimensional Rashba billiards, revealing unique spectral features and spin structures due to spin-orbit coupling.

Contribution

It provides an analytical Green's function for Rashba billiards and explores their density of states, energy spectrum, and spin structure, highlighting differences from spin-rotational invariant systems.

Findings

Rashba billiards have a always negative energy spectrum.

Density of states exhibits singular behavior at certain negative energies.

Eigenstates show a finite out-of-plane spin projection.

Abstract

We study the energy levels of non-interacting electrons confined to move in two-dimensional billiard regions and having a spin-dependent dynamics due to a finite Rashba spin splitting. The Green's function for such Rashba billiards is constructed analytically and used to find the area and perimeter contributions to the density of states, as well as the smooth counting function. We show that, in contrast to systems with spin-rotational invariance, Rashba billiards always possess a negative energy spectrum. A semi-classical analysis is presented to interpret the singular behavior of the density of states at certain negative energies. Our detailed analysis of the spin structure of Rashba billiards reveals a finite out-of-plane spin projection for electron eigenstates.