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 free space 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 corresponding 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 for circular Rashba billiards. Our detailed analysis of the spin structure of circular Rashba billiards reveals a finite out-of-plane spin projection for electron eigenstates.
PACS.73.21.La Quantum dots 71.70.Ej Spin-orbit coupling, Zeeman and Stark splitting, Jahn-Teller effect 05.45.Mt Quantum chaos; semiclassical methods 03.65.Sq Semiclassical theories and applications
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