AUTHOR=Kulinskii Vladimi L., Panchenko Dmitry Yu
TITLE=Point-Like Rashba Interactions as Singular Self-Adjoint Extensions of the Schrödinger Operator in One Dimension
JOURNAL=Frontiers in Physics
VOLUME=7
YEAR=2019
PAGES=44
URL=https://www.frontiersin.org/article/10.3389/fphy.2019.00044
DOI=10.3389/fphy.2019.00044
ISSN=2296-424X
ABSTRACT=We consider singular self-adjoint extensions for the Schrödinger operator of spin-1/2 particle in one dimension. The corresponding boundary conditions at a singular point are obtained. There are boundary conditions with the spin-flip mechanism, i.e., for these point-like interactions the spin operator does not commute with the Hamiltonian. One of these extensions is the analog of zero-range δ-potential. The other one is the analog of so called δ^{(1)}-interaction. We show that in physical terms such contact interactions can be identified as the point-like analogs of Rashba Hamiltonian (spin-momentum coupling) due to material heterogeneity of different types. The dependence of the transmission coefficient of some simple devices on the strength of the Rashba coupling parameter is discussed. Additionally, we show how these boundary conditions can be obtained from the Dirac Hamiltonian in the non-relativistic limit.