Point-Like Rashba Interactions as Singular Self-Adjoint Extensions of the Schrödinger Operator in One Dimension
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Дата
2019
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Анотація
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.
Опис
Ключові слова
Schrödinger operator, self-adjoint extension, Rashba interaction, spin-flip, Pauli Hamiltonian, Dirac Hamiltonian
Бібліографічний опис
Frontiers in Physics