A "hybrid plane" with spin-orbit interaction

Abstract

In this paper we attempt to reconstruct one of the last projects of Volodya Geyler which remained unfinished. We study motion of a quantum particle in the plane to which a halfline lead is attached assuming that the particle has spin $\frac{1}{2}$ and the plane component of the Hamiltonian contains a spin-orbit interaction of either Rashba or Dresselhaus type. We construct the class of admissible Hamiltonians and derive an explicit expression for the Green function applying it to the scattering in such a system.

LaTeX, 9 pages; in memoriam Vladimir A. Geyler (1943-2007)

References in corpus (3)

• Large gaps in point-coupled periodic systems of manifolds
• A remark on Krein's resolvent formula and boundary conditions
• Explicit Green functions for spin-orbit Hamiltonians

Cited by in corpus (6)

• Finite element method to solve the spectral problem for arbitrary self-adjoint extensions of the Laplace-Beltrami operator on manifolds with a boundary
• Resonances in Models of Spin Dependent Point Interactions
• Dynamics of an electron confined to a "hybrid plane" and interacting with a magnetic field
• A quantum hybrid with a thin antenna at the vertex of a wedge
• Spectrum of a family of spin-orbit coupled Hamiltonians with singular perturbation
• Computation of unitary group for the Rashba spin-orbit coupled operator, with application to point-interactions