On the discrete spectrum of spin-orbit Hamiltonians with singular interactions

TL;DR

This paper proves the existence of infinitely many bound states below the continuous spectrum for certain spin-orbit Hamiltonians with measure perturbations, extending previous results to include Rashba and Dresselhaus cases.

Contribution

It provides a variational proof demonstrating the presence of infinitely many bound states for spin-orbit Hamiltonians with singular interactions, broadening the scope of earlier findings.

Findings

Infinitely many bound states exist below the continuous spectrum.

Results apply to Rashba and Dresselhaus spin-orbit Hamiltonians.

Extension of previous work to measure potentials.

Abstract

We give a variational proof of the existence of infinitely many bound states below the continuous spectrum for spin-orbit Hamiltonians (including the Rashba and Dresselhaus cases) perturbed by measure potentials thus extending the results of J.Bruening, V.Geyler, K.Pankrashkin: J. Phys. A 40 (2007) F113--F117.