Quantum systems with position-dependent mass and spin-orbit interaction via Rashba and Dresselhaus terms

Abstract

We consider a particle with spin 1/2 with position-dependent mass moving in a plane. Considering separately Rashba and Dresselhaus spin-orbit interactions, we write down the Hamiltonian for this problem and solve it for Dirichlet boundary conditions. Our radial wavefunctions have two contributions: homogeneous ones which are written as Bessel functions of non-integer orders—that depend on angular momentum m—and particular solutions which are obtained after decoupling the non-homogeneous system. In this process, we find non-homogeneous Bessel equation, Laguerre, as well as biconfluent Heun equation. We also present the probability densities for m = 0, 1, 2 in an annular quantum well. Our results indicate that the background as well as the spin-orbit interaction naturally splits the spinor components.

A complete set of eigenstates for position-dependent massive particles in a Morse-like scenario

“…Also recently, numerous other theoretical studies have been conducted on two-dimensional position-dependent mass Schrödinger equation (PDMSE). These include the two-dimensional quantum rotor with two effective masses [67], kinetic operator in cylindrical coordinates [68], exact solutions for the PDMSE in an annular billiard with impenetrable walls [69], and a particle with spin 1/2 moving in a plane [70].…”