Exact Hamiltonians with Rashba and cubic Dresselhaus spin-orbit couplings on a curved surface

Abstract

The exact Hamiltonians for Rashba and cubic Dresselhaus spin-orbit couplings on a curved surface with an arbitrary shape are rigorously derived. Two orthogonal principal curvatures dominate the electronic spin transport, and the asymptotic behavior of the normal confined potential on a curved surface is insignificant. For a curved surface with a large curvature, the higher order momentum terms play an important role in controlling spin transport. The Rashba spin-orbit coupling on a curved surface only induces the extra pseudopotential term, and the cubic Dresselhaus spin-orbit coupling on a curved surface can induce the extra pseudokinetic and pseudomomentum terms. Because of the extra curvature-induced terms and the associated pseudomagnetic fields, spin transport on a curved surface is very different from that on a flat surface. The Hamiltonians on both cylindrical and spherical surfaces are explicitly derived here, and the associated physical properties of electrons are studied in detail.