Quantum mechanics of a spin-orbit coupled electron constrained to a space curve

TL;DR

This paper derives an effective one-dimensional quantum equation for electrons with spin-orbit coupling constrained to a space curve, revealing how torsion influences quantum potentials and providing a model for nanoscale helical wires.

Contribution

It introduces a method to derive a Hermitian 1D Schrödinger-Pauli equation for spin-orbit coupled electrons on space curves, including torsion effects.

Findings

Torsion generates an additional quantum geometric potential.

Derived an analytic Hamiltonian for spin-orbit electrons in a helical wire.

Confirmed the validity of the thin-wall quantization procedure.

Abstract

We derive the effective one-dimensional Schrodinger-Pauli equation for electrons constrained to move on a space curve. The electrons are confined using a double thin-wall quantization procedure with adiabatic separation of fast and slow quantum degrees of freedom. This procedure is capable of yielding a correct Hermitian one-dimensional Schrodinger-Pauli operator. We find that the torsion of the space curve generates an additional quantum geometric potential, adding to the well-known curvature-induced one. Finally, we derive an analytic form of the one-dimensional Hamiltonian for spin-orbit coupled electrons in a nanoscale helical wire.