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arxiv: 1504.00840 · v1 · pith:EKQB74GGnew · submitted 2015-04-03 · ❄️ cond-mat.mes-hall

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

classification ❄️ cond-mat.mes-hall
keywords curveelectronsone-dimensionalquantumspaceconstrainedcoupledderive
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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.

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