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

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.

5 pages, no figures

References in corpus (3)

• Ultrathin compound semiconductor on insulator layers for high performance nanoscale transistors
• Quantum mechanics on curved 2D systems with electric and magnetic fields
• Strongly anisotropic ballistic magnetoresistance in compact three-dimensional semiconducting nanoarchitectures

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