Coupling curvature to a uniform magnetic field; an analytic and numerical study

Abstract

The Schrodinger equation for an electron near an azimuthally symmetric curved surface $\Sigma$ in the presence of an arbitrary uniform magnetic field $\mathbf{B}$ is developed. A thin layer quantization procedure is implemented to bring the electron onto $\Sigma$, leading to the well known geometric potential $V_C\propto h^2-k$ and a second potential that couples $A_N$, the component of $\mathbf{A}$ normal to $\Sigma$ to mean surface curvature, as well as a term dependent on the normal derivative of $A_N$ evaluated on $\Sigma$. Numerical results in the form of ground state energies as a function of the applied field in several orientations are presented for a toroidal model.

12 pages, 3 figures

References in corpus (6)

• Persistent and radiation-induced currents in distorted quantum rings
• Photovoltaic effect in bent quantum wires
• Mesoscopic Electron and Phonon Transport through a Curved Wire
• Net current generation in a 1D quantum ring at zero magnetic field
• Wave functions in the neighborhood of a toroidal surface; hard vs. soft constraint
• Electron wave functions on $T^2$ in a static magnetic field of arbitrary direction

Cited by in corpus (17)

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• Nonrelativistic quantum dynamics on a cone with and without a constraining potential
• Quantum particle confined to a thin-layer volume: Non-uniform convergence toward the curved surface
• Low-Temperature Resistivity Anomalies in Periodic Curved Surfaces
• Curvature effects on surface electron states in ballistic nanostructures
• Pauli Equation on a Curved Surface and Rashba Splitting on a Corrugated Surface
• Hamiltonian for a particle in a magnetic field on a curved surface in orthogonal curvilinear coordinates
• Torsion-induced persistent current in a twisted quantum ring
• Quantum dynamics of a particle constrained to lie on a surface
• Anomalous phase shift in a twisted quantum loop
• Critical temperature and specific heat for Cooper pairing on a spherical surface
• Hermitian and Gauge-Covariant Hamiltonians for a particle in a magnetic field on Cylindrical and Spherical Surfaces
• Quantum particle on a surface: Catenary surface and Paraboloid of revolution
• Electron gases in toroidal shells: mode coupling and state functions