Aharonov-Bohm effect in higher genus materials

Abstract

Flux periodicity of conducting electrons on a closed surface with genus two $g=2$ (double torus) are investigated theoretically. We examine flux periodicity of the ground-state energy and of the wave functions as a function of applied magnetic field. A fundamental flux period of the ground-state energy is twice a fundamental unit of magnetic flux for uniformly applied magnetic field, which is shown to be valid for a simple ladder geometry and carbon double torus. Flux periodicity of the wave functions in a double torus is complicate as compared with a simple torus ($g=1$), and an adiabatic addition of magnetic fluxes does not provide a good quantum number for the energy eigenstates. The results are extended to higher genus materials and the implications of the results are discussed.

4 pages, 6 figures

References in corpus (1)

• Observation of Persistent Currents in Mesoscopic Connected Rings

Cited by in corpus (5)

• Coupling curvature to a uniform magnetic field; an analytic and numerical study
• 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
• Fractional flux periodicity of a twisted planar square lattice
• The wave functions in the presence of constraints - Persistent Current in Coupled Rings