Aharonov-Bohm effect in higher genus materials

TL;DR

This paper investigates the Aharonov-Bohm effect in higher genus materials, revealing unique flux periodicities of ground-state energy and wave functions on double torus geometries, with implications for topological quantum systems.

Contribution

It provides a theoretical analysis of flux periodicity in higher genus materials, extending understanding beyond simple torus geometries and discussing implications for quantum states.

Findings

Ground-state energy has a flux period twice the fundamental flux unit.

Wave function flux periodicity is more complex in double tori.

Adiabatic flux addition does not yield good quantum numbers for energy states.

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.