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Alternate Sign Reversal in Magnetic Flux-Induced Persistent Current in an Isolated Mesoscopic Ring by Half-the-Ring Electrostatic Potential

We calculate the energy spectrum for an electron in an isolated ideal one-dimensional mesoscopic ring subject to magnetic flux threading the ring and electrostatic potential applied to one half of the ring. The problem is reduced to that of Kronig-Penney potential with Beyers and Yang boundary condition around the ring. The energy band E is periodic in magnetic phase shift θ and approximately periodic in electrostatic phase shift φ. At low electrostatic potential, E(θ) bands are shifted in half the potential. Where the E(θ) bands are degenerate, band gaps are formed by electrostatic potential. Above some critical strength of electrostatic potential, narrow energy bands with wide gap are formed that are propagating in one half of the ring and decaying in the other half. From the E(θ) band, magnetic-flux-induced persistent current is calculated. Possibility of its alternate sign reversal by increasing the strength of the electrostatic potential is discussed.