Electronic states on the helicoidal surface

Abstract

It is shown that free electrons on the helicoidal surface are affected by an effective potential, which vanishes in the s channel and gives rise to both metastable as well as stable bound states. The effective potential depends linearly on the “angular momentum” quantum number and the spin state resulting in a partially nondegenerate energy spectrum. The vanishing of the potential in the s channel illustrates a “miraculous” exact cancellation which is present for all quantum states. An attractive effective potential term arising from the spin connection cancels exactly a repulsive potential term, which is identical to the potential which affects relativistic bosons on the helicoidal surface.