Bound states and energy shifts resulting from corrugations

Abstract

In the thin-layer quantization formalism, we give the effective Hamiltonian describing the noninteracting electron confined to the corrugated torus. In the presence of the geometric potential, we find that the low-energy part of the electron energy spectrum strongly depends on the corrugations of torus. Specifically, the bound states and the energy shifts both result from the geometry of the corrugated torus. Moreover, the eigenstates probability density distributions can be reconstructed by designing the corrugations, to predominantly localize the electron at the peaks and valleys of corrugations on the torus.

Keywords

• Geometric potential
• Bound states
• Energy shifts