Geometric effects on the electronic structure and the bound states in annular corrugated wires

TL;DR

This paper investigates how geometric corrugations on annular wires influence their electronic properties, revealing that corrugations can enhance transition energies, increase bound states, and alter probability density distributions.

Contribution

It introduces an effective Hamiltonian for electrons on corrugated annular surfaces and demonstrates how corrugations significantly affect energy levels and bound states.

Findings

Corrugations increase transition energies.

Number of energy levels equals number of corrugations.

Larger corrugations lead to more bound states.

Abstract

In the spirit of the thin-layer quantization scheme, we give the effective Hamiltonian describing the noninteracting electrons confined to an annular corrugated surface, and find that the geometrically induced potential is considerably influenced by corrugations. By using numerical calculation, we investigate the eigenenergies and the corresponding eigenstates, and find that the transition energies can be sufficiently improved by adding corrugations. Particularly, the transition energy between the adjacent eigenstates corresponds to energy levels difference based on the wavefunction of annular wire, and the number of the energy levels is equal to the number of corrugations. And the larger magnitude of corrugations is capable of increasing the number of bound states. In addition, the distribution of ground state probability density is reconstructed by the corrugations, and the energy shift is generated.