A scattering model of 1D quantum wire regular polygons

TL;DR

This paper develops an analytical scattering model for quantum states in 1D wire polygons, revealing how their spectra depend on geometric and scattering properties, with explicit formulas for energy levels.

Contribution

It introduces a novel analytical approach to model quantum states in polygonal 1D wires using vertex scattering matrices derived from bend models.

Findings

Spectrum classified into doublets and singlets based on circulation.

Explicit formulas for energy eigenvalues provided.

Each polygon's spectrum uniquely characterized by its geometry.

Abstract

We calculate the quantum states of regular polygons made of 1D quantum wires treating each polygon vertex as a scatterer. The vertex scattering matrix is analytically obtained from the model of a circular bend of a given angle of a 2D nanowire. In the single mode limit the spectrum is classified in doublets of vanishing circulation, twofold split by the small vertex reflection, and singlets with circulation degeneracy. Simple analytic expressions of the energy eigenvalues are given. It is shown how each polygon is characterized by a specific spectrum.