Dirac operator spectrum in tubes and layers with a zigzag type boundary

TL;DR

This paper investigates the spectral properties of Dirac operators in complex tube and layer geometries with zigzag boundaries, extending understanding of their behavior through Laplacian relationships.

Contribution

It introduces new spectral results for Dirac operators in nontrivial geometries with zigzag boundaries, linking them to Dirichlet Laplacian properties.

Findings

Spectral characteristics of Dirac operators in tube and layer geometries.

Connections between Dirac operator spectra and Dirichlet Laplacian properties.

Insights into boundary effects on spectral behavior.

Abstract

We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in $\mathbb{R}^2$ and $\mathbb{R}^3$ of tube or layer shapes with a zigzag type boundary using the corresponding properties of the Dirichlet Laplacian.