Schr\"odinger operator on the zigzag half-nanotube in magnetic field

TL;DR

This paper analyzes the spectral properties of a magnetic Schr"odinger operator on zigzag half-nanotubes, revealing how eigenvalues and resonances depend on magnetic fields using Jacobi operator analysis.

Contribution

It provides a comprehensive description of eigenvalues and resonances for the magnetic Schr"odinger operator on zigzag nanotubes, linking spectral features to magnetic field variations.

Findings

Eigenvalues and resonances are fully characterized.

Dependence of spectral features on magnetic field is established.

Reduction to Jacobi operator analysis simplifies the problem.

Abstract

We consider the zigzag half-nanotubes (tight-binding approximation) in a uniform magnetic field which is described by the magnetic Schr\"odinger operator with a periodic potential plus a finitely supported perturbation. We describe all eigenvalues and resonances of this operator, and theirs dependence on the magnetic field. The proof is reduced to the analysis of the periodic Jacobi operators on the half-line with finitely supported perturbations.