Zero modes in a system of Aharonov-Bohm fluxes

TL;DR

This paper investigates the existence and properties of zero-energy solutions (zero modes) of two-dimensional Pauli operators influenced by Aharonov-Bohm fluxes arranged periodically or irregularly, with implications for quantum systems.

Contribution

It introduces a detailed analysis of zero modes in systems with periodic and perturbed Aharonov-Bohm flux arrangements, expanding understanding of their spectral properties.

Findings

Zero modes exist in periodic flux arrangements.

Perturbations can preserve or alter zero modes depending on their scarcity.

The study provides conditions for the stability of zero modes under irregular perturbations.

Abstract

We study zero modes of two-dimensional Pauli operators with Aharonov--Bohm fluxes in the case when the solenoids are arranged in periodic structures like chains or lattices. We also consider perturbations to such periodic systems which may be infinite and irregular but they are always supposed to be sufficiently scarce.