Aharonov-Bohm effect with many vortices

TL;DR

This paper extends the Aharonov-Bohm effect to a system with many vortices arranged in a lattice, revealing how such configurations influence quantum wave functions and create barriers to particle penetration.

Contribution

It provides an explicit wave function solution for a particle in a vortex lattice and analyzes the spectral properties and barrier effects in this extended Aharonov-Bohm scenario.

Findings

Vortex lattice creates a repulsive barrier to low-energy particles.

Wave function solutions reveal spectral characteristics of the system.

Penetration probability decays exponentially with distance from the edge.

Abstract

The Aharonov-Bohm effect is the prime example of a zero-field-strength configuration where a non-trivial vector potential acquires physical significance, a typical quantum mechanical effect. We consider an extension of the traditional A-B problem, by studying a two-dimensional medium filled with many point-like vortices. Systems like this might be present within a Type II superconducting layer in the presence of a strong magnetic field perpendicular to the layer, and have been studied in different limits. We construct an explicit solution for the wave function of a scalar particle moving within one such layer when the vortices occupy the sites of a square lattice and have all the same strength, equal to half of the flux quantum. From this construction we infer some general characteristics of the spectrum, including the conclusion that such a flux array produces a repulsive barrier to an incident low-energy charged particle, so that the penetration probability decays exponentially with distance from the edge.