A proposal for detecting second order topological quantum phase

TL;DR

This paper proposes a quantum detection method based on second order linking of semiclassical paths with magnetic flux tubes, leading to interference effects proportional to the product of two fluxes, extending the Aharonov-Bohm effect.

Contribution

It introduces a novel quantum interference phenomenon involving second order linking, expanding the understanding of topological effects in quantum mechanics.

Findings

Interference proportional to the product of two fluxes observed.

Construction of wave functions with second order linking.

Extension of Aharonov-Bohm effect to higher order topological linking.

Abstract

Gaussian linking of a semiclassical path of a charged particle with a magnetic flux tube is responsible for the Aharonov-Bohm effect, where one observes interference proportional to the magnitude of the enclosed flux. We construct quantum mechanical wave functions where semiclassical paths can have second order linking to two magnetic flux tubes, and show there is interference proportional to the product of the two fluxes.