Higher-order topological phase: generalizations of the Aharonov-Bohm and Josephson effects

摘要

In the magnetic Aharonov-Bohm effect a semiclassical path of a charged particle is gaussian linked with a magnetic flux tube and one observes an interference phase angle proportional to the magnitude of the enclosed flux. We first generalize to the case of knotted paths. Then we argue that quantum mechanical wave functions with semiclassical paths that have higher order linking to multiple magnetic flux tubes have interference angle proportional to the product of the fluxes. Similar results hold for generalizing the Josephson effect.