Group Work 301: "The Ahanarov-Bohm effect - topology and Berry curvature"

Abstract: The discovery of the Ahanarov-Bohm effect in 1959 demonstrated that electron interference fringes could be shifted by a localised magnetic field, despite the field being zero at the location of the electron. There are two interpretations of this effect: the first implies that the vector potential must be considered a real quantity in quantum theory, if the principle of locality is to be upheld; secondly, the effect can be considered a non-local interaction between the electron and magnetic flux, retaining the classical idea of a non-physical vector potential. This review begins with an introduction to the Ahanarov-Bohm effect and a discussion of the gauge freedom of the vector potential, before exploring its connection to the geometric phase. Experimental confirmations are reviewed and applications to topological insulators and the Anomalous Hall Effect are presented.