Partial phases in a circling electron

An extended electronic cloud can acquire different AharonovBohm (AB) phases in its parts when these parts experience different solenoidal fields. This is demonstrated by two models that describe an electron moving within a confining circular tube around a solenoidal vector potential and outside a magnetic field domain (just as in a usual AB set up): one in which the motion of the electron along the tube is restricted and moves adiabatically and another in which it extends freely and without restriction on its speed. When the electron cloud is split into two parts circling in opposite directions, we show that when the two parts of the electronic cloud rejoin, they do so with different phases. This set-up complements (and confirms the finding of) our previous work [Europhys. Lett. 93, 20001 (2011)], in which the vector source was moving and the electron position was fixed.