Revisiting the missing He–McKellar–Wilkens geometric quantum phase

We discuss the missing He–McKellar–Wilkens geometric quantum phase in Landau levels for a neutral particle with a permanent electric dipole moment in the presence of an infinity wall. We also discuss the influence of the missing He–McKellar–Wilkens geometric quantum phase on the energy levels of a neutral particle confined to a one-dimensional quantum ring. Further, we explore this influence of the missing He–McKellar–Wilkens geometric quantum phase on the energy levels by calculating the persistent spin currents.