Electronic zero modes of vortices in Hall states of gapped graphene

Understand

Recent observation of a metal-insulator phase transition in the $\nu=0$ Hall state of graphene has inspired the idea that charge carriers in the metallic state could be fractionally charged vortices.

• We examine the question of whether vortices in particular gapped states of graphene and subject to external magnetic and pseudo-magnetic fields could have the mid-gap zero mode electron states which would allow them to be charged.