Electrical manipulation of edge states in graphene and the effect on quantum Hall transport

We investigate the properties of Dirac electrons in a finite graphene sample under a perpendicular magnetic field that emerge when an in-plane electric bias is also applied. The numerical analysis of the Hofstadter spectrum and of the edge-type wave functions evidence the presence of shortcut edge states that appear under the influence of the electric field. The states are characterized by a specific spatial distribution, which follows only partially the perimeter, and exhibit ridges that connect opposite sides of the graphene plaquette. Two kinds of such states have been found in different regions of the spectrum, and their particular spatial localization is shown along with the diamagnetic moments that reveal their chirality. By simulating a four-lead Hall device, we investigate the transport properties and observe unconventional plateaus of the integer quantum Hall effect that are associated with the presence of the shortcut edge states. We show the contributions of the novel states to the conductance matrix that determine the new transport properties. The shortcut edge states resulting from the splitting of the $n=0$ Landau level represent a special case, giving rise to nontrivial transverse and longitudinal resistance.