Properties of Edge States at the Graphene P-N Junction Interface

The Landau level edge states from the p- and the n-section of a graphene P/N junction (\textit{pn}J) interact with each other differently across the junction depending upon the properties of the junction and the graphene. Full equilibration was reported for a two terminal graphene \textit{pn}J device in Williams et al. [1]. In our four-terminal device, however, only the lowest Landau level edge state is equilibrated across the \textit{pn}J [2]. When the two devices are compared, the LL energy spacings, the length of the edge states along the \textit{pn}J interface, and the carrier mobility are similar. Electrostatic simulations for our device geometry and that of [1] contrast the rate of change of the electrostatic potential across the \textit{pn}Js. Edge states at an electrostatically smooth junction are spatially further apart than those at a relatively abrupt junction, which decreases the probability of edge states mixing. Thus, we attribute the difference in equilibration in our device and that of [1] to the dramatic difference in the shape of the electrostatic junction. [1] J. R. Williams, L. DiCarlo, and C. M. Marcus, Science 317, 638 (2007) [2] Nikolai N. Klimov, Son T. Le, \textit{et al.}, Phys. Rev. B: Rapid Comm. (2015