Theory of Graphene-Insulator-Graphene Tunnel Junctions

Graphene-insulator-graphene vertical tunneling structures are discussed from a theoretical perspective. Momentum conservation in such devices leads to highly nonlinear current-voltage characteristics, which with gates on the tunnel junction form potentially useful transistor structures. Two prior theoretical treatments of such devices are discussed; the treatments are shown to be formally equivalent, although some differences in their implementations are identified. The limit of zero momentum conservation in the theory is explicitly considered, with a formula involving the density-of-states of the graphene electrodes recovered in this limit. Various predictions of the theory are compared to experiment.