Electron-Hole Bound State in Graphene

The dispersion for monolayer graphene shows a gap-less spectrum. Such monolayer graphene can be gated by a charged Carbon Nanotube(CNT) placed at a distance from the graphene sheet and create both potential barriers and wells for the charge carriers in monolayer graphene. If two oppositely charged CNTs are placed at some distance, a potential well and a barrier are formed for an electron. In such systems, the barrier for a hole acts as a well for an electron and vice versa. We analytically study the formation of the electron-hole bound state in such systems and their consequences for many-body physics.