Disordered p-n junction in graphene

Graphene is a new material whose unique electronic structure endows it with many unusual properties [1]. A monolayer graphene is a gapless two-dimensional (2D) semiconductor with a massless electron-hole symmetric spectrum near the corners of the Brillouin zone, ǫ(k) = ±~v|k|, where v ≈ 10 cm/s. The concentration of these “Dirac” quasiparticles can be accurately controlled by the electric field effect [2, 3]. An exciting experimental development is the ability to apply such fields locally, by means of submicron gates. Using this technique, graphene p-n junctions (GPNJ) have been recently demonstrated [4, 5, 6]. Even within idealized models that neglect disorder and electron interactions, GPNJ were predicted to display a number of intriguing phenomena. They include Klein tunneling [7, 8, 9], Veselago lensing [10], microwaveinduced [11] and Andreev [12] reflection, and strong ballistic magnetoresistance [8, 13]. Nontrivial corrections to these predictions and the potential for new physics are expected when interactions and disorder are included in the model. For example, long-range Coulomb interactions are responsible for nonlinear screening in GPNJ, which can modify its resistance substantially [14]. The purpose of this paper is to investigate how the junction resistance is affected by disorder. We show that in existing GPNJ this effect is indeed strong and suggest what can be done to reduce it in future. We consider a generic model of an electrostatic GPNJ, in which a grounded graphene sheet in the x-y plane is controlled by two coplanar metallic gates with voltages V1 and V2. The gates are separated by distance b from graphene and a distance 2d from each other. Under a symmetric gate bias, V2 = −V1 = V (Fig. 1), the graphene carrier density n(x) varies linearly in the middle of the junction,