Effect of contact induced states on minimum conductivity in graphene

The objective of this paper is to point out that contact induced states can help explain the structure dependence of the minimum conductivity observed experimentally. Contact induced states are similar to the well-known metal induced gap states in metal-semiconductor Schottky junctions, which typically penetrate a few atomic lengths into the semiconductor, while the depth of penetration decreases with increasing band gap. However, in graphene we find that these states penetrate a much longer distance of the order of the width of the contacts. As a result, ballistic graphene samples with a length less than their width at Dirac points can exhibit a length-dependent resistance that is not ``Ohmic'' in origin but arises from a reduced role of contact induced states. While earlier theoretical works have shown that ballistic graphene samples can exhibit a minimum conductivity, our numerical results demonstrate that this minimum conductivity depends strongly on the structure and configuration of the channel and contacts. In diffusive samples, our results still show that the contact induced states effect needs to be taken into account in explaining minimum conductivity and its dependence on the structure (two terminal vs four terminal) and configuration used.