The Proximity Effect And Josephson Current In Graphene SNS Josephson Junctions

By means of mean field approximation we get the Bogoliubov-de Gennes (BdG) equation of the tight-binding Hamiltonian for the graphene lattice system. Based on the self-consistent solution of the BdG equations, we investigate superconducting pairing potential, proximity effect and Josephson current in superconductor-normal conductor—superconductor(SNS) Josephson junction in graphene. This paper mainly includes several parts as that:in the first chapter, we first introduce the basic types of carbon-based crystals such as the graphene, the fullerence and carbon nanotubes, then the discovery process of graphene, the preparation methods of graphene and practical application of carbon-based crystals have made introduction. In the second chapter, we introduce the crystal structure of the monolayer graphene, band structure of graphene and electrical properties of graphene, then the disorder effects on the properties of graphene. We focus on the third chapter. In this chapter, we self-consistently calculate the s-wave superconducting pairing potential of graphene firstly, then we take the graphene SNS Josephson junction as model, and we investigate1) in the undoped graphene, the relationship between superconducting pairing potential and the chemical potential.2) the effect of disorder of graphene on the pairing potential by changing the chemical potential in superconducting area and normal area.3) the proximity effect and the Josephson current in SNS Josephson junction of graphene by changing the chemical potential in superconducting area and the length of normal area, we conclude that the proximity effect is the most apparent and the Josephson current is the largest when the chemical potential of the superconducting area and normal conductive area both are in Varrt Hoff Singularities. We also study the relationship of the proximity effect and the Josephson current in SNS Josephson junction of graphene with the length of the normal area.