ELECTRON-HOLE SUPERCONDUCTIVITY IN BI-LAYER GRAPHENE SUPERCONDUCTORS

Abstract

Superconductivity has been discovered in many different types of materials, such as metals, metallic alloys, doped semiconductors, cuprate oxides, heavy fermion superconductors, and so on; and now recently bi-layer and trilayer graphene superconductors. What is common among all these superconductors is that the super-current is due to the frictionless flow of pairs of charge carriers, called Cooper pairs, and the charge carriers can be electrons, holes in pairs, or electron-hole pairs. In this manuscript, the role of electron-hole pairs in determining the superconductivity in bi-layer graphene superconductors is studied theoretically. It is based on the spontaneous inter-layer phase coherence in a bi-layer quantum Hall system studied using graphene layers. The phase coherence state is assumed to be a gas of super-fluid electron-hole pairs whose components (electrons and holes) belong to two different layers which are one above the other and are separated by a dielectric of a very small thickness (d), and the value of d, should be such that the state of phase coherence is not disturbed. For such a superconductor, specific heat (Cv), entropy (S), and transition temperature (Tc) have been calculated and compared with values known so far