Superconductivity in Layered Systems of Dirac Electrons

Abstract

Dirac electrons have been discovered in many advanced materials including, among others, graphene, cuprates, pnictides and rare-earth dichalchogenides. These materials are either two-dimensional, such as graphene or exhibit a layered structure formed by planes where the most relevant physics occurs. Interestingly many of them undergo a transition to a superconducting phase, under appropriate conditions. However, the kinematical properties of Dirac electrons, which imply the absence of a Fermi surface at zero doping, rules out the traditional, phonon-mediated BCS mechanism of superconductivity. In this chapter, we describe a theoretical study of the superconducting properties of layered systems of Dirac electrons, assuming the existence of some mechanism behind it. We analyze in detail the phase diagram identifying quantum critical points, the effects of temperature, magnetic field, chemical potential (doping), number of layers, as well as the interplay of the SC with an excitonic interaction. The results unequivocally indicate that a novel mechanism, other than the traditional BCS, is required to explain the superconductivity of Dirac electrons.