BCS superconductivity of Dirac electrons in graphene layers

TL;DR

This paper investigates the potential for superconductivity in graphene's Dirac electrons using the BCS model, focusing on how doping and interaction strength influence critical temperature, energy gap, and magnetic properties.

Contribution

It provides a detailed analysis of superconductivity in Dirac electron systems, highlighting the effects of doping and interaction strength on critical parameters and identifying a quantum critical point at zero doping.

Findings

Critical temperature vanishes below a finite interaction at zero doping.

Finite critical temperature exists for any nonzero doping level.

Behavior of London penetration depth and coherence length analyzed.

Abstract

Possible superconductivity of electrons with the Dirac spectrum is analyzed using the BCS model. We calculate the critical temperature, the superconducting energy gap, and supercurrent as functions of the doping level and of the pairing interaction strength. Zero doping is characterized by existence of the quantum critical point such that the critical temperature vanishes below some finite value of the interaction strength. However, the critical temperature remains finite for any nonzero electron or hole doping level when the Fermi energy is shifted away from the Dirac point of the normal-state electron spectrum. We analyze the behavior of the characteristic length scales, i.e., the London penetration depth and the coherence length, which determine the critical magnetic fields.