Superconductivity in graphene stacks: from the bilayer to graphite

TL;DR

This paper investigates superconductivity in graphene stacks and graphite, deriving a mean-field model to analyze how interlayer hopping influences the critical temperature, revealing higher transition temperatures in graphite that could explain experimental observations.

Contribution

It introduces a mean-field effective potential for multilayer graphene, showing how interlayer hopping enhances superconductivity and explaining intrinsic superconductivity in graphite.

Findings

Hopping between layers increases the critical temperature at low chemical potential.

Graphite exhibits a higher transition temperature than bilayer graphene at small chemical potentials.

The critical temperature follows a dome-shaped dependence on chemical potential.

Abstract

We study the superconducting phase transition, both in a graphene bilayer and in graphite. For that purpose we derive the mean-field effective potential for a stack of graphene layers presenting hopping between adjacent sheets. For describing superconductivity, we assume there is an on-site attractive interaction between electrons and determine the superconducting critical temperature as a function of the chemical potential. This displays a dome-shaped curve, in agreement with previous results for two-dimensional Dirac fermions. We show that the hopping between adjacent layers increases the critical temperature for small values of the chemical potential. Finally, we consider a minimal model for graphite and show that the transition temperature is higher than that for the graphene bilayer for small values of chemical potential. This might explain why intrinsic superconductivity is observed in graphite.