Surface superconductivity in rhombohedral graphite

TL;DR

This paper investigates surface superconductivity in rhombohedral graphite, revealing how surface states and their dispersion influence the superconducting properties and potentially explaining recent high-temperature graphite superconductivity observations.

Contribution

It demonstrates how higher order couplings modify surface state dispersion and affect the relation between the order parameter and coupling strength in surface superconductivity.

Findings

Surface states are topologically protected with flat band dispersion under nearest neighbor coupling.

Including higher order couplings introduces quadratic dispersion and breaks particle-hole symmetry.

Surface superconductivity exhibits different regimes depending on coupling strength, with a linear relation between order parameter and coupling at high coupling.

Abstract

We show that rhombohedral graphite may support surface superconductivity with an unusual relation between the BCS coupling constant and the order parameter. This feature results from the properties of the states localized on the graphite surfaces. In a description including only the nearest neighbour coupling of the graphene layers, the surface states are topologically protected and have a flat band dispersion. We show that including higher order couplings destroys this flat band character and leads to a particle-hole symmetry breaking quadratic dispersion with a large effective mass. Employing this dispersion, we then show its effect on superconductivity and find two regimes of parameters, depending on the relation between the strength of the coupling constant and the details of the quadratic dispersion. For low coupling strengths, superconductivity is localized on the surfaces, but the order parameter is exponentially suppressed as in a conventional BCS superconductor, whereas for large coupling strengths we obtain surface superconductivity with a linear relation between the order parameter and the coupling constant. Our results may explain the recent findings of graphite superconductivity with a relatively high transition temperature.