Mean field superconductivity approach in two dimensions: Hydrogen in Graphite

Within the BCS theory of superconductivity we calculate the superconducting gap at zero temperature for metallic hydrogen-graphene system in order to estimate the superconducting critical temperature of quasi two dimensional highly oriented pyrolytic graphite. The obtained results are given as a function of the hydrogen-induced density of carriers $n$ and their effective mass $m^\star$. The obtained gap shows a Maxwell-like distribution with a maximum of $\sim 60$K at $n \sim 3 \times 10^{14}$cm$^{-2}$ and $m^\star/m = 1$. The theoretical results are discussed taking into account recent experimental evidence for granular superconductivity in graphite.