Possibility of superconductivity due to electron-phonon interaction in graphene

We discuss the possibility of superconductivity in graphene taking into account both electron-phonon and electron-electron Coulomb interactions. The analysis is carried out assuming that the Fermi energy is far away from the Dirac points, such that the density of the particles (electrons or holes) is high. We derive proper Eliashberg equations that allow us to estimate the critical superconducting temperature. The most favorable is pairing of electrons belonging to different valleys in the spectrum. By using values of electron-phonon coupling estimated in other publications, we obtain the critical temperature $T_c$ as a function of the electron (hole) density. This temperature can reach the order of 10 K at the Fermi energy of order $1–2$ eV. We show that the dependence of the intervalley pairing on the impurity concentration should be weak.

Figure 1

Pseudopotentials ${\mu }_{11}$ (blue line) and ${\mu }_{12}$ (green crosses) as function of the charge carrier density $n$.

Figure 2

Critical temperature calculated with Eq. (3.42). The curves show $T_c$ as function of the electron density $n$. Solid lines correspond to $\kappa =2.5$, while dashed lines are curves for $\kappa =3.8$. The bottom blue lines correspond to $C=3.5$ and the top green lines to $C=5.$