Superconducting States of Pure and Doped Graphene

We study the superconducting phases of the two-dimensional honeycomb lattice of graphene. We find two spin singlet pairing states; $s$ wave and an exotic $p+ip$ that is possible because of the special structure of the honeycomb lattice. At half filling, the $p+ip$ phase is gapless and superconductivity is a hidden order. We discuss the possibility of a superconducting state in metal coated graphene.

Figure 1

Graphene coated with metal. Small black (white) circles belong to the $A$ ($B$) sublattices; Large (red) circles represent the metal atoms.

Figure 2

$p+ip$ order parameter in momentum space: (a) close to the Dirac point and (b) away from it. Dark (black) line is the real part, gray (red) is the imaginary part, and dashed is the amplitude of the order parameter.

Figure 3

Mean-field phase diagram: (a) $\mu \ne 0$; (b) and $\mu =0$. Dashed lines are first-order transitions, continuous lines are second order.

Figure 4

(a) Low energy excitations in the metal-graphene system. Dark and gray regions are the particle-hole continuum of the metal and of graphene, respectively. (b) Real (solid) and imaginary (dashed) parts of the effective interaction (6), in units of $2\pi e^2{v}_0/({ϵ}_0\mu )\sim 45\mathrm{eV}\AA {}^2$ vs momentum normalized by $\mu /v_0$, for $\omega =0.1\mu$, $\mu =2\mathrm{eV}$, $E_F=0.4\mathrm{eV}$.