Kohn-Luttinger superconductivity in graphene

We investigate the development of superconductivity in graphene when the Fermi level becomes close to one of the Van Hove singularities of the electron system. The origin of the pairing instability lies in the strong anisotropy of the $e\text{−}e$ scattering at the Van Hove filling, which leads to a channel with attractive coupling when making the projection of the BCS vertex on the symmetry modes with nontrivial angular dependence along the Fermi line. We show that the scale of the superconducting instability may be pushed up to temperatures larger than 10 K, depending on the ability to tune the system to the proximity of the Van Hove singularity.

Figure 1

(Color online) Plot of energy contour lines around the saddle points of the valence band of graphene, obtained from a tight-binding model with first-, second-, and third-neighbor hopping parameters given by Eqs. (1, 2, 3) for $s=0.1$.

Figure 2

(Color online) Plot of the hopping parameters $t$ (full line), $d$ (dashed line), and $t^{\prime }$ (dotted line) given in eV units as functions of the overlap integral $s$ and satisfying the constraints [Eqs. (1, 2, 3)].

Figure 3

Lowest-order particle-hole corrections to the BCS vertex for a bare on-site interaction. Full and dashed lines represent the propagation of electrons around different saddle points.

Figure 4

(Color online) Plot of the scale $\Delta /2$ at which the eigenvalue ${\lambda }_2$ diverges (full line) and the critical temperature $T_c$ (dashed line), as a function of the deviation $\mu$ of the VHS from the Fermi level.

Figure 5

(Color online) Plot of the ratio between the superconducting gap $\Delta$ and the critical temperature $T_c$, as a function of the deviation $\mu$ of the VHS from the Fermi level. The dashed line stands for the BCS value $\Delta /k_B{T}_c\approx 1.76$.