Superconductivity induced by the intervalley Coulomb scattering in a few layers of graphene

We study the intervalley scattering induced by the Coulomb repulsion as a purely electronic mechanism for the origin of superconductivity in a few layers of graphene. The pairing is strongly favored by the presence of van Hove singularities in the density of states. We consider three different heterostructures: twisted bilayer graphene, rhombohedral trilayer graphene, and Bernal bilayer graphene. We obtain trends and estimates of the superconducting critical temperature in agreement with the experimental findings, which might identify the intervalley Coulomb scattering as a universal pairing mechanism in a few layers of graphene.

Figure 1

$T_c$ as a function of the filling, obtained for $\epsilon /{\epsilon }_0=4$ and $\theta =1.{05}^{\circ },1.{12}^{\circ },1.{16}^{\circ }$.

Figure 2

(a) Band structure and (b) DOS corresponding to the two central bands of the TBG, obtained for $\theta =1.{05}^{\circ }$ and $\nu =-1,0,1$. The continuous and the dashed lines refer to the $K$ and $K^{\prime }$ valleys, respectively, while the horizontal lines identify the Fermi energies. The DOS is expressed in units of ${\mathrm{meV}}^{-1}{A}_m^{-1}$, where $A_m=\sqrt{3}{L}_m^2/2$ is the area of the moiré unit cell.

Figure 3

$T_c$ of the (a) hole-doped RTG and (b) BBG as a function of $n_e$, obtained for $\epsilon /{\epsilon }_0=4$ and ${\mathrm{\Delta }}_1$ as coded in the inset panel.

Figure 4

(a) Band structure and (b) DOS of the RTG close to the CNP, obtained for ${\mathrm{\Delta }}_1=25$, 40, 50, and 60 meV, and color coded as in Fig. 3. Here, $q=0$ at the $K$ point. The horizontal dashed lines indicate the Fermi levels corresponding to the densities that maximize $T_c$ in Fig. 3.