Superconductivity from collective excitations in magic-angle twisted bilayer graphene

A purely electronic mechanism is proposed for the unconventional superconductivity recently observed in twisted bilayer graphene (tBG) close to the magic angle. Using the Migdal-Eliashberg framework on a one-parameter effective lattice model for tBG we show that a superconducting state can be achieved by means of collective electronic modes in tBG. We posit robust features of the theory, including an asymmetrical superconducting dome and the magnitude of the critical temperature that are in agreement with experiments.

Figure 1

Cartoon illustration of a mechanism for superconductivity: (a) within BCS theory, moiré phonons [18] have an attractive pairing below the Debye frequency ${\omega }_D$; (b) although plasmonic mediated interaction is repulsive, the frequency dependence gives rise to pairing within Eliashberg theory; (c) analytic single-mode approximation [Eq. (2)] for the Dirac model with renormalized $v_F\sim 1.5\times {10}^4{\mathrm{ms}}^{-1}, {\omega }_b\sim 15$ meV gives a $T_C$ for a finite density window between the dotted and the crossed lines. The dotted lines indicate the threshold density and the crossed black line indicates the cutoff imposed by the finite bandwidth. The enhanced density window supporting superconductivity with increasing $r_s$ agrees well with the full numerical results.

Figure 2

Critical temperature $T_C$ as a function of electron density in tBG (close to the magic angle). The presence of an asymmetrical superconducting dome around $n={10}^{12}{\mathrm{cm}}^{-2}$ and $T_C=O\left(10\text{K}\right)$ are the main predictions of this theory. The inset shows a comparison of numerically obtained $\lambda \left(i\omega \right)$ and the fit using Eq. (10). The evaluated parameters $\mu$ and ${\omega }_b$ are shown, and the position of ${\omega }_b$ is indicated by the dotted line.

Figure 3

Critical temperature $T_C$ as a function of twist angle in tBG for three different carrier densities. The dotted lines show the $T_C$ obtained from the full numerical solution of Eq. (1). The analytical solution from Eq. (2) using the parameters ${\omega }_b, E_F$, and $\mu$ (or $r_s$) from the numerical solution is shown by corresponding solid lines. The inset shows ${\omega }_b$ as a function of $\theta$ determined by fitting the numerical calculation of $\lambda \left(i\omega \right)$. The dashed line shows, for comparison, ${\omega }_p^D\left(k_F\right)$, the plasmon frequency within a Dirac model which has a qualitatively similar enhancement at low twist angles.