High-$T_\textrm{C}$ Superconductivity Originating from Interlayer Coulomb Coupling in Gate-Charged Twisted Bilayer Graphene Moir$\'{e}$ Superlattices

Unconventional superconductivity in bilayer graphene has been reported for twist angles $\theta$ near the first magic angle and charged electrostatically with holes near half filling of the lower flat bands. A maximum superconducting transition temperature $T_\textrm{C}$ $\approx$ 1.7 K was reported for a device with $\theta$ = 1.05$\deg$ at ambient pressure and a maximum $T_\textrm{C}$ $\approx$ 3.1 K for a device with $\theta$ = 1.27$\deg$ under 1.33 GPa hydrostatic pressure. A high-$T_\textrm{C}$ model for the superconductivity is proposed herein, where pairing is mediated by Coulomb coupling between charges in the two graphene sheets. The expression derived for the optimal transition temperature, $T_\textrm{C0}$ = $k_\textrm{B}^{-1}$$\Lambda$(|$n_\textrm{opt}$ - $n_\textrm{0}$|/2)$^{1/2}$$e^2$/$\zeta$, is a function of mean bilayer separation distance $\zeta$, measured gated charge areal densities $n_\textrm{opt}$ and $n_\textrm{0}$ corresponding to maximum $T_\textrm{C}$ and superconductivity onset, respectively, and the length constant $\Lambda$ = 0.00747(2) $\mathring{\textrm{A}}$. Based on existing experimental carrier densities and theoretical estimates for $\zeta$, $T_\textrm{C0}$ = 1.94(4) K is calculated for the $\theta$ = 1.05$\deg$ ambient-pressure device and $T_\textrm{C0}$ = 3.02(3) K for the $\theta$ = 1.27$\deg$ pressurized device. Experimental mean-field transition temperatures $T_\textrm{C}^\textrm{mf}$ = 1.83(5) K and $T_\textrm{C}^\textrm{mf}$ = 2.86(5) K are determined by fitting superconducting fluctuation theory to resistance transition data for the ambient-pressure and pressurized devices, respectively; the theoretical results for $T_\textrm{C0}$ are in remarkable agreement with these experimental values. Corresponding Berezinskii-Kosterlitz-Thouless temperatures $T_\textrm{BKT}$ of 0.96(3) K and 2.2(2) K are also determined and interpreted.