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

Abstract

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 $T_{\text{C}}$ $\approx$ 1.7 K was reported for a device with $\theta$ = 1.05$°$ at ambient pressure and a maximum $T_{\text{C}}$ $\approx$ 3.1 K for a device with $\theta$ = 1.27$°$ under 1.33 GPa hydrostatic pressure. A high-$T_{\text{C}}$ 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, $T_{\text{C0}}$ = $k_{\text{B}}^{-1}$$\Lambda$(|$n_{\text{opt}}$ - $n_{\text{0}}$|/2)${}^{1/2}$$e^2$/$\zeta$, is a function of mean bilayer separation distance $\zeta$, measured gated charge areal densities $n_{\text{opt}}$ and $n_{\text{0}}$ corresponding to maximum $T_{\text{C}}$ and superconductivity onset, respectively, and the length constant $\Lambda$ = 0.00747(2) $\mathring{\text{A}}$. Based on existing experimental carrier densities and theoretical estimates for $\zeta$, $T_{\text{C0}}$ = 1.94(4) K is calculated for the $\theta$ = 1.05$°$ ambient-pressure device and $T_{\text{C0}}$ = 3.02(3) K for the $\theta$ = 1.27$°$ pressurized device. Experimental mean-field transition temperatures $T_{\text{C}}^{\text{mf}}$ = 1.83(5) K and $T_{\text{C}}^{\text{mf}}$ = 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 $T_{\text{C0}}$ are in remarkable agreement with these experimental values. Corresponding Berezinskii-Kosterlitz-Thouless temperatures $T_{\text{BKT}}$ of 0.96(3) K and 2.2(2) K are also determined and interpreted.

12 pages, 2 tables, 2 figures, 93 references