Title: Double-dome Unconventional Superconductivity in Twisted Trilayer Graphene

Abstract: Graphene moir\'e systems are ideal environments for investigating complex phase diagrams and gaining fundamental insights into the mechanisms underlying exotic states of matter, as they permit controlled manipulation of electronic properties. Magic-angle twisted trilayer graphene (MATTG) has emerged as a key platform to explore moir\'e superconductivity, owing to the robustness of its superconducting order and the displacement-field tunability of its energy bands. Recent measurements strongly suggest that superconductivity in MATTG is unconventional. Here, we report the first direct observation of double-dome superconductivity in MATTG. The temperature, magnetic field, and bias current dependence of the superconductivity of doped holes collectively show that it is significantly suppressed near moir\'e filling $\nu^* = -2.6$, leading to a double dome in the phase diagram within a finite window of the displacement field. The temperature dependence of the normal-state resistance and the $I-V$ curves straddling $\nu^*$ are suggestive of a phase transition and the potentially distinct nature of superconductivity in the two domes. Hartree-Fock calculations incorporating mild strain yield an incommensurate Kekul\'e spiral state whose effective spin polarization peaks in the regime where superconductivity is suppressed in experiments. This allows us to draw conclusions about the normal state as well as the unconventional nature of the superconducting order parameter.