Superconducting magic-angle twisted trilayer graphene with competing magnetic order and moiré inhomogeneities.

The microscopic mechanism of unconventional superconductivity in magic-angle twisted trilayer graphene is poorly understood. We show direct evidence for an in-plane magnetic order competing with the superconducting state motivated by theoretical proposals. We use two complementary electrical transport measurements. First, in statistically significant switching events in the superconducting state of magic-angle twisted trilayer graphene, we observe non-monotonic and hysteretic responses in the switching distributions as a function of temperature and in-plane magnetic field. Additionally, the system behaves like a network of Josephson junctions due to lattice-relaxation-induced moiré inhomogeneity. Second, in normal regions doped slightly away from the superconducting regime, hysteretic and linear positive magnetoresistance with the in-plane magnetic field shows evidence for an in-plane magnetic order. Furthermore, we estimate superfluid stiffness J ≈ 0.15 K with strong temperature dependence and show a broadened Berezinskii-Kosterlitz-Thouless transition. Our observations may constrain possible intervalley-coherent magnetic orders and the superconductivity arising from its fluctuations.