Valley ferromagnetism and superconductivity in magic-angle trilayer graphene

The observation of superconductivity and anomalous Hall effect in magic-angle graphene moir\'e systems raises an outstanding open question regarding the relationship between these two phenomena. In this work, we report the observation of a distinctive electronic order, valley ferromagnetism, in magic-angle twisted trilayer graphene, which provides the missing link connecting superconductivity and anomalous Hall effect. By characterizing the nonreciprocal transport response as a function of the azimuth direction of current flow, we identify the symmetry of valley ferromagnetism, superconductivity, and anomalous Hall effect induced by orbital ferromagnetism. Valley ferromagnetism simultaneously breaks two-fold inplane rotation $C_2$ and time-reversal symmetry $T$, but preserves their product $C_2T$ symmetry. As a result, it does not couple with external magnetic field directly. This is distinct from the orbital ferromagnetism, which further breaks $C_2T$ and is trainable with the B-field. Most interestingly, the superconducting phase inherits $C_2$ and $T$ symmetry breaking from the metallic phase above the transition temperature, which points towards an underlying Fermi surface with the valley ferromagnetic order. The coexistence of superconductivity and valley ferromagnetism offers a new perspective for understanding the pairing symmetry and the electronic order in a moir\'e flatband.