Title: Momentum polarized superconductivity in twisted trilayer graphene

Abstract: The spin-configuration of a Cooper pair is often informative of the pairing symmetry. According to the BCS theory, a conventional, s-wave superconductor arises from Cooper pairing in the singlet channel. Whereas a triplet Cooper pair is directly linked to a spatial wavefunction in the p- or f-wave channel, a hallmark of unconventional superconductivity. In multilayer graphene, the nature of the pairing instability is further complicated by emergent orders in the momentum-space. As spin is no longer the only quantum number, information regarding the exchange-driven instabilities in the momentum space is crucial for describing the pairing symmetry. In this work, we use angle-resolved nonreciprocal transport measurement to investigate the influence of the momentum-space instabilities. Across the moir\'e band filling, we uncover a new cascade phenomenon, where a series of transitions between momentum-polarized states appear outside the regular sequence of Dirac revivals. Moreover, we demonstrate a coexistence between superconductivity and spontaneous momentum polarization, which is evidenced by a one-fold symmetric angular dependence in the zero-field superconducting diode effect. Such a coexistence has intriguing implications on the nature of the pairing instability.