  The critical current of a superconductor can be different for opposite
directions of current flow when both time-reversal and inversion symmetry are
broken. %When time-reversal and inversion symmetry are simultaneously broken,
the critical current of a 2D superconductor is expected to depend on the
directions of current flow. Such nonreciprocal behavior in superconducting
transport, which creates a superconducting diode, has recently been
demonstrated experimentally by breaking these symmetries with an applied
magnetic field \cite{Ando2020diodes} or by construction of a magnetic tunnel
junction \cite{Diez2021magnetic}. Here we report an intrinsic superconducting
diode effect which is present at zero external magnetic field in mirror
symmetric twisted trilayer graphene (tTLG). Such nonreciprocal behavior, with
sign that can be reversed through training with an out-of-plane magnetic field,
provides direct evidence of the microscopic coexistence between
superconductivity and time-reversal symmetry breaking. In addition to the
magnetic-field trainability, we show that the zero-field diode effect can be
controlled by varying carrier density or twist angle. In accordance with these
experimental controls, a natural interpretation for the origin of the intrinsic
diode effect is an imbalance in valley occupation of the underlying Fermi
surface, which likely leads to finite-momentum Cooper pairing and nematicity in
the superconducting phase.
