Spontaneous time reversal symmetry breaking in twisted double bilayer graphene

Twisting two individual graphene layers at small angles can dramatically alter the band structure, leading in some cases to nearly flat bands dominated by electron-electron interactions, where correlated electronic states have been observed. A particular case of such structures is twisted double bilayer graphene (tDBG), composed of two Bernal stacked bilayer graphene sheets with a twist between them, where the emergence of correlated states can be controlled by twist angle (θ), carrier density, and displacement field. Signatures of broken spin and/or valley symmetries have been reported in both insulating and metallic correlated states in tDBG, although the precise description of such states remains elusive. Here, we study the magnetotransport properties of a dual gated tDBG sample with twist angle (θ∼1.3°), similar to samples measured in previous reports where in-plane magnetic field dependence of the resistivity gave evidence for spin polarization of the correlated insulators at integer filling, = 2 and 3. The in-plane magnetoresistance of correlated insulator states in our sample is consistent with previous reports, but in addition we observe hysteresis in longitudinal and transverse resistivity as a function of out-of-plane field for the correlated metallic state at fractional filling 3.5- 4.  These hysteretic anomalous Hall signatures suggest spontaneous time-reversal symmetry breaking associated with valley ferromagnetism. The out-of-plane hysteresis is suppressed but not eliminated by additional in-plane fields up to 1T, perhaps reflecting an interplay between spin and valley degrees of freedom in the system.