Spin magnetometry as a probe of stripe superconductivity in twisted bilayer graphene

The discovery of alternating superconducting and insulating ground-states in magic angle graphene has suggested an intriguing analogy with cuprate high-$T_c$ materials. Here we argue that the network states of small angle twisted bilayer graphene (TBG) afford a further perspective on the cuprates by emulating their stripe-ordered phases, as in La$_{1.875}$Ba$_{0.125}$CuO$_4$. We show that the spin and valley quantum numbers of stripes in TBG graphene fractionalize, developing characteristic signatures in the tunneling density of states and the magnetic noise spectrum of impurity spins. By examining the coupling between the charge rivers we determine the superconducting transition temperature. Our study suggests that magic angle graphene can be used for a controlled emulation of stripe superconductivity and quantum sensing experiments of emergent anyonic excitations.