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Interactions among electrons create novel many-body quantum phases of matterwith wavefunctions that often reflect electronic correlation effects, brokensymmetries, and novel collective excitations. A wide range of quantum phaseshas been discovered in MATBG, including correlated insulating, unconventionalsuperconducting, and magnetic topological phases. The lack of microscopicinformation, including precise knowledge of possible broken symmetries, hasthus far hampered our understanding of MATBG's correlated phases. Here we usehigh-resolution scanning tunneling microscopy to directly probe thewavefunctions of the correlated phases in MATBG. The squares of thewavefunctions of gapped phases, including those of the correlated insulators,pseudogap, and superconducting phases, show distinct patterns of brokensymmetry with a $\sqrt{3}$ x $\sqrt{3}$ super-periodicity on the grapheneatomic lattice that has a complex spatial dependence on the moir\'esuperlattice scale. We introduce a symmetry-based analysis to describe ourmeasurements of the wavefunctions of MATBG's correlated phases with a set ofcomplex-valued local order parameters. For the correlated insulators in MATBG,at fillings of $\nu$ = $\pm$ 2 electrons per moir\'e unit cell relative tocharge neutrality, we compare the observed quantum textures to those expectedfor proposed theoretical ground states. In typical MATBG devices, the texturesof correlated insulators' wavefunctions closely match those of thetheoretically proposed IKS order, while in ultra-low-strain samples our datahas local symmetries like those of a T-IVC phase. We also study thewavefunction of MATBG's superconducting state, revealing strong signatures ofintervalley coherence that can only be distinguished from those of theinsulator with our phase-sensitive measurements.

Quantum textures of the many-body wavefunctions in magic-angle graphene