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

Abstract

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that reflect electronic correlation effects, broken symmetries and collective excitations. Many quantum phases have been discovered in magic-angle twisted bilayer graphene (MATBG), including correlatedinsulating1, unconventional superconducting2-5 and magnetic topological6-9 phases. The lack of microscopic information10,11 of possible broken symmetries has hampered our understanding of these phases12-17. Here we use high-resolution scanning tunnelling microscopy to study the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlatedinsulating, pseudogap and superconducting phases, show distinct broken-symmetry patterns with a √3 × √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré scale. We introduce a symmetry-based analysis using a set of complex-valued local order parameters, which show intricate textures that distinguish the various correlated phases. We compare the observed quantum textures of the correlated insulators at fillings of ±2 electrons per moiré unit cell to those expected for proposed theoretical ground states. In typical MATBG devices, these textures closely match those of the proposed incommensurate Kekulé spiral order15, whereas in ultralow-strain samples, our data have local symmetries like those of a time-reversal symmetric intervalley coherent phase12. Moreover, the superconducting state of MATBG shows strong signatures of intervalley coherence, only distinguishable from those of the insulator with our phase-sensitive measurements.