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 correlated insulating, unconventional superconducting, and magnetic topological phases. The lack of microscopic information of possible broken symmetries has hampered our understanding of these phases. In this talk, I will discuss a series of experiments where we use high-resolution scanning tunneling microscopy to study the wavefunctions of the correlated phases in MATBG [1]. The squares of the wavefunctions of gapped phases, including those of the correlated insulators, pseudogap, and superconducting phases, show distinct broken symmetry patterns with a √3 x √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 v = ±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 (IKS) order [2], while in ultra-low-strain samples our data has local symmetries like those of a time-reversal symmetric intervalley coherent (T-IVC) phase [3]. Moreover, MATBG’s superconducting state shows strong signatures of intervalley coherence, distinguishable only from those of the insulator with our phase-sensitive measurements.
This work was primarily supported by the Gordon and Betty Moore Foundation’s EPiQS initiative grants GBMF9469 and DOE-BES grant DE-FG02-07ER46419.
[1] Nuckolls, K. P. et al. arXiv preprint arXiv:2303.00024 (to appear in Nature) (2023).
[2] Kwan, Y. H. et al. Phys. Rev. X 11, 041063 (2021).
[3] Kang, J. & Vafek, O. Phys. Rev. Lett. 122, 246401 (2019).