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

Kevin P. Nuckolls, Ryan L. Lee, Myungchul Oh, Dillon Wong, Tomohiro Soejima, Jung Pyo Hong, Dumitru Călugăru, Jonah Herzog-Arbeitman, B. Andrei Bernevig, Kenji Watanabe, Takashi Taniguchi, Nicolas Regnault, Michael P. Zaletel and Ali Yazdani ()
Additional contact information
Kevin P. Nuckolls: Princeton University
Ryan L. Lee: Princeton University
Myungchul Oh: Princeton University
Dillon Wong: Princeton University
Tomohiro Soejima: University of California
Jung Pyo Hong: Princeton University
Dumitru Călugăru: Princeton University
Jonah Herzog-Arbeitman: Princeton University
B. Andrei Bernevig: Princeton University
Kenji Watanabe: Research Center for Functional Materials, National Institute for Materials Science
Takashi Taniguchi: International Center for Materials Nanoarchitectonics, National Institute for Materials Science
Nicolas Regnault: Laboratoire de Physique de l’Ecole normale supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité
Michael P. Zaletel: University of California
Ali Yazdani: Princeton University

Nature, 2023, vol. 620, issue 7974, 525-532

Abstract: 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 correlated insulating1, 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 correlated insulating, 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.

Date: 2023
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DOI: 10.1038/s41586-023-06226-x

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