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

Journal Article · 16 August 2023 · Nature (London)

DOI: https://doi.org/10.1038/s41586-023-06226-x · OSTI ID:2500345

Nuckolls, Kevin P.  ^[1]; Lee, Ryan L. ^[1]; Oh, Myungchul  ^[1]; Wong, Dillon  ^[1]; Soejima, Tomohiro ^[2]; Hong, Jung Pyo ^[1]; Călugăru, Dumitru  ^[1]; Herzog-Arbeitman, Jonah  ^[1]; Bernevig, B. Andrei  ^[3]; Watanabe, Kenji  ^[4]; Taniguchi, Takashi  ^[4]; Regnault, Nicolas ^[5]; Zaletel, Michael P. ^[6]; Yazdani, Ali  ^[1]

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1. Princeton University, NJ (United States)
2. University of California, Berkeley, CA (United States)
3. Princeton University, NJ (United States); Donostia International Physics Center (Spain); IKERBASQUE, Basque Foundation for Science, Bilbao (Spain)
4. National Institute for Materials Science, Tsukuba (Japan)
5. Université Paris-Diderot (France)
6. University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)

Interactions among electrons create novel many-body quantum phases of matter with wavefunctions that often reflect electronic correlation effects, broken symmetries, and novel collective excitations. A wide range of quantum phases has been discovered in MATBG, including correlated insulating, unconventional superconducting, and magnetic topological phases. The lack of microscopic information, including precise knowledge of possible broken symmetries, has thus far hampered our understanding of MATBG's correlated phases. Here we use high-resolution scanning tunneling microscopy to directly probe the wavefunctions of the correlated phases in MATBG. The squares of the wavefunctions of gapped phases, including those of the correlated insulators, pseudogap, and superconducting phases, show distinct patterns of broken symmetry with a √3 x √3 super-periodicity on the graphene atomic lattice that has a complex spatial dependence on the moiré superlattice scale. We introduce a symmetry-based analysis to describe our measurements of the wavefunctions of MATBG's correlated phases with a set of complex-valued local order parameters. For the correlated insulators in MATBG, at fillings of ±2 electrons per moiré unit cell relative to charge neutrality, we compare the observed quantum textures to those expected for proposed theoretical ground states. In typical MATBG devices, the textures of correlated insulators' wavefunctions closely match those of the theoretically proposed IKS order, while in ultra-low-strain samples our data has local symmetries like those of a T-IVC phase. Here, we also study the wavefunction of MATBG's superconducting state, revealing strong signatures of intervalley coherence that can only be distinguished from those of the insulator with our phase-sensitive measurements.

• Research Organization: Princeton University, NJ (United States)
• Sponsoring Organization: BSF Israel US foundation; EPiQS Initiative; European Union’s Horizon 2020 research and innovation programme; Gordon and Betty Moore Foundation; Gordon and Betty Moore Foundation’s EPiQS initiative; JSPS KAKENHI; MEXT; NSF-MRSEC; Office of Naval Research (ONR); Simons Investigator; USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division (MSE)
• Grant/Contract Number: AC02-05CH11231; FG02-07ER46419
• OSTI ID: 2500345
• Journal Information: Nature (London), Journal Name: Nature (London) Journal Issue: 7974 Vol. 620; ISSN 0028-0836
• Publisher: Nature Publishing GroupCopyright Statement
• Country of Publication: United States
• Language: English