Moiré metrology of energy landscapes in van der Waals heterostructures

Dorri Halbertal, Nathan R. Finney, Sai S. Sunku, Alexander Kerelsky, Carmen Rubio-Verdú, Sara Shabani, Lede Xian, Stephen Carr, Shaowen Chen, Charles Zhang, Lei Wang, Derick Gonzalez-Acevedo, Alexander S. McLeod, Daniel Rhodes, Kenji Watanabe, Takashi Taniguchi, Efthimios Kaxiras, Cory R. Dean, James C. Hone, Abhay N. PasupathyDante M. Kennes, Angel Rubio, D. N. Basov

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


The emerging field of twistronics, which harnesses the twist angle between two-dimensional materials, represents a promising route for the design of quantum materials, as the twist-angle-induced superlattices offer means to control topology and strong correlations. At the small twist limit, and particularly under strain, as atomic relaxation prevails, the emergent moiré superlattice encodes elusive insights into the local interlayer interaction. Here we introduce moiré metrology as a combined experiment-theory framework to probe the stacking energy landscape of bilayer structures at the 0.1 meV/atom scale, outperforming the gold-standard of quantum chemistry. Through studying the shapes of moiré domains with numerous nano-imaging techniques, and correlating with multi-scale modelling, we assess and refine first-principle models for the interlayer interaction. We document the prowess of moiré metrology for three representative twisted systems: bilayer graphene, double bilayer graphene and H-stacked MoSe2/WSe2. Moiré metrology establishes sought after experimental benchmarks for interlayer interaction, thus enabling accurate modelling of twisted multilayers.

Original languageEnglish (US)
Article number242
JournalNature communications
Issue number1
StatePublished - Dec 2021
Externally publishedYes

Bibliographical note

Funding Information:
Research at Columbia on moiré superlattices is supported as part of Programmable Quantum Materials, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences (BES), under award DESC0019443. STM instrumentation for STM experiments was developed with support from the Air Force Office of Scientific Research via grant FA9550-16-1-0601. Synthesis of MoSe2 and WSe2crystals was supported by the NSF MRSEC program through Columbia in the Center for Precision Assembly of Superstratic and Superatomic Solids (DMR-2011738). A.R. acknowledges support by the European Research Council (ERC-2015-AdG-694097), Grupos Consolidados (IT1249-19), SFB925 and the Flatiron Institute, a division of the Simons Foundation. We acknowledge funding by the Deutsche For-schungsgemeinschaft (DFG) under Germany’s Excellence Strategy - Cluster of Excellence Matter and Light for Quantum Computing (ML4Q) EXC 2004/1—390534769, funding by Advanced Imaging of Matter (AIM) EXC 2056—390715994, funding by the DFG under RTG 1995 and RTG 2247 and by DFG within the Priority Program SPP 2244 “2DMP”. We acknowledge support from the Max Planck-New York City Center for Non-Equilibrium Quantum Phenomena. Work at Harvard was supported by the STC Center for Integrated Quantum Materials NSF Grant No. DMR1231319 and ARO MURI Award No. W911NF-14-0247. D.H. was supported by a grant from the Simons Foundation (579913). N.R.F. acknowledges support from the Stewardship Science Graduate Fellowship program provided under cooperative agreement number DE-NA0003864. C.R.V. acknowledges funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 844271. D.N.B. is the Vannevar Bush Faculty Fellow ONR-VB: N00014-19-1-263 and the Moore Investigator in Quantum Materials EPIQS #9455.

Publisher Copyright:
© 2021, The Author(s).


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