DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Moiré metrology of energy landscapes in van der Waals heterostructures

Abstract

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.

Authors:
ORCiD logo [1]; ORCiD logo [2];  [3];  [3];  [3];  [3]; ORCiD logo [4];  [5]; ORCiD logo [3];  [3]; ORCiD logo [3];  [3]; ORCiD logo [3];  [3]; ORCiD logo [6];  [6]; ORCiD logo [7]; ORCiD logo [3]; ORCiD logo [2]; ORCiD logo [3] more »; ORCiD logo [8]; ORCiD logo [9]; ORCiD logo [3] « less
  1. Columbia Univ., New York, NY (United States). Dept. of Physics
  2. Columbia Univ., New York, NY (United States). Dept. of Mechanical Engineering
  3. Columbia Univ., New York, NY (United States). Dept. of Physics
  4. Max Planck Inst. for the Structure and Dynamics of Matter, Hamburg (Germany). Center Free-Electron Laser Science
  5. Harvard Univ., Cambridge, MA (United States). Dept. of Physics
  6. National Inst. for Material Science, Tsukuba (Japan)
  7. Harvard Univ., Cambridge, MA (United States). John A. Paulson School of Engineering and Applied Sciences
  8. Max Planck Inst. for the Structure and Dynamics of Matter, Hamburg (Germany). Center Free-Electron Laser Science; RWTH Aachen Univ. (Germany). Institut fur Theorie der Statistischen Physik
  9. Max Planck Inst. for the Structure and Dynamics of Matter, Hamburg (Germany). Center Free-Electron Laser Science; Flatiron Institute, New York, NY (United States). Center for Computational Quantum Physics
Publication Date:
Research Org.:
Columbia Univ., New York, NY (United States); Krell Institute, Ames, IA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1816209
Grant/Contract Number:  
NA0003864; SC0019443
Resource Type:
Accepted Manuscript
Journal Name:
Nature Communications
Additional Journal Information:
Journal Volume: 12; Journal Issue: 1; Journal ID: ISSN 2041-1723
Publisher:
Nature Publishing Group
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Halbertal, Dorri, Finney, Nathan R., Sunku, Sai S., Kerelsky, Alexander, Rubio-Verdú, Carmen, Shabani, Sara, Xian, Lede, Carr, Stephen, Chen, Shaowen, Zhang, Charles, Wang, Lei, Gonzalez-Acevedo, Derick, McLeod, Alexander S., Rhodes, Daniel, Watanabe, Kenji, Taniguchi, Takashi, Kaxiras, Efthimios, Dean, Cory R., Hone, James C., Pasupathy, Abhay N., Kennes, Dante M., Rubio, Angel, and Basov, D. N. Moiré metrology of energy landscapes in van der Waals heterostructures. United States: N. p., 2021. Web. doi:10.1038/s41467-020-20428-1.
Halbertal, Dorri, Finney, Nathan R., Sunku, Sai S., Kerelsky, Alexander, Rubio-Verdú, Carmen, Shabani, Sara, Xian, Lede, Carr, Stephen, Chen, Shaowen, Zhang, Charles, Wang, Lei, Gonzalez-Acevedo, Derick, McLeod, Alexander S., Rhodes, Daniel, Watanabe, Kenji, Taniguchi, Takashi, Kaxiras, Efthimios, Dean, Cory R., Hone, James C., Pasupathy, Abhay N., Kennes, Dante M., Rubio, Angel, & Basov, D. N. Moiré metrology of energy landscapes in van der Waals heterostructures. United States. https://doi.org/10.1038/s41467-020-20428-1
Halbertal, Dorri, Finney, Nathan R., Sunku, Sai S., Kerelsky, Alexander, Rubio-Verdú, Carmen, Shabani, Sara, Xian, Lede, Carr, Stephen, Chen, Shaowen, Zhang, Charles, Wang, Lei, Gonzalez-Acevedo, Derick, McLeod, Alexander S., Rhodes, Daniel, Watanabe, Kenji, Taniguchi, Takashi, Kaxiras, Efthimios, Dean, Cory R., Hone, James C., Pasupathy, Abhay N., Kennes, Dante M., Rubio, Angel, and Basov, D. N. Mon . "Moiré metrology of energy landscapes in van der Waals heterostructures". United States. https://doi.org/10.1038/s41467-020-20428-1. https://www.osti.gov/servlets/purl/1816209.
@article{osti_1816209,
title = {Moiré metrology of energy landscapes in van der Waals heterostructures},
author = {Halbertal, Dorri and Finney, Nathan R. and Sunku, Sai S. and Kerelsky, Alexander and Rubio-Verdú, Carmen and Shabani, Sara and Xian, Lede and Carr, Stephen and Chen, Shaowen and Zhang, Charles and Wang, Lei and Gonzalez-Acevedo, Derick and McLeod, Alexander S. and Rhodes, Daniel and Watanabe, Kenji and Taniguchi, Takashi and Kaxiras, Efthimios and Dean, Cory R. and Hone, James C. and Pasupathy, Abhay N. and Kennes, Dante M. and Rubio, Angel and Basov, D. N.},
abstractNote = {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.},
doi = {10.1038/s41467-020-20428-1},
journal = {Nature Communications},
number = 1,
volume = 12,
place = {United States},
year = {Mon Jan 11 00:00:00 EST 2021},
month = {Mon Jan 11 00:00:00 EST 2021}
}

Works referenced in this record:

Double-slit photoelectron interference in strong-field ionization of the neon dimer
journal, January 2019


Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

Measurement of the cleavage energy of graphite
journal, August 2015

  • Wang, Wen; Dai, Shuyang; Li, Xide
  • Nature Communications, Vol. 6, Issue 1
  • DOI: 10.1038/ncomms8853

Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene
journal, October 2019


van der Waals heterostructures combining graphene and hexagonal boron nitride
journal, January 2019

  • Yankowitz, Matthew; Ma, Qiong; Jarillo-Herrero, Pablo
  • Nature Reviews Physics, Vol. 1, Issue 2
  • DOI: 10.1038/s42254-018-0016-0

Unconventional superconductivity in magic-angle graphene superlattices
journal, March 2018


Hubbard Model Physics in Transition Metal Dichalcogenide Moiré Bands
journal, July 2018


Strain solitons and topological defects in bilayer graphene
journal, June 2013

  • Alden, J. S.; Tsen, A. W.; Huang, P. Y.
  • Proceedings of the National Academy of Sciences, Vol. 110, Issue 28
  • DOI: 10.1073/pnas.1309394110

Quantum Monte Carlo Calculation of the Binding Energy of Bilayer Graphene
journal, September 2015


Moiré Patterns as a Probe of Interplanar Interactions for Graphene on h-BN
journal, September 2014


Soldering to a single atomic layer
journal, November 2007

  • Girit, Çağlar Ö.; Zettl, A.
  • Applied Physics Letters, Vol. 91, Issue 19
  • DOI: 10.1063/1.2812571

Diffusivity Reveals Three Distinct Phases of Interlayer Excitons in MoSe 2 / WSe 2 Heterobilayers
journal, March 2021


Van der Waals density functionals applied to solids
journal, May 2011


Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene
journal, July 2019


Mapping the twist-angle disorder and Landau levels in magic-angle graphene
journal, May 2020


From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999


Topologically Protected Helical States in Minimally Twisted Bilayer Graphene
journal, July 2018


Chemical accuracy for the van der Waals density functional
journal, December 2009

  • Klimeš, Jiří; Bowler, David R.; Michaelides, Angelos
  • Journal of Physics: Condensed Matter, Vol. 22, Issue 2
  • DOI: 10.1088/0953-8984/22/2/022201

Untying the insulating and superconducting orders in magic-angle graphene
journal, July 2020


Moiré engineering of electronic phenomena in correlated oxides
journal, April 2020


Benchmarking Quantum Chemical Methods: Are We Heading in the Right Direction?
journal, April 2017

  • Mata, Ricardo A.; Suhm, Martin A.
  • Angewandte Chemie International Edition, Vol. 56, Issue 37
  • DOI: 10.1002/anie.201611308

Cascade of phase transitions and Dirac revivals in magic-angle graphene
journal, June 2020


van der Waals Heterostructures with High Accuracy Rotational Alignment
journal, February 2016


Superconductivity and strong correlations in moiré flat bands
journal, May 2020


Global Control of Stacking-Order Phase Transition by Doping and Electric Field in Few-Layer Graphene
journal, April 2020


Correlated states in twisted double bilayer graphene
journal, March 2020


Chemistry and Quantum Mechanics in 2019: Give Us Insight and Numbers
journal, January 2019

  • Neese, Frank; Atanasov, Mihail; Bistoni, Giovanni
  • Journal of the American Chemical Society, Vol. 141, Issue 7
  • DOI: 10.1021/jacs.8b13313

A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
journal, April 2010

  • Grimme, Stefan; Antony, Jens; Ehrlich, Stephan
  • The Journal of Chemical Physics, Vol. 132, Issue 15
  • DOI: 10.1063/1.3382344

Moiré excitons: From programmable quantum emitter arrays to spin-orbit–coupled artificial lattices
journal, November 2017


Approaching the Intrinsic Limit in Transition Metal Diselenides via Point Defect Control
journal, June 2019


van der Waals bilayer energetics: Generalized stacking-fault energy of graphene, boron nitride, and graphene/boron nitride bilayers
journal, October 2015


Multiflat Bands and Strong Correlations in Twisted Bilayer Boron Nitride: Doping-Induced Correlated Insulator and Superconductor
journal, July 2019


Relaxation and domain formation in incommensurate two-dimensional heterostructures
journal, December 2018


Hubbard model physics in transition metal dichalcogenide moiré bands
text, January 2018


One-dimensional flat bands in twisted bilayer germanium selenide
journal, February 2020


Photonic crystals for nano-light in moiré graphene superlattices
journal, December 2018


Electrically Tunable Valley Dynamics in Twisted WSe 2 / WSe 2 Bilayers
journal, May 2020


Electronic correlations in twisted bilayer graphene near the magic angle
journal, August 2019


Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996


Observation of moiré excitons in WSe2/WS2 heterostructure superlattices
journal, February 2019


Exact continuum model for low-energy electronic states of twisted bilayer graphene
journal, August 2019


Moire bands in twisted double-layer graphene
journal, July 2011

  • Bistritzer, R.; MacDonald, A. H.
  • Proceedings of the National Academy of Sciences, Vol. 108, Issue 30
  • DOI: 10.1073/pnas.1108174108

Tunable spin-polarized correlated states in twisted double bilayer graphene
journal, July 2020


Atomic reconstruction in twisted bilayers of transition metal dichalcogenides
journal, May 2020


Nano-photocurrent Mapping of Local Electronic Structure in Twisted Bilayer Graphene
journal, February 2020


Skyrmions in the Moiré of van der Waals 2D Magnets
journal, October 2018


One-Dimensional Electrical Contact to a Two-Dimensional Material
journal, October 2013


Twist Angle-Dependent Atomic Reconstruction and Moiré Patterns in Transition Metal Dichalcogenide Heterostructures
journal, March 2020

  • Rosenberger, Matthew R.; Chuang, Hsun-Jen; Phillips, Madeleine
  • ACS Nano, Vol. 14, Issue 4
  • DOI: 10.1021/acsnano.0c00088

Stacking Domains and Dislocation Networks in Marginally Twisted Bilayers of Transition Metal Dichalcogenides
journal, May 2020


Independent superconductors and correlated insulators in twisted bilayer graphene
journal, June 2020


Semiempirical GGA-type density functional constructed with a long-range dispersion correction
journal, January 2006

  • Grimme, Stefan
  • Journal of Computational Chemistry, Vol. 27, Issue 15, p. 1787-1799
  • DOI: 10.1002/jcc.20495

Tuning superconductivity in twisted bilayer graphene
journal, January 2019


Twist Angle-Dependent Atomic Reconstruction and Moiré Patterns in Transition Metal Dichalcogenide Heterostructures
journal, March 2020

  • Rosenberger, Matthew R.; Chuang, Hsun-Jen; Phillips, Madeleine
  • ACS Nano, Vol. 14, Issue 4
  • DOI: 10.1021/acsnano.0c00088

Electrode-Free Anodic Oxidation Nanolithography of Low-Dimensional Materials
journal, November 2018


Transport Through a Network of Topological Channels in Twisted Bilayer Graphene
journal, October 2018


Commensurate–incommensurate transition in graphene on hexagonal boron nitride
journal, April 2014

  • Woods, C. R.; Britnell, L.; Eckmann, A.
  • Nature Physics, Vol. 10, Issue 6
  • DOI: 10.1038/nphys2954

Energy Minimization of Two Dimensional Incommensurate Heterostructures
journal, August 2019

  • Cazeaux, Paul; Luskin, Mitchell; Massatt, Daniel
  • Archive for Rational Mechanics and Analysis, Vol. 235, Issue 2
  • DOI: 10.1007/s00205-019-01444-y

Reliable Exfoliation of Large-Area High-Quality Flakes of Graphene and Other Two-Dimensional Materials
journal, September 2015


Strongly correlated electrons and hybrid excitons in a moiré heterostructure
journal, April 2020


Giant oscillations in a triangular network of one-dimensional states in marginally twisted graphene
journal, September 2019