Low-energy moiré phonons in twisted bilayer van der Waals heterostructures

Lu, Jonathan Z.; Zhu, Ziyan; Angeli, Mattia; Larson, Daniel T.; Kaxiras, Efthimios

doi:10.1103/physrevb.106.144305

Low-energy moiré phonons in twisted bilayer van der Waals heterostructures

Journal Article · Mon Oct 10 04:00:00 EDT 2022 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.106.144305· OSTI ID:1998028

^[1]; ^[2]; ^[3]; ^[3]; Kaxiras, Efthimios ^[3]

Harvard University, Cambridge, MA (United States); SLAC
Harvard University, Cambridge, MA (United States); SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)
Harvard University, Cambridge, MA (United States)

We develop a low-energy continuum model for phonons in twisted moiré bilayers, based on a configuration-space approach. In this approach, interatomic force constants are obtained from density functional theory (DFT) calculations of untwisted bilayers with various in-plane shifts. This allows for efficient computation of phonon properties for any small twist angle, while maintaining DFT-level accuracy. Based on this framework, we show how the low-energy phonon modes, including interlayer shearing and layer-breathing modes, vary with the twist angle. As the twist angle decreases, the frequencies of the low-energy modes are reordered and the atomic displacement fields corresponding to phonon eigenmodes break translational symmetry, developing periodicity on the moiré length scale. Here, we demonstrate the capabilities of our model by calculating the phonon properties of three specific structures: bilayer graphene, bilayer molybdenum disulfide (MoS₂), and molybdenum diselenide-tungsten diselenide (MoSe₂-WSe₂).

View Accepted Manuscript (DOE)

Research Organization:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF); Simons Foundation; Army Research Office (ARO)

Grant/Contract Number:: AC02-76SF00515; SC0019300

OSTI ID:: 1998028

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 14 Vol. 106; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (63)

The Hiphive Package for the Extraction of High‐Order Force Constants by Machine Learning Eriksson, Fredrik; Fransson, Erik; Erhart, Paul Advanced Theory and Simulations, Vol. 2, Issue 5 https://doi.org/10.1002/adts.201800184	journal	February 2019
Energy Minimization of Two Dimensional Incommensurate Heterostructures Cazeaux, Paul; Luskin, Mitchell; Massatt, Daniel Archive for Rational Mechanics and Analysis, Vol. 235, Issue 2 https://doi.org/10.1007/s00205-019-01444-y	journal	August 2019
Raman scattering study of the phonon dispersion in twisted bilayer graphene Campos-Delgado, Jessica; Cançado, Luiz G.; Achete, Carlos A. Nano Research, Vol. 6, Issue 4 https://doi.org/10.1007/s12274-013-0304-z	journal	March 2013
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Kresse, G.; Furthmüller, J. Computational Materials Science, Vol. 6, Issue 1, p. 15-50 https://doi.org/10.1016/0927-0256(96)00008-0	journal	July 1996
LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales Thompson, Aidan P.; Aktulga, H. Metin; Berger, Richard Computer Physics Communications, Vol. 271 https://doi.org/10.1016/j.cpc.2021.108171	journal	February 2022
Accurate and Numerically Efficient r ² SCAN Meta-Generalized Gradient Approximation Furness, James W.; Kaplan, Aaron D.; Ning, Jinliang The Journal of Physical Chemistry Letters, Vol. 11, Issue 19 https://doi.org/10.1021/acs.jpclett.0c02405	journal	September 2020
Intrinsic Electric Field-Induced Properties in Janus MoSSe van der Waals Structures Li, Fengping; Wei, Wei; Wang, Hao The Journal of Physical Chemistry Letters, Vol. 10, Issue 3 https://doi.org/10.1021/acs.jpclett.8b03463	journal	January 2019
Chiral Phonons in Moiré Superlattices Suri, Nishchay; Wang, Chong; Zhang, Yinhan Nano Letters, Vol. 21, Issue 23 https://doi.org/10.1021/acs.nanolett.1c03692	journal	November 2021
Low-Frequency Interlayer Raman Modes to Probe Interface of Twisted Bilayer MoS ₂ Huang, Shengxi; Liang, Liangbo; Ling, Xi Nano Letters, Vol. 16, Issue 2 https://doi.org/10.1021/acs.nanolett.5b05015	journal	January 2016
Twisted Bilayer Graphene: Moiré with a Twist Dai, Shuyang; Xiang, Yang; Srolovitz, David J. Nano Letters, Vol. 16, Issue 9 https://doi.org/10.1021/acs.nanolett.6b02870	journal	August 2016
Nanoserpents: Graphene Nanoribbon Motion on Two-Dimensional Hexagonal Materials Ouyang, Wengen; Mandelli, Davide; Urbakh, Michael Nano Letters, Vol. 18, Issue 9 https://doi.org/10.1021/acs.nanolett.8b02848	journal	August 2018
Spectroscopic Signatures of Interlayer Coupling in Janus MoSSe/MoS ₂ Heterostructures Zhang, Kunyan; Guo, Yunfan; Larson, Daniel T. ACS Nano, Vol. 15, Issue 9 https://doi.org/10.1021/acsnano.1c03779	journal	August 2021
Moiré Phonons in Twisted Bilayer MoS ₂ Lin, Miao-Ling; Tan, Qing-Hai; Wu, Jiang-Bin ACS Nano, Vol. 12, Issue 8 https://doi.org/10.1021/acsnano.8b05006	journal	July 2018
Tailoring the Electronic Structure in Bilayer Molybdenum Disulfide via Interlayer Twist van der Zande, Arend M.; Kunstmann, Jens; Chernikov, Alexey Nano Letters, Vol. 14, Issue 7 https://doi.org/10.1021/nl501077m	journal	June 2014
Correlated insulator behaviour at half-filling in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Demir, Ahmet Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26154	journal	March 2018
Unconventional superconductivity in magic-angle graphene superlattices Cao, Yuan; Fatemi, Valla; Fang, Shiang Nature, Vol. 556, Issue 7699 https://doi.org/10.1038/nature26160	journal	March 2018
Evolution of interlayer coupling in twisted molybdenum disulfide bilayers Liu, Kaihui; Zhang, Liming; Cao, Ting Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms5966	journal	September 2014
Resonant Raman spectroscopy of twisted multilayer graphene Wu, Jiang-Bin; Zhang, Xin; Ijäs, Mari Nature Communications, Vol. 5, Issue 1 https://doi.org/10.1038/ncomms6309	journal	November 2014
Observation of long-lived interlayer excitons in monolayer MoSe2–WSe2 heterostructures Rivera, Pasqual; Schaibley, John R.; Jones, Aaron M. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms7242	journal	February 2015
Correlated electronic phases in twisted bilayer transition metal dichalcogenides Wang, Lei; Shih, En-Min; Ghiotto, Augusto Nature Materials, Vol. 19, Issue 8 https://doi.org/10.1038/s41563-020-0708-6	journal	June 2020
Phonon renormalization in reconstructed MoS2 moiré superlattices Quan, Jiamin; Linhart, Lukas; Lin, Miao-Ling Nature Materials, Vol. 20, Issue 8 https://doi.org/10.1038/s41563-021-00960-1	journal	March 2021
Dynamic band-structure tuning of graphene moiré superlattices with pressure Yankowitz, Matthew; Jung, Jeil; Laksono, Evan Nature, Vol. 557, Issue 7705 https://doi.org/10.1038/s41586-018-0107-1	journal	May 2018
Signatures of moiré-trapped valley excitons in MoSe2/WSe2 heterobilayers Seyler, Kyle L.; Rivera, Pasqual; Yu, Hongyi Nature, Vol. 567, Issue 7746 https://doi.org/10.1038/s41586-019-0957-1	journal	February 2019
Evidence for moiré excitons in van der Waals heterostructures Tran, Kha; Moody, Galan; Wu, Fengcheng Nature, Vol. 567, Issue 7746 https://doi.org/10.1038/s41586-019-0975-z	journal	February 2019
Observation of moiré excitons in WSe2/WS2 heterostructure superlattices Jin, Chenhao; Regan, Emma C.; Yan, Aiming Nature, Vol. 567, Issue 7746 https://doi.org/10.1038/s41586-019-0976-y	journal	February 2019
Resonantly hybridized excitons in moiré superlattices in van der Waals heterostructures Alexeev, Evgeny M.; Ruiz-Tijerina, David A.; Danovich, Mark Nature, Vol. 567, Issue 7746 https://doi.org/10.1038/s41586-019-0986-9	journal	March 2019
Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene Lu, Xiaobo; Stepanov, Petr; Yang, Wei Nature, Vol. 574, Issue 7780 https://doi.org/10.1038/s41586-019-1695-0	journal	October 2019
Tunable correlated states and spin-polarized phases in twisted bilayer–bilayer graphene Cao, Yuan; Rodan-Legrain, Daniel; Rubies-Bigorda, Oriol Nature https://doi.org/10.1038/s41586-020-2260-6	journal	May 2020
Tunable spin-polarized correlated states in twisted double bilayer graphene Liu, Xiaomeng; Hao, Zeyu; Khalaf, Eslam Nature, Vol. 583, Issue 7815 https://doi.org/10.1038/s41586-020-2458-7	journal	July 2020
Localization of lattice dynamics in low-angle twisted bilayer graphene Gadelha, Andreij C.; Ohlberg, Douglas A. A.; Rabelo, Cassiano Nature, Vol. 590, Issue 7846 https://doi.org/10.1038/s41586-021-03252-5	journal	February 2021
A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu Grimme, Stefan; Antony, Jens; Ehrlich, Stephan The Journal of Chemical Physics, Vol. 132, Issue 15 https://doi.org/10.1063/1.3382344	journal	April 2010
Generalized Kubo formulas for the transport properties of incommensurate 2D atomic heterostructures Cancès, Eric; Cazeaux, Paul; Luskin, Mitchell Journal of Mathematical Physics, Vol. 58, Issue 6 https://doi.org/10.1063/1.4984041	journal	June 2017
Moire bands in twisted double-layer graphene Bistritzer, R.; MacDonald, A. H. Proceedings of the National Academy of Sciences, Vol. 108, Issue 30 https://doi.org/10.1073/pnas.1108174108	journal	July 2011
Γ valley transition metal dichalcogenide moiré bands Angeli, Mattia; MacDonald, Allan H. Proceedings of the National Academy of Sciences, Vol. 118, Issue 10 https://doi.org/10.1073/pnas.2021826118	journal	March 2021
Coulomb interaction, phonons, and superconductivity in twisted bilayer graphene Cea, Tommaso; Guinea, Francisco Proceedings of the National Academy of Sciences, Vol. 118, Issue 32 https://doi.org/10.1073/pnas.2107874118	journal	August 2021
A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons Brenner, Donald W.; Shenderova, Olga A.; Harrison, Judith A. Journal of Physics: Condensed Matter, Vol. 14, Issue 4 https://doi.org/10.1088/0953-8984/14/4/312	journal	January 2002
Discrete-to-continuum modelling of weakly interacting incommensurate two-dimensional lattices Español, Malena I.; Golovaty, Dmitry; Wilber, J. Patrick Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 474, Issue 2209 https://doi.org/10.1098/rspa.2017.0612	journal	January 2018
Moiré phonons in twisted bilayer graphene Koshino, Mikito; Son, Young-Woo Physical Review B, Vol. 100, Issue 7 https://doi.org/10.1103/PhysRevB.100.075416	journal	August 2019
Moiré-pattern fluctuations and electron-phason coupling in twisted bilayer graphene Ochoa, Héctor Physical Review B, Vol. 100, Issue 15 https://doi.org/10.1103/PhysRevB.100.155426	journal	October 2019
Modeling mechanical relaxation in incommensurate trilayer van der Waals heterostructures Zhu, Ziyan; Cazeaux, Paul; Luskin, Mitchell Physical Review B, Vol. 101, Issue 22 https://doi.org/10.1103/PhysRevB.101.224107	journal	June 2020
Chiral valley phonons and flat phonon bands in moiré materials Maity, Indrajit; Mostofi, Arash A.; Lischner, Johannes Physical Review B, Vol. 105, Issue 4 https://doi.org/10.1103/PhysRevB.105.L041408	journal	January 2022
Relaxation effects in twisted bilayer graphene: A multiscale approach Leconte, Nicolas; Javvaji, Srivani; An, Jiaqi Physical Review B, Vol. 106, Issue 11 https://doi.org/10.1103/PhysRevB.106.115410	journal	September 2022
Ab initiomolecular dynamics for liquid metals Kresse, G.; Hafner, J. Physical Review B, Vol. 47, Issue 1, p. 558-561 https://doi.org/10.1103/PhysRevB.47.558	journal	January 1993
Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium Kresse, G.; Hafner, J. Physical Review B, Vol. 49, Issue 20, p. 14251-14269 https://doi.org/10.1103/PhysRevB.49.14251	journal	May 1994
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
Registry-dependent interlayer potential for graphitic systems Kolmogorov, Aleksey N.; Crespi, Vincent H. Physical Review B, Vol. 71, Issue 23 https://doi.org/10.1103/PhysRevB.71.235415	journal	June 2005
Twistronics: Manipulating the electronic properties of two-dimensional layered structures through their twist angle Carr, Stephen; Massatt, Daniel; Fang, Shiang Physical Review B, Vol. 95, Issue 7 https://doi.org/10.1103/PhysRevB.95.075420	journal	February 2017
Lattice relaxation and energy band modulation in twisted bilayer graphene Nam, Nguyen N. T.; Koshino, Mikito Physical Review B, Vol. 96, Issue 7 https://doi.org/10.1103/PhysRevB.96.075311	journal	August 2017
Relaxation and domain formation in incommensurate two-dimensional heterostructures Carr, Stephen; Massatt, Daniel; Torrisi, Steven B. Physical Review B, Vol. 98, Issue 22 https://doi.org/10.1103/PhysRevB.98.224102	journal	December 2018
Emergent D 6 symmetry in fully relaxed magic-angle twisted bilayer graphene Angeli, M.; Mandelli, D.; Valli, A. Physical Review B, Vol. 98, Issue 23 https://doi.org/10.1103/PhysRevB.98.235137	journal	December 2018
Discrete-to-continuum modeling of weakly interacting incommensurate chains Español, Malena I.; Golovaty, Dmitry; Wilber, J. Patrick Physical Review E, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevE.96.033003	journal	September 2017
Chiral Phonons at High-Symmetry Points in Monolayer Hexagonal Lattices Zhang, Lifa; Niu, Qian Physical Review Letters, Vol. 115, Issue 11 https://doi.org/10.1103/PhysRevLett.115.115502	journal	September 2015
Hubbard Model Physics in Transition Metal Dichalcogenide Moiré Bands Wu, Fengcheng; Lovorn, Timothy; Tutuc, Emanuel Physical Review Letters, Vol. 121, Issue 2 https://doi.org/10.1103/PhysRevLett.121.026402	journal	July 2018
Theory of Phonon-Mediated Superconductivity in Twisted Bilayer Graphene Wu, Fengcheng; MacDonald, A. H.; Martin, Ivar Physical Review Letters, Vol. 121, Issue 25 https://doi.org/10.1103/PhysRevLett.121.257001	journal	December 2018
Topological Insulators in Twisted Transition Metal Dichalcogenide Homobilayers Wu, Fengcheng; Lovorn, Timothy; Tutuc, Emanuel Physical Review Letters, Vol. 122, Issue 8 https://doi.org/10.1103/PhysRevLett.122.086402	journal	February 2019
Twisted Bilayer Graphene: A Phonon-Driven Superconductor Lian, Biao; Wang, Zhijun; Bernevig, B. Andrei Physical Review Letters, Vol. 122, Issue 25 https://doi.org/10.1103/PhysRevLett.122.257002	journal	June 2019
All Magic Angles in Twisted Bilayer Graphene are Topological Song, Zhida; Wang, Zhijun; Shi, Wujun Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/PhysRevLett.123.036401	journal	July 2019
Correlated Insulating States in Twisted Double Bilayer Graphene Burg, G. William; Zhu, Jihang; Taniguchi, Takashi Physical Review Letters, Vol. 123, Issue 19 https://doi.org/10.1103/PhysRevLett.123.197702	journal	November 2019
Nature of the Correlated Insulator States in Twisted Bilayer Graphene Xie, Ming; MacDonald, A. H. Physical Review Letters, Vol. 124, Issue 9 https://doi.org/10.1103/PhysRevLett.124.097601	journal	March 2020
Generalized Gradient Approximation Made Simple Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868 https://doi.org/10.1103/PhysRevLett.77.3865	journal	October 1996
Structural Relaxation Made Simple Bitzek, Erik; Koskinen, Pekka; Gähler, Franz Physical Review Letters, Vol. 97, Issue 17 https://doi.org/10.1103/PhysRevLett.97.170201	journal	October 2006
Phonons in twisted transition-metal dichalcogenide bilayers: Ultrasoft phasons and a transition from a superlubric to a pinned phase Maity, Indrajit; Naik, Mit H.; Maiti, Prabal K. Physical Review Research, Vol. 2, Issue 1 https://doi.org/10.1103/PhysRevResearch.2.013335	journal	March 2020
Valley Jahn-Teller Effect in Twisted Bilayer Graphene Angeli, M.; Tosatti, E.; Fabrizio, M. Physical Review X, Vol. 9, Issue 4 https://doi.org/10.1103/PhysRevX.9.041010	journal	October 2019

Similar Records

Tuning commensurability in twisted van der Waals bilayers

Journal Article · Tue Jan 16 23:00:00 EST 2024 · Nature (London) · OSTI ID:2346125

Moiré metrology of energy landscapes in van der Waals heterostructures

Journal Article · Sun Jan 10 23:00:00 EST 2021 · Nature Communications · OSTI ID:1816209

Evidence for moiré excitons in van der Waals heterostructures

Journal Article · Sun Feb 24 23:00:00 EST 2019 · Nature (London) · OSTI ID:1503250

Related Subjects

2-dimensional systems
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Continuum mechanics
Density functional theory
Graphene
Lattice dynamics
Phonons
Transition metal dichalcogenides
Twisted heterostructures

Low-energy moiré phonons in twisted bilayer van der Waals heterostructures

Citation Formats

References (63)

Similar Records

Related Subjects