Multiphonon diffuse scattering in solids from first principles: Application to layered crystals and two-dimensional materials
Abstract
Time-resolved diffuse scattering experiments have gained increasing attention due to their potential to reveal nonequilibrium dynamics of crystal lattice vibrations with full momentum resolution. Although progress has been made in interpreting experimental data on the basis of one-phonon scattering, understanding the role of individual phonons can be sometimes hindered by multiphonon excitations. In Ref. [M. Zacharias, H. Seiler, F. Caruso, D. Zahn, F. Giustino, P. C. Kelires, and R. Ernstorfer, Phys. Rev. Lett. 127, 207401 (2021)], we have introduced a rigorous approach for the calculation of the all-phonon inelastic scattering intensity of solids from first-principles. In the present work, we describe our implementation in detail and show that multiphonon interactions are captured efficiently by exploiting translational and time-reversal symmetries of the crystal. We demonstrate its predictive power by calculating the scattering patterns of monolayer molybdenum disulfide (MoS2), bulk MoS2, and black phosphorus (bP), and we obtain excellent agreement with our measurements of thermal electron diffuse scattering. Remarkably, our results show that multiphonon excitations dominate in bP across multiple Brillouin zones, while in MoS2 they play a less pronounced role. We expand our analysis for each system and examine the effect of individual atomic and interatomic vibrational motion on the diffusemore »
- Authors:
-
[1];
[2];
[3];
[2];
[4];
[1];
[5]
- Cyprus Univ. of Technology, Limassol (Cyprus)
- Fritz Haber Institute of the Max Planck Society, Berlin (Germany)
- Univ. of Kiel (Germany)
- Univ. of Texas, Austin, TX (United States)
- Fritz Haber Institute of the Max Planck Society, Berlin (Germany); Technical Univ. of Berlin (Germany)
- Publication Date:
- Research Org.:
- Univ. of Texas, Austin, TX (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES); Swiss National Science Foundation (SNSF); European Research Council (ERC)
- OSTI Identifier:
- 1979679
- Grant/Contract Number:
- SC0020129; P2SKP2_184100; ERC-2015-CoG-682843
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review. B
- Additional Journal Information:
- Journal Volume: 104; Journal Issue: 20; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; materials science; physics; electron-phonon coupling; electronic structure; phonons; scattering theory; thermal properties; ultrafast phenomena; nonequilibrium systems; electron diffraction; ultrafast pump-probe spectroscopy; X-ray diffuse scattering
Citation Formats
Zacharias, Marios, Seiler, Hélène, Caruso, Fabio, Zahn, Daniela, Giustino, Feliciano, Kelires, Pantelis C., and Ernstorfer, Ralph. Multiphonon diffuse scattering in solids from first principles: Application to layered crystals and two-dimensional materials. United States: N. p., 2021.
Web. doi:10.1103/physrevb.104.205109.
Zacharias, Marios, Seiler, Hélène, Caruso, Fabio, Zahn, Daniela, Giustino, Feliciano, Kelires, Pantelis C., & Ernstorfer, Ralph. Multiphonon diffuse scattering in solids from first principles: Application to layered crystals and two-dimensional materials. United States. https://doi.org/10.1103/physrevb.104.205109
Zacharias, Marios, Seiler, Hélène, Caruso, Fabio, Zahn, Daniela, Giustino, Feliciano, Kelires, Pantelis C., and Ernstorfer, Ralph. Tue .
"Multiphonon diffuse scattering in solids from first principles: Application to layered crystals and two-dimensional materials". United States. https://doi.org/10.1103/physrevb.104.205109. https://www.osti.gov/servlets/purl/1979679.
@article{osti_1979679,
title = {Multiphonon diffuse scattering in solids from first principles: Application to layered crystals and two-dimensional materials},
author = {Zacharias, Marios and Seiler, Hélène and Caruso, Fabio and Zahn, Daniela and Giustino, Feliciano and Kelires, Pantelis C. and Ernstorfer, Ralph},
abstractNote = {Time-resolved diffuse scattering experiments have gained increasing attention due to their potential to reveal nonequilibrium dynamics of crystal lattice vibrations with full momentum resolution. Although progress has been made in interpreting experimental data on the basis of one-phonon scattering, understanding the role of individual phonons can be sometimes hindered by multiphonon excitations. In Ref. [M. Zacharias, H. Seiler, F. Caruso, D. Zahn, F. Giustino, P. C. Kelires, and R. Ernstorfer, Phys. Rev. Lett. 127, 207401 (2021)], we have introduced a rigorous approach for the calculation of the all-phonon inelastic scattering intensity of solids from first-principles. In the present work, we describe our implementation in detail and show that multiphonon interactions are captured efficiently by exploiting translational and time-reversal symmetries of the crystal. We demonstrate its predictive power by calculating the scattering patterns of monolayer molybdenum disulfide (MoS2), bulk MoS2, and black phosphorus (bP), and we obtain excellent agreement with our measurements of thermal electron diffuse scattering. Remarkably, our results show that multiphonon excitations dominate in bP across multiple Brillouin zones, while in MoS2 they play a less pronounced role. We expand our analysis for each system and examine the effect of individual atomic and interatomic vibrational motion on the diffuse scattering signals. We further demonstrate the high-throughput capability of our approach by reporting all-phonon scattering maps of two-dimensional MoSe2, WSe2, WS2, graphene, and CdI2, rationalizing in each case the effect of multiphonon processes. As a side point, we show that the special displacement method reproduces the thermally distorted configuration that generates precisely the all-phonon diffuse pattern. In conclusion, the present methodology opens the way for systematic calculations of the scattering intensity in crystals and the accurate interpretation of static and time-resolved inelastic scattering experiments.},
doi = {10.1103/physrevb.104.205109},
journal = {Physical Review. B},
number = 20,
volume = 104,
place = {United States},
year = {Tue Nov 09 00:00:00 EST 2021},
month = {Tue Nov 09 00:00:00 EST 2021}
}
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Works referenced in this record:
Full Elasticity Tensor from Thermal Diffuse Scattering
journal, January 2017
- Wehinger, Björn; Mirone, Alessandro; Krisch, Michael
- Physical Review Letters, Vol. 118, Issue 3
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
Optical Control of Non-Equilibrium Phonon Dynamics
journal, June 2019
- Krishnamoorthy, Aravind; Lin, Ming-Fu; Zhang, Xiang
- Nano Letters, Vol. 19, Issue 8
Toward precise simulations of the coupled ultrafast dynamics of electrons and atomic vibrations in materials
journal, April 2021
- Tong, Xiao; Bernardi, Marco
- Physical Review Research, Vol. 3, Issue 2
Two-phonon contributions to the inelastic x-ray scattering spectra ofMgB 2
journal, January 2007
- Baron, A. Q. R.; Uchiyama, H.; Heid, R.
- Physical Review B, Vol. 75, Issue 2
Tracking the ultrafast nonequilibrium energy flow between electronic and lattice degrees of freedom in crystalline nickel
journal, March 2020
- Maldonado, P.; Chase, T.; Reid, A. H.
- Physical Review B, Vol. 101, Issue 10
Nonadiabatic Kohn Anomaly in a Doped Graphene Monolayer
journal, December 2006
- Lazzeri, Michele; Mauri, Francesco
- Physical Review Letters, Vol. 97, Issue 26
Time- and momentum-resolved phonon population dynamics with ultrafast electron diffuse scattering
journal, December 2019
- René de Cotret, Laurent P.; Pöhls, Jan-Hendrik; Stern, Mark J.
- Physical Review B, Vol. 100, Issue 21
Anharmonic free energies and phonon dispersions from the stochastic self-consistent harmonic approximation: Application to platinum and palladium hydrides
journal, February 2014
- Errea, Ion; Calandra, Matteo; Mauri, Francesco
- Physical Review B, Vol. 89, Issue 6
Fully anharmonic nonperturbative theory of vibronically renormalized electronic band structures
journal, July 2020
- Zacharias, Marios; Scheffler, Matthias; Carbogno, Christian
- Physical Review B, Vol. 102, Issue 4
Simulation of thermal diffuse scattering including a detailed phonon dispersion curve
journal, February 2001
- A. Muller, David; Edwards, Byard; J. Kirkland, Earl
- Ultramicroscopy, Vol. 86, Issue 3-4
Fourier-transform inelastic X-ray scattering from time- and momentum-dependent phonon–phonon correlations
journal, October 2013
- Trigo, M.; Fuchs, M.; Chen, J.
- Nature Physics, Vol. 9, Issue 12
Nonequilibrium Lattice Dynamics in Monolayer MoS 2
journal, February 2021
- Caruso, Fabio
- The Journal of Physical Chemistry Letters, Vol. 12, Issue 6
QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials
journal, September 2009
- Giannozzi, Paolo; Baroni, Stefano; Bonini, Nicola
- Journal of Physics: Condensed Matter, Vol. 21, Issue 39, Article No. 395502
Analytical representation of atomic scattering factors
journal, April 1957
- Vand, V.; Eiland, P. F.; Pepinsky, R.
- Acta Crystallographica, Vol. 10, Issue 4
Unified theory of electron–phonon renormalization and phonon-assisted optical absorption
journal, August 2014
- Patrick, Christopher E.; Giustino, Feliciano
- Journal of Physics: Condensed Matter, Vol. 26, Issue 36
Theoretical Low Temperature Spectra of the Thallium Activated Potassium Chloride Phosphor
journal, April 1951
- Williams, Ferd E.
- Physical Review, Vol. 82, Issue 2
Beyond the molecular movie: Dynamics of bands and bonds during a photoinduced phase transition
journal, November 2018
- Nicholson, C. W.; Lücke, A.; Schmidt, W. G.
- Science, Vol. 362, Issue 6416
Assessing the Role of Intermolecular Interactions in a Perylene-Based Nanowire Using First-Principles Many-Body Perturbation Theory
journal, April 2019
- Huang, Tianlun; Lewis, D. Kirk; Sharifzadeh, Sahar
- The Journal of Physical Chemistry Letters, Vol. 10, Issue 11
Momentum-Resolved View of Electron-Phonon Coupling in Multilayer
journal, July 2017
- Waldecker, L.; Bertoni, R.; Hübener, H.
- Physical Review Letters, Vol. 119, Issue 3
Higher-order Laue zone diffraction from crystals containing transverse stacking faults
journal, March 1990
- Jesson, D. E.; Steeds, J. W.
- Philosophical Magazine A, Vol. 61, Issue 3
Electron–phonon coupling in semiconductors within the GW approximation
journal, December 2018
- Karsai, Ferenc; Engel, Manuel; Flage-Larsen, Espen
- New Journal of Physics, Vol. 20, Issue 12
An open-source software ecosystem for the interactive exploration of ultrafast electron scattering data
journal, September 2018
- René de Cotret, Laurent P.; Otto, Martin R.; Stern, Mark J.
- Advanced Structural and Chemical Imaging, Vol. 4, Issue 1
Optical Properties of Zn 2 Mo 3 O 8 : Combination of Theoretical and Experimental Study
journal, October 2017
- Biswas, Tathagata; Ravindra, Pramod; Athresh, Eashwer
- The Journal of Physical Chemistry C, Vol. 121, Issue 44
Mapping momentum-dependent electron-phonon coupling and nonequilibrium phonon dynamics with ultrafast electron diffuse scattering
journal, April 2018
- Stern, Mark J.; René de Cotret, Laurent P.; Otto, Martin R.
- Physical Review B, Vol. 97, Issue 16
Notes on Generating Functions of Polynomials: (2) Hermite Polynomials
journal, July 1933
- Watson, G. N.
- Journal of the London Mathematical Society, Vol. s1-8, Issue 3
Variational Principles for Scattering Processes. I
journal, August 1950
- Lippmann, B. A.; Schwinger, Julian
- Physical Review, Vol. 79, Issue 3
Anisotropic Nonequilibrium Lattice Dynamics of Black Phosphorus
journal, March 2020
- Zahn, Daniela; Hildebrandt, Patrick-Nigel; Vasileiadis, Thomas
- Nano Letters, Vol. 20, Issue 5
Imaging nonequilibrium atomic vibrations with x-ray diffuse scattering
journal, December 2010
- Trigo, M.; Chen, J.; Vishwanath, V. H.
- Physical Review B, Vol. 82, Issue 23
Phonon-assisted processes in the ultraviolet-transient optical response of graphene
journal, December 2019
- Novko, Dino; Kralj, Marko
- npj 2D Materials and Applications, Vol. 3, Issue 1
Differentiating contributions of electrons and phonons to the thermoreflectance spectra of gold
journal, October 2021
- Liu, Kexin; Shi, Xinping; Angeles, Frank
- Physical Review Materials, Vol. 5, Issue 10
Soft-phonon-driven superconductivity in CaAlSi as seen by inelastic x-ray scattering
journal, April 2008
- Kuroiwa, S.; Baron, A. Q. R.; Muranaka, T.
- Physical Review B, Vol. 77, Issue 14
Anharmonic stabilization and band gap renormalization in the perovskite
journal, November 2015
- Patrick, Christopher E.; Jacobsen, Karsten W.; Thygesen, Kristian S.
- Physical Review B, Vol. 92, Issue 20
First-principles study of direct and indirect optical absorption in BaSnO 3
journal, February 2018
- Kang, Youngho; Peelaers, Hartwin; Krishnaswamy, Karthik
- Applied Physics Letters, Vol. 112, Issue 6
Electron-phonon interactions from first principles
journal, February 2017
- Giustino, Feliciano
- Reviews of Modern Physics, Vol. 89, Issue 1
Boron phosphide as a -type transparent conductor: Optical absorption and transport through electron-phonon coupling
journal, June 2020
- Ha, Viet-Anh; Karasulu, Bora; Maezono, Ryo
- Physical Review Materials, Vol. 4, Issue 6
Transient (000)-order attenuation effects in ultrafast transmission electron diffraction
journal, March 2011
- Ligges, Manuel; Rajković, Ivan; Streubühr, Carla
- Journal of Applied Physics, Vol. 109, Issue 6
Structural dynamics of surfaces by ultrafast electron crystallography: Experimental and multiple scattering theory
journal, December 2011
- Schäfer, Sascha; Liang, Wenxi; Zewail, Ahmed H.
- The Journal of Chemical Physics, Vol. 135, Issue 21
The Franck‐Condon Principle and Its Application to Crystals
journal, November 1952
- Lax, Melvin
- The Journal of Chemical Physics, Vol. 20, Issue 11
Efficient pseudopotentials for plane-wave calculations
journal, January 1991
- Troullier, N.; Martins, José Luriaas
- Physical Review B, Vol. 43, Issue 3
Determination of phonon dispersion relations by X-ray thermal diffuse scattering
journal, January 2005
- Xu, Ruqing; Chiang, Tai C.
- Zeitschrift für Kristallographie - Crystalline Materials, Vol. 220, Issue 12
The scattering of high energy electrons by the thermal vibrations of crystals
journal, October 1965
- Hall, C. R.
- Philosophical Magazine, Vol. 12, Issue 118
Exciton–Phonon Interactions in Monolayer Germanium Selenide from First Principles
journal, April 2021
- Huang, Tianlun Allan; Zacharias, Marios; Lewis, D. Kirk
- The Journal of Physical Chemistry Letters, Vol. 12, Issue 15
Isolation and characterization of few-layer black phosphorus
journal, June 2014
- Castellanos-Gomez, Andres; Vicarelli, Leonardo; Prada, Elsa
- 2D Materials, Vol. 1, Issue 2
Observation of large multiple scattering effects in ultrafast electron diffraction on monocrystalline silicon
journal, February 2018
- González Vallejo, Isabel; Gallé, Geoffrey; Arnaud, Brice
- Physical Review B, Vol. 97, Issue 5
Stochastic Approach to Phonon-Assisted Optical Absorption
journal, October 2015
- Zacharias, Marios; Patrick, Christopher E.; Giustino, Feliciano
- Physical Review Letters, Vol. 115, Issue 17
Temperature dependence of the optical properties of silicon nanocrystals
journal, June 2020
- Zacharias, Marios; Kelires, Pantelis C.
- Physical Review B, Vol. 101, Issue 24
Mechanisms of electron-phonon coupling unraveled in momentum and time: The case of soft phonons in TiSe 2
journal, May 2021
- Otto, Martin R.; Pöhls, Jan-Hendrik; René de Cotret, Laurent P.
- Science Advances, Vol. 7, Issue 20
Direct Measurement of Anharmonic Decay Channels of a Coherent Phonon
journal, September 2018
- Teitelbaum, Samuel W.; Henighan, Thomas; Huang, Yijing
- Physical Review Letters, Vol. 121, Issue 12
Phonons and related crystal properties from density-functional perturbation theory
journal, July 2001
- Baroni, Stefano; de Gironcoli, Stefano; Dal Corso, Andrea
- Reviews of Modern Physics, Vol. 73, Issue 2
Electron-Phonon Coupling and Energy Flow in a Simple Metal beyond the Two-Temperature Approximation
journal, April 2016
- Waldecker, Lutz; Bertoni, Roman; Ernstorfer, Ralph
- Physical Review X, Vol. 6, Issue 2
Direct determination of mode-projected electron-phonon coupling in the time domain
journal, December 2019
- Na, M. X.; Mills, A. K.; Boschini, F.
- Science, Vol. 366, Issue 6470
Nonequilibrium electron and lattice dynamics of strongly correlated Bi 2 Sr 2 CaCu 2 O 8+δ single crystals
journal, April 2018
- Konstantinova, Tatiana; Rameau, Jonathan D.; Reid, Alexander H.
- Science Advances, Vol. 4, Issue 4
Ultrafast disordering of vanadium dimers in photoexcited VO 2
journal, November 2018
- Wall, Simon; Yang, Shan; Vidas, Luciana
- Science, Vol. 362, Issue 6414
First-principles electron transport with phonon coupling: Large scale at low cost
journal, October 2017
- Gunst, Tue; Markussen, Troels; Palsgaard, Mattias L. N.
- Physical Review B, Vol. 96, Issue 16
Efficient First-Principles Calculation of Phonon-Assisted Photocurrent in Large-Scale Solar-Cell Devices
journal, July 2018
- Palsgaard, Mattias; Markussen, Troels; Gunst, Tue
- Physical Review Applied, Vol. 10, Issue 1
High-energy X-ray diffuse scattering
journal, April 2009
- Ramsteiner, I. B.; Schöps, A.; Reichert, H.
- Journal of Applied Crystallography, Vol. 42, Issue 3
Experimental basics for femtosecond electron diffraction studies
journal, May 2007
- Dwyer, Jason R.; Jordan, Robert E.; Hebeisen, Christoph T.
- Journal of Modern Optics, Vol. 54, Issue 7
Compact femtosecond electron diffractometer with 100 keV electron bunches approaching the single-electron pulse duration limit
journal, January 2015
- Waldecker, Lutz; Bertoni, Roman; Ernstorfer, Ralph
- Journal of Applied Physics, Vol. 117, Issue 4
Efficient First-Principles Methodology for the Calculation of the All-Phonon Inelastic Scattering in Solids
journal, November 2021
- Zacharias, Marios; Seiler, Hélène; Caruso, Fabio
- Physical Review Letters, Vol. 127, Issue 20
Separable dual-space Gaussian pseudopotentials
journal, July 1996
- Goedecker, S.; Teter, M.; Hutter, J.
- Physical Review B, Vol. 54, Issue 3
On the interpretation of the forbidden spots observed in the electron diffraction patterns of flat Au triangular nanoparticles
journal, August 2008
- Reyes-Gasga, J.; Gómez-Rodríguez, A.; Gao, Xiaoxia
- Ultramicroscopy, Vol. 108, Issue 9
Temperature-dependent band gaps in several semiconductors: from the role of electron–phonon renormalization
journal, September 2020
- Zhang, Yiming; Wang, Ziyu; Xi, Jinyang
- Journal of Physics: Condensed Matter, Vol. 32, Issue 47
Theory of the special displacement method for electronic structure calculations at finite temperature
journal, March 2020
- Zacharias, Marios; Giustino, Feliciano
- Physical Review Research, Vol. 2, Issue 1
Lattice dynamics of anharmonic solids from first principles
journal, November 2011
- Hellman, O.; Abrikosov, I. A.; Simak, S. I.
- Physical Review B, Vol. 84, Issue 18
EPW: Electron–phonon coupling, transport and superconducting properties using maximally localized Wannier functions
journal, December 2016
- Poncé, S.; Margine, E. R.; Verdi, C.
- Computer Physics Communications, Vol. 209
Efficient procedure for the evaluation of multiple scattering and multiphonon corrections in inelastic neutron-scattering experiments
journal, July 1998
- Dawidowski, J.; Bermejo, F. J.; Granada, J. R.
- Physical Review B, Vol. 58, Issue 2
Theoretical investigations on the relation between crystal dynamics and x-ray scattering
journal, January 1942
- Born, Max
- Reports on Progress in Physics, Vol. 9, Issue 1
Nonadiabatic Kohn Anomaly in Heavily Boron-Doped Diamond
journal, July 2017
- Caruso, Fabio; Hoesch, Moritz; Achatz, Philipp
- Physical Review Letters, Vol. 119, Issue 1
Accessing the Anisotropic Nonthermal Phonon Populations in Black Phosphorus
journal, July 2021
- Seiler, Hélène; Zahn, Daniela; Zacharias, Marios
- Nano Letters, Vol. 21, Issue 14
Density functional perturbation theory for gated two-dimensional heterostructures: Theoretical developments and application to flexural phonons in graphene
journal, August 2017
- Sohier, Thibault; Calandra, Matteo; Mauri, Francesco
- Physical Review B, Vol. 96, Issue 7
Effects of electron-phonon coupling on absorption spectrum: edge of hexagonal boron nitride
journal, December 2018
- Karsai, Ferenc; Humer, Moritz; Flage-Larsen, Espen
- Physical Review B, Vol. 98, Issue 23
Correlations in Space and Time and Born Approximation Scattering in Systems of Interacting Particles
journal, July 1954
- Van Hove, Léon
- Physical Review, Vol. 95, Issue 1
Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds
journal, February 2018
- Mounet, Nicolas; Gibertini, Marco; Schwaller, Philippe
- Nature Nanotechnology, Vol. 13, Issue 3
Accurate optical spectra through time-dependent density functional theory based on screening-dependent hybrid functionals
journal, July 2020
- Tal, Alexey; Liu, Peitao; Kresse, Georg
- Physical Review Research, Vol. 2, Issue 3
Practical methods in ab initio lattice dynamics
journal, September 1997
- Ackland, G. J.; Warren, M. C.; Clark, S. J.
- Journal of Physics: Condensed Matter, Vol. 9, Issue 37
Advanced capabilities for materials modelling with Quantum ESPRESSO
journal, October 2017
- Giannozzi, P.; Andreussi, O.; Brumme, T.
- Journal of Physics: Condensed Matter, Vol. 29, Issue 46