Abstract
We investigate the anharmonic phonon scattering across a weakly interacting interface by developing a quantum mechanics-based theory. We find that the contribution from anharmonic three-phonon scatterings to interfacial thermal conductance can be cast into Landauer formula with transmission function being temperature-dependent. Surprisingly, in the weak coupling limit, the transmission due to anharmonic phonon scattering is unbounded with increasing temperature, which is physically impossible for two-phonon processes. We further reveal that the anharmonic contribution in a real heterogeneous interface (e.g., between graphene and monolayer molybdenum disulfide) can dominate over the harmonic process even at room temperature, highlighting the important role of anharmonicity in weakly interacting heterogeneous systems.
Impact statement
Two-dimensional (2D) van der Waals heterostructures that are built by vertically stacking different 2D materials not only serve as a new platform for exploring new materials physics, but also open up enormous possibilities for applications, such as in nanoelectronic and photonic devices. Because each layer in such heterostructures acts both as a bulk and an interface, this construct can have limited thermal transport across the layers, and yet our understanding on heat dissipation in such systems is still limited due to quantum effect and phononic anharmonicity. Here, we develop a quantum-mechanical theory to describe thermal conduction across such systems by considering interlayer phonon scatterings and placing both harmonic and anharmonic scattering under the same framework. We apply the theory to explore the thermal transport across different heterostructures and reveal the following findings: (1) The contribution of three-phonon processes can be cast into Landauer form with the transmission function being temperature-dependent. (2) The transmission of three-phonon processes is unbounded and increases linearly with temperature in the high temperature limit. (3) The anharmonic contribution in real heterostructures (e.g., graphene-MoS\(_2\)) can dominate over the harmonic contribution even at room temperature, highlighting the important role of anharmonicity in weakly interacting heterogeneous systems.
Graphical Abstract
Similar content being viewed by others
Data availability
The data will be made available on reasonable request.
References
A.K. Geim, I.V. Grigorieva, Nature 499, 419 (2013)
K.S. Novoselov, A. Mishchenko, A. Carvalho, A.H. Castro Neto, Science 353 (2016)
K. Roy, M. Padmanabhan, S. Goswami, T.P. Sai, G. Ramalingam, S. Raghavan, A. Ghosh, Nat. Nanotechnol. 8, 826 (2013)
A. Woessner, M.B. Lundeberg, Y. Gao, A. Principi, P. Alonso-González, M. Carrega, K. Watanabe, T. Taniguchi, G. Vignale, M. Polini, J. Hone, R. Hillenbrand, F.H.L. Koppens, Nat. Mater. 14, 421 (2015)
L. Britnell, R.V. Gorbachev, R. Jalil, B.D. Belle, F. Schedin, A. Mishchenko, T. Georgiou, M.I. Katsnelson, L. Eaves, S.V. Morozov, N.M.R. Peres, J. Leist, A.K. Geim, K.S. Novoselov, L.A. Ponomarenko, Science 335, 947 (2012)
A. Azizi, S. Eichfeld, G. Geschwind, K. Zhang, B. Jiang, D. Mukherjee, L. Hossain, A.F. Piasecki, B. Kabius, J.A. Robinson, N. Alem, ACS Nano 9, 4882 (2015)
K. Chang, W. Chen, ACS Nano 5, 4720 (2011)
L. David, R. Bhandavat, G. Singh, ACS Nano 8, 1759 (2014)
H. Wang, D. Tran, J. Qian, F. Ding, D. Losic, Adv. Mater. Interfaces 6, 1900915 (2019)
Y. Li, H. Wang, L. Xie, Y. Liang, G. Hong, H. Dai, J. Am. Chem. Soc. 133, 7296 (2011)
L. Britnell, R.M. Ribeiro, A. Eckmann, R. Jalil, B.D. Belle, A. Mishchenko, Y.-J. Kim, R.V. Gorbachev, T. Georgiou, S.V. Morozov, A.N. Grigorenko, A.K. Geim, C. Casiraghi, A.H.C. Neto, K.S. Novoselov, Science 340, 1311 (2013)
B. Liu, F. Meng, C.D. Reddy, J.A. Baimova, N. Srikanth, S.V. Dmitriev, K. Zhou, RSC Adv. 5, 29193 (2015)
Z. Ding, Q.-X. Pei, J.-W. Jiang, W. Huang, Y.-W. Zhang, Carbon 96, 888 (2016)
K.-J. Tielrooij, N.C.H. Hesp, A. Principi, M.B. Lundeberg, E.A.A. Pogna, L. Banszerus, Z. Mics, M. Massicotte, P. Schmidt, D. Davydovskaya, D.G. Purdie, I. Goykhman, G. Soavi, A. Lombardo, K. Watanabe, T. Taniguchi, M. Bonn, D. Turchinovich, C. Stampfer, A.C. Ferrari, G. Cerullo, M. Polini, F.H.L. Koppens, Nat. Nanotechnol. 13, 41 (2018)
M.S. Alborzi, A. Rajabpour, A. Montazeri, Int. J. Therm. Sci. 150, 106237 (2020)
K. Gordiz, A. Henry, New J. Phys. 17, 103002 (2015)
N.Q. Le, C.A. Polanco, R. Rastgarkafshgarkolaei, J. Zhang, A.W. Ghosh, P.M. Norris, Phys. Rev. B 95, 144302 (2017)
Y. Zhou, M. Hu, Phys. Rev. B 95, 115313 (2017)
F. Tian, B. Song, X. Chen, N.K. Ravichandran, Y. Lv, K. Chen, S. Sullivan, J. Kim, Y. Zhou, T.-H. Liu, M. Goni, Z. Ding, J. Sun, G.A.G. Udalamatta Gamage, H. Sun, H. Ziyaee, S. Huyan, L. Deng, J. Zhou, A.J. Schmidt, S. Chen, C.-W. Chu, P.Y. Huang, D. Broido, L. Shi, G. Chen, Z. Ren, Science 361, 582 (2018)
Y. Zhou, D. Segal, J. Chem. Phys. 133, 1 (2010)
W. Li, J. Carrete, N.A. Katcho, N. Mingo, Comput. Phys. Commun. 185, 1747 (2014)
B. Peng, H. Zhang, H. Shao, Y. Xu, X. Zhang, H. Zhu, Sci. Rep. 6, 2 (2016). arXiv:1508.02156
Y. Hu, Y. Yin, S. Li, H. Zhou, D. Li, G. Zhang, Nano Lett. 20, 7619 (2020)
N. Mingo, Phys. Rev. B 74, 125402 (2006)
J.-S. Wang, N. Zeng, J. Wang, C.K. Gan, Phys. Rev. E 75, 061128 (2007)
W. Zhang, T.S. Fisher, N. Mingo, J. Heat Transfer 129, 483 (2007)
Y. Xu, J.-S. Wang, W. Duan, B.-L. Gu, B. Li, Phys. Rev. B 78, 224303 (2008)
J. Dai, Z. Tian, Phys. Rev. B 101, 041301 (2020)
J. Thingna, J.L. García-Palacios, J.-S. Wang, Phys. Rev. B 85, 195452 (2012)
J. Thingna, H. Zhou, J.-S. Wang, J. Chem. Phys. 141, 194101 (2014)
H. Zhou, G. Zhang, J.S. Wang, Y.W. Zhang, Phys. Rev. B 101, 235305 (2020)
J.-S. Wang, J. Wang, J.T. Lü, Eur. Phys. J. B 62, 381 (2008)
P. Giannozzi, S. Baroni, N. Bonini, M. Calandra, R. Car, C. Cavazzoni, D. Ceresoli, G.L. Chiarotti, M. Cococcioni, I. Dabo, A.D. Corso, S. de Gironcoli, S. Fabris, G. Fratesi, R. Gebauer, U. Gerstmann, C. Gougoussis, A. Kokalj, M. Lazzeri, L. Martin-Samos, N. Marzari, F. Mauri, R. Mazzarello, S. Paolini, A. Pasquarello, L. Paulatto, C. Sbraccia, S. Scandolo, G. Sclauzero, A.P. Seitsonen, A. Smogunov, P. Umari, R.M. Wentzcovitch, J. Phys. Condens. Matter 21, 395502 (2009)
Y. Cai, J. Lan, G. Zhang, Y.-W. Zhang, Phys. Rev. B 89, 035438 (2014)
H. Zhou, Z.-Y. Ong, G. Zhang, Y.-W. Zhang, Nanoscale 14, 9209 (2022)
A.K. Rappe, C.J. Casewit, K.S. Colwell, W.A. Goddard, W.M. Skiff, J. Am. Chem. Soc. 114, 10024 (1992)
J. van Baren, G. Ye, J.-A. Yan, Z. Ye, P. Rezaie, P. Yu, Z. Liu, R. He, C.H. Lui, 2D Mater. 6, 025022 (2019)
Z. Wei, J. Yang, W. Chen, K. Bi, D. Li, Y. Chen, Appl. Phys. Lett. 104, 081903 (2014)
Q. Fu, J. Yang, Y. Chen, D. Li, D. Xu, Appl. Phys. Lett. 106, 031905 (2015)
Acknowledgment
This work was supported by the National Research Foundation, Singapore under Award No. NRF-CRP24- 2020-0002. Zhang Y.W. acknowledges the support from Singapore A*STAR SERC CRF Award. The use of computing resources at the A*STAR Computational Centre and National Supercomputer Centre, Singapore is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Below is the link to the electronic supplementary material.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Zhou, H., Zhang, G., Wang, JS. et al. Anharmonic quantum thermal transport across a van der Waals interface. MRS Bulletin 48, 614–622 (2023). https://doi.org/10.1557/s43577-022-00456-6
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/s43577-022-00456-6