Mass-spring model for elastic wave propagation in multilayered van der Waals metamaterials

doi:10.1007/s10483-024-3153-9

Abstract

Abstract:

Multilayered van der Waals (vdW) materials have attracted increasing interest because of the manipulability of their superior optical, electrical, thermal, and mechanical properties. A mass-spring model (MSM) for elastic wave propagation in multilayered vdW metamaterials is reported in this paper. Molecular dynamics (MD) simulations are adopted to simulate the propagation of elastic waves in multilayered vdW metamaterials. The results show that the graphene/MoS₂ metamaterials have an elastic wave bandgap in the terahertz range. The MSM for the multilayered vdW metamaterials is proposed, and the numerical simulation results show that this model can well describe the dispersion and transmission characteristics of the multilayered vdW metamaterials. The MSM can predict elastic wave transmission characteristics in multilayered vdW metamaterials stacked with different two-dimensional (2D) materials. The results presented in this paper offer theoretical help for the vibration reduction of multilayered vdW semiconductors.

Key words: multilayered van der Waals (vdW) metamaterial, molecular dynamics (MD), mass-spring model (MSM), dispersion relation, transmission characteristic

2010 MSC Number:

74H45

Yabin JING, Lifeng WANG, Yuqiang GAO. Mass-spring model for elastic wave propagation in multilayered van der Waals metamaterials. Applied Mathematics and Mechanics (English Edition), 2024, 45(7): 1107-1118.

TrendMD

Figures/Tables 11

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References 39

1	DEAN, C. R., YOUNG, A. F., MERIC, I., LEE, C., WANG, L., SORGENFREI, S., WATANABE, K., TANIGUCHI, T., KIM, P., SHEPARD, K. L., and HONE, J. Boron nitride substrates for high-quality graphene electronics. Nature Nanotechnology, 5 (10), 722- 726 (2010)
2	BERTOLAZZI, S., KRASNOZHON, D., and KIS, A. Nonvolatile memory cells based on MoS₂/graphene heterostructures. ACS Nano, 7 (4), 3246- 3252 (2013)
3	GUO, J., WANG, L. Y., YU, Y. W., WANG, P. Q., HUANG, Y., and DUAN, X. F. SnSe/MoS₂ van der Waals heterostructure junction field-effect transistors with nearly ideal subthreshold slope. Advanced Materials, 31 (49), 1902962 (2019)
4	SUN, X. X., ZHU, C. G., YI, J. L., XIANG, L., MA, C., LIU, H. W., ZHENG, B. Y., LIU, Y., YOU, W. X., ZHANG, W. J., LIANG, D. L., SHUAI, Q., ZHU, X. L., DUAN, H. G., LIAO, L., LIU, Y., LI, D., and PAN, A. L. Reconfigurable logic-in-memory architectures based on a two-dimensional van der Waals heterostructure device. Nature Electronics, 5 (11), 752- 760 (2022)
5	OH, G. H., AN, J. G., KIM, S. I., SHIN, J. C., PARK, J. H., and KIM, T. W. Ultralow subthreshold swing 2D/2D heterostructure tunneling field-effect transistor with ion-gel gate dielectrics. ACS Applied Electronic Materials, 5 (1), 196- 204 (2023)
6	XUE, H., DAI, Y. Y., KIM, W., WANG, Y. D., BAI, X. Y., QI, M., HALONEN, K., LIPSANEN, H., and SUN, Z. P. High photoresponsivity and broadband photodetection with a band-engineered WSe₂/SnSe₂ heterostructure. Nanoscale, 11 (7), 3240- 3247 (2019)
7	LI, C. Y., WU, Z. M., ZHANG, C. Y., PENG, S. L., HAN, J. Y., HE, M. Y., DONG, X., GOU, J., WANG, J., and JIANG, Y. D. Self-powered photodetector with high performance based on all-2D NbSe₂/MoSe₂ van der Waals heterostructure. Advanced Optical Materials, 11 (22), 2300905 (2023)
8	XU, J. P., LUO, X. G., LIN, X., ZHANG, X., LIU, F., YAN, Y. T., HU, S. Q., ZHANG, M. W., HAN, N. N., GAN, X. T., CHENG, Y. C., and HUANG, W. Approaching the robust linearity in dual-floating van der Waals photodiode. Advanced Functional Materials, 34 (12), 2310811 (2023)
9	ISLAM, M. R., AFROJ, S., and KARIM, N. Scalable production of 2D material heterostructure textiles for high-performance wearable supercapacitors. ACS Nano, 17 (18), 18481- 18493 (2023)
10	CHEN, Y. Q., YU, J., ZHUGE, F. W., HE, Y. H., ZHANG, Q. F., YU, S. W., LIU, K. L., LI, L., MA, Y., and ZHAI, T. Y. An asymmetric hot carrier tunneling van der Waals heterostructure for multibit optoelectronic memory. Materials Horizons, 7 (5), 1331- 1340 (2020)
11	ZHA, J. J., SHI, S. H., CHATURVEDI, A., HUANG, H. X., YANG, P., YAO, Y., LI, S. Y., XIA, Y. P., ZHANG, Z. M., WANG, W., WANG, H. D., WANG, S. C., YUAN, Z., YANG, Z. B., HE, Q. Y., TAI, H. L., TEO, W. H. T., YU, H. Y., HO, J. C., WANG, Z. R., ZHANG, H., and TAN, C. L. Electronic/optoelectronic memory device enabled by tellurium-based 2D van der Waals heterostructure for in-sensor reservoir computing at the optical communication band. Advanced Materials, 35 (20), 211598 (2023)
12	ZHA, J. J., XIA, Y. P., SHI, S. H., HUANG, H. X., LI, S. Y., QIAN, C., WANG, H. D., YANG, P., ZHANG, Z. M., MENG, Y., WANG, W., YANG, Z. B., YU, H. Y., HO, J. C., WANG, Z. R., and TAN, C. L. A 2D heterostructure-based multifunctional floating gate memory device for multimodal reservoir computing. Advanced Materials, 36 (3), 2308502 (2023)
13	BRITNELL, L., GORBACHEV, R. V., GEIM, A. K., PONOMARENKO, L. A., MISHCHENKO, A., GREENAWAY, M. T., FROMHOLD, T. M., NOVOSELOV, K. S., and EAVES, L. Resonant tunnelling and negative differential conductance in graphene transistors. Nature Communications, 4, 1794 (2013)
14	ZHANG, Z. H., ZHANG, B. Q., WANG, Y. M., WANG, M. Y., ZHANG, Y. F., LI, H., ZHANG, J. W., and SONG, A. M. Toward high-peak-to-valley-ratio graphene resonant tunneling diodes. Nano Letters, 23 (17), 8132- 8139 (2023)
15	HE, X. Q., KITIPORNCHAI, S., and LIEW, K. M. Buckling analysis of multi-walled carbon nanotubes: a continuum model accounting for van der Waals interaction. Journal of the Mechanics and Physics of Solids, 53 (2), 303- 326 (2005)
16	HE, X. Q., KITIPORNCHAI, S., and LIEW, K. M. Resonance analysis of multi-layered graphene sheets used as nanoscale resonators. Nanotechnology, 16 (10), 2086- 2091 (2005)
17	KITIPORNCHAI, S., HE, X. Q., and LIEW, K. M. Continuum model for the vibration of multilayered graphene sheets. Physical Review B, 72 (7), 075443 (2005)
18	ZHANG, Y. Q., WANG, L. F., and JIANG, J. N. Thermal vibration of MoS₂/black phosphorus bi-layered heterostructure. Physica E-Low-Dimensional Systems & Nanostructures, 114, 113597 (2019)
19	HOU, D. C., WANG, L. F., and ZHANG, Y. Q. Effects of wan der Waals forces on the vibration of stacked multilayered graphene/black phosphorus heterostructures. International Journal of Structural Stability and Dynamics, 21 (8), 2150115 (2021)
20	HUANG, Z. C., HE, Z. Z., ZHU, Y. B., and WU, H. A. A general theory for the bending of multilayer van der Waals materials. Journal of the Mechanics and Physics of Solids, 171, 105144 (2023)
21	REN, Q., WANG, X. Y., LUN, Y. Z., WANG, X. Y., and HONG, J. W. Near-zero Poisson's ratio and suppressed mechanical anisotropy in strained black phosphorene/SnSe van der Waals heterostructure: a first-principles study. Applied Mathematics and Mechanics (English Edition), 43 (5), 627- 636 (2022) doi: 10.1007/s10483-022-2844-7
22	FLOREZ, O., ARREGUI, G., ALBRECHTSEN, M., NG, R. C., GOMIS-BRESCO, J., STOBBE, S., SOTOMAYOR-TORRES, C. M., and GARCIA, P. D. Engineering nanoscale hypersonic phonon transport. Nature Nanotechnology, 17 (9), 947- 951 (2022)
23	MADIOT, G., NG, R. C., ARREGUI, G., FLOREZ, O., ALBRECHTSEN, M., STOBBE, S., GARCIA, P. D., and SOTOMAYOR-TORRES, C. M. Optomechanical generation of coherent GHz vibrations in a phononic waveguide. Physical Review Letters, 130 (10), 106903 (2023)
24	CHAN, J., ALEGRE, T. P. M., SAFAVI-NAEINI, A. H., HILL, J. T., KRAUSE, A., GROBLACHER, S., ASPELMEYER, M., and PAINTER, O. Laser cooling of a nanomechanical oscillator into its quantum ground state. nature, 478 (7367), 89- 92 (2011)
25	MACCABE, G. S., REN, H. J., LUO, J., COHEN, J. D., ZHOU, H. Y., SIPAHIGIL, A., MIRHOSSEINI, M., and PAINTER, O. Nano-acoustic resonator with ultralong phonon lifetime. Science, 370 (6518), 840- 843 (2020)
26	LU, L., RU, C. Q., and GUO, X. M. Vibration isolation of few-layer graphene sheets. International Journal of Solids and Structures, 185, 78- 88 (2020)
27	LU, L., RU, C. Q., and GUO, X. M. Metamaterial vibration of tensioned circular few-layer graphene sheets. Journal of Applied Mechanics-Transactions of the ASME, 87 (6), 061009 (2020)
28	PLIMPTON, S. Fast parallel algorithms for short-range molecular dynamics. Journal of Computational Physics, 117 (1), 1- 19 (1995)
29	STUKOWSKI, A. Visualization and analysis of atomistic simulation data with OVITO-the open visualization tool. Modelling and Simulation in Materials Science and Engineering, 18 (1), 015012 (2010)
30	LIANG, T., PHILLPOT, S. R., and SINNOTT, S. B. Parametrization of a reactive many-body potential for Mo-S systems. Physical Review B, 79 (24), 245110 (2009)
31	LIANG, T., PHILLPOT, S. R., and SINNOTT, S. B. Erratum: parametrization of a reactive many-body potential for Mo-S systems (vol 79, 245110, 2009). Physical Review B, 85 (19), 199903 (2012)
32	STUART, S. J., TUTEIN, A. B., and HARRISON, J. A. A reactive potential for hydrocarbons with intermolecular interactions. Journal of Chemical Physics, 112 (14), 6472- 6486 (2000)
33	STEWART, J. A., and SPEAROT, D. E. Atomistic simulations of nanoindentation on the basal plane of crystalline molybdenum disulfide (MoS₂). Modelling and Simulation in Materials Science and Engineering, 21 (4), 045003 (2013)
34	SAITO, R., MATSUO, R., KIMURA, T., DRESSELHAUS, G., and DRESSELHAUS, M. S. Anomalous potential barrier of double-wall carbon nanotube. Chemical Physics Letters, 348 (3-4), 187- 193 (2001)
35	JENSEN, J. S. Phononic band gaps and vibrations in one- and two-dimensional mass-spring structures. Journal of Sound and Vibration, 266 (5), 1053- 1078 (2003)
36	GAO, Y. Q., and WANG, L. F. Ultrawide coupled bandgap in hybrid periodic system with multiple resonators. Journal of Applied Physics, 127 (20), 204901 (2020)
37	WANG, B. Y., LIU, J. X., SOH, A. K., and LIANG, N. G. On band gaps of nonlocal acoustic lattice metamaterials: a robust strain gradient model. Applied Mathematics and Mechanics (English Edition), 43 (1), 1- 20 (2022) doi: 10.1007/s10483-021-2795-5
38	ZHAO, Y. P., HOU, X. H., ZHANG, K., and DENG, Z. C. Symplectic analysis for regulating wave propagation in a one-dimensional nonlinear graded metamaterial. Applied Mathematics and Mechanics (English Edition), 44 (5), 745- 758 (2023) doi: 10.1007/s10483-023-2985-6
39	JIN, Y., JIA, X. Y., WU, Q. Q., HE, X., YU, G. C., WU, L. Z., and LUO, B. L. Design of vibration isolators by using the Bragg scattering and local resonance band gaps in a layered honeycomb meta-structure. Journal of Sound and Vibration, 521, 116721 (2022)

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