Dynamics of fluctuations and thermal buckling in graphene from a phase-field crystal model

Enzo Granato; K. R. Elder; S. C. Ying; T. Ala-Nissila

doi:10.1103/PhysRevB.107.035428

Dynamics of fluctuations and thermal buckling in graphene from a phase-field crystal model

Enzo Granato, K. R. Elder, S. C. Ying, T. Ala-Nissila

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Abstract

We study the effects of thermal fluctuations and pinned boundaries in graphene membranes by using a phase-field crystal model with out-of-plane deformations. For sufficiently long times, the linear diffusive behavior of height fluctuations in systems with free boundaries becomes a saturation regime, while at intermediate times the behavior is still subdiffusive as observed experimentally. Under compression, we find mirror buckling fluctuations where the average height changes from above to below the pinned boundaries, with the average time between fluctuations diverging below a critical temperature corresponding to a thermally induced buckling transition. Near the transition, we find a nonlinear height response in agreement with recent renormalization-group calculations and observed in experiments on graphene membranes under an external transverse force with clamped boundaries.

Original language	English
Article number	035428
Pages (from-to)	1-8
Number of pages	8
Journal	Physical Review B
Volume	107
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevB.107.035428
Publication status	Published - 15 Jan 2023
MoE publication type	A1 Journal article-refereed

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10.1103/PhysRevB.107.035428

Dynamics of fluctuations and thermal buckling in graphene from a phase-field crystal modelFinal published version, 2.31 MB

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title = "Dynamics of fluctuations and thermal buckling in graphene from a phase-field crystal model",

abstract = "We study the effects of thermal fluctuations and pinned boundaries in graphene membranes by using a phase-field crystal model with out-of-plane deformations. For sufficiently long times, the linear diffusive behavior of height fluctuations in systems with free boundaries becomes a saturation regime, while at intermediate times the behavior is still subdiffusive as observed experimentally. Under compression, we find mirror buckling fluctuations where the average height changes from above to below the pinned boundaries, with the average time between fluctuations diverging below a critical temperature corresponding to a thermally induced buckling transition. Near the transition, we find a nonlinear height response in agreement with recent renormalization-group calculations and observed in experiments on graphene membranes under an external transverse force with clamped boundaries.",

author = "Enzo Granato and Elder, {K. R.} and Ying, {S. C.} and T. Ala-Nissila",

note = "Funding Information: E.G. was supported by the National Council for Scientific and Technological Development-CNPq and computer facilities from CENAPAD-SP. K.R.E. would like to acknowledge support of the National Science Foundation (NSF) under Grant No. DMR-2006456 and Oakland University Technology Services high performance computing facility (Matilda). T.A-N. has been supported in part by the Academy of Finland through its QTF Center of Excellence program Grant No. 312298. Publisher Copyright: {\textcopyright} 2023 American Physical Society. ",

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AU - Ala-Nissila, T.

N1 - Funding Information: E.G. was supported by the National Council for Scientific and Technological Development-CNPq and computer facilities from CENAPAD-SP. K.R.E. would like to acknowledge support of the National Science Foundation (NSF) under Grant No. DMR-2006456 and Oakland University Technology Services high performance computing facility (Matilda). T.A-N. has been supported in part by the Academy of Finland through its QTF Center of Excellence program Grant No. 312298. Publisher Copyright: © 2023 American Physical Society.

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N2 - We study the effects of thermal fluctuations and pinned boundaries in graphene membranes by using a phase-field crystal model with out-of-plane deformations. For sufficiently long times, the linear diffusive behavior of height fluctuations in systems with free boundaries becomes a saturation regime, while at intermediate times the behavior is still subdiffusive as observed experimentally. Under compression, we find mirror buckling fluctuations where the average height changes from above to below the pinned boundaries, with the average time between fluctuations diverging below a critical temperature corresponding to a thermally induced buckling transition. Near the transition, we find a nonlinear height response in agreement with recent renormalization-group calculations and observed in experiments on graphene membranes under an external transverse force with clamped boundaries.

AB - We study the effects of thermal fluctuations and pinned boundaries in graphene membranes by using a phase-field crystal model with out-of-plane deformations. For sufficiently long times, the linear diffusive behavior of height fluctuations in systems with free boundaries becomes a saturation regime, while at intermediate times the behavior is still subdiffusive as observed experimentally. Under compression, we find mirror buckling fluctuations where the average height changes from above to below the pinned boundaries, with the average time between fluctuations diverging below a critical temperature corresponding to a thermally induced buckling transition. Near the transition, we find a nonlinear height response in agreement with recent renormalization-group calculations and observed in experiments on graphene membranes under an external transverse force with clamped boundaries.

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Dynamics of fluctuations and thermal buckling in graphene from a phase-field crystal model

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Dynamics of fluctuations and thermal buckling in graphene from a phase-field crystal model

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