Anharmonic effects on thermodynamic properties of a graphene monolayer

Silva, A. L. C. da; Cândido, Ladir; Rabelo, J. N. Teixeira; Hai, Guo‐Qiang; Peeters, F. M.

doi:10.1209/0295-5075/107/56004

Cited by 26 publications

(25 citation statements)

References 36 publications

(51 reference statements)

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“…The thermal expansion of graphene has been found to be negative in the measured temperature range between 200 and 400 K [7], while earlier experiments [8] had led to the estimate that a transition to positive values occurs near 350 K. Also from the side of theory, the situation is still under debate. While ab-initio DFT calculations [9] show that the thermal contraction in graphene subsists up to 2000 K, atomistic Monte Carlo simulations [10] show a crossover from contraction to expansion near 900 K. From the study of anharmonic effects within the unsymmetrized self-consistent field method, it is found [11] that α T becomes positive for T > T α = 358 K, in agreement with Ref. [8].…”

Section: Introductionsupporting

confidence: 77%

Theory of thermal expansion in 2D crystals

Michel

Costamagna

Peeters

2015

Phys. Status Solidi B

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The thermal expansion αT in layered crystals is of fundamental and technological interest. As suggested by I. M. Lifshitz in 1952, in thin solid films (crystalline membranes) a negative contribution to αT is due to anharmonic couplings between in‐plane stretching modes and out‐of‐plane bending (flexural modes). Genuine in‐plane anharmonicities give a positive contribution to αT. The competition between these two effects can lead to a change of sign (crossover) from a negative value of αT in a temperature (T) range T≤Tα to a positive value of αT for T>Tα in layered crystals. Here, we present an analytical lattice dynamical theory of these phenomena for a two‐dimensional (2D) hexagonal crystal. We start from a Hamiltonian that comprises anharmonic terms of third and fourth order in the lattice displacements. The in‐plane and out‐of‐plane contributions to the thermal expansion are studied as functions of T for crystals of different sizes. Besides, renormalization of the flexural mode frequencies plays a crucial role in determining the crossover temperature Tα. Numerical examples are given for graphene where the anharmonic couplings are determined from experiments. The theory is applicable to other layer crystals wherever the anharmonic couplings are known.

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Section: Introductionsupporting

confidence: 77%

Theory of thermal expansion in 2D crystals

Michel

Costamagna

Peeters

2015

Phys. Status Solidi B

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“…Qualitatively similar results were obtained in Refs. [31,32]. Experiments confirm that the thermal ex-pansion coefficient of graphene at room temperature is negative, with the absolute value as large as 0.1 eV −1 [33].…”

Section: Introductionmentioning

confidence: 82%

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

et al. 2016

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We explore thermodynamics of a quantum membrane, with a particular application to suspended graphene membrane and with a particular focus on the thermal expansion coefficient. We show that an interplay between quantum and classical anharmonicity-controlled fluctuations leads to unusual elastic properties of the membrane. The effect of quantum fluctuations is governed by the dimensionless coupling constant, g0 ≪ 1, which vanishes in the classical limit ( → 0) and is equal to ≃ 0.05 for graphene. We demonstrate that the thermal expansion coefficient αT of the membrane is negative and remains nearly constant down to extremely low temperatures, T0 ∝ exp(−2/g0). We also find that αT diverges in the classical limit: αT ∝ − ln(1/g0) for g0 → 0. For graphene parameters, we estimate the value of the thermal expansion coefficient as αT ≃ −0.23 eV −1 , which applies below the temperature Tuv ∼ g0κ0 ∼ 500 K (where κ0 ∼ 1 eV is the bending rigidity) down to T0 ∼ 10 −14 K. For T < T0, the thermal expansion coefficient slowly (logarithmically) approaches zero with decreasing temperature. This behavior is surprising since typically the thermal expansion coefficient goes to zero as a power-law function. We discuss possible experimental consequences of this anomaly. We also evaluate classical and quantum contributions to the specific heat of the membrane and investigate the behavior of the Grüneisen parameter.

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“…Such a coupling was originally suggested 13 as a membrane effect and explains the negative coefficient of thermal expansion in layered structures. Ab-initio density functional theory (DFT) calculations 14 show that the thermal contraction in graphene subsists up to T > 2000 K. Atomistic Monte Carlo simulations 15 exhibit a crossover from contraction to expansion near 900 K. Most recently the thermal expansion in monolayer graphene has been calculated by the unsymmetrized self consistent field method 16 . Monte Carlo simulations also suggest that the formation of ripples 6 due to anharmonic coupling leads to the stabilization of graphene as a 2D crystal 17 .…”

Section: Introductionmentioning

confidence: 99%

Theory of anharmonic phonons in two-dimensional crystals

2015

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Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semi-empirical model for anharmonic couplings of third and fourth order, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Grüneisen parameters, the thermal tension and the thermal expansion coefficients as function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions we obtain the renormalization and decay rate of in-plane and flexural phonons as function of temperature, wave vector and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There we find that the transition temperature Tα from negative to positive thermal expansion is lowered with smaller system size. Renormalization of the flexural mode has the opposite effect and leads to values of Tα ≈300 K for systems of macroscopic size. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of Normal and Umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals.

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Anharmonic effects on thermodynamic properties of a graphene monolayer

Cited by 26 publications

References 36 publications

Theory of thermal expansion in 2D crystals

Theory of thermal expansion in 2D crystals

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

Theory of anharmonic phonons in two-dimensional crystals

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