Long-scale dynamics of crystalline membranes

Лебедев, В. В.; Kats, E. I.

doi:10.1103/physrevb.85.045416

Cited by 12 publications

(19 citation statements)

References 47 publications

(90 reference statements)

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“…On the other hand, a small difference C P −C V is due to quantum fluctuations and shows a very non-trivial behavior as a function of the ratio T /T σ , see Eqs. (60), (61), and (62). The same ratio T /T σ determines the temperature and stress dependence of the Grüneisen parameter, which turns out to be negative for all temperatures and tensions, being monotonous function of T (for fixed σ) and showing a minimum as a function of σ (for fixed T ) for σ ≃ σ * .…”

Section: Discussionmentioning

confidence: 99%

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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Section: Discussionmentioning

confidence: 99%

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

et al. 2016

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“…Recent theoretical work has suggested that the linewidth in carbon nanotube 8 or graphene 9 resonators could result from fluctuations in the tension caused by the thermally excited modes. However, the work on carbon nanotubes considers tension fluctuations, which is not immediately applicable to two-dimensional membranes.…”

Section: S4: Dissipation and Line Broadening From Intermodal Interactmentioning

confidence: 99%

Graphene Nanoelectromechanical Systems as Stochastic-Frequency Oscillators

et al. 2014

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In this Supporting Information section, we present derivations of the equations used in the main text as well as derivations of background material. Sections S1-S2 derive basic equations for the mechanics of the graphene sheet. Section S3 presents calculations of the magnitude of the expected signal when using the frequency modulated (FM) method for excitation and detection described in the main text.The remainder of the supplement can be divided into sections concerning the linewidth in the linear damping regime (Sections S4-S5) and phenomena in the nonlinear regime (S6-S7). Specifically, section S4 first presents derivations of the non-dissipative line broadening due to stiffness fluctuations induced by the coupling between the fundamental and the rest of the thermally excited membrane modes. Section S4 then considers dissipative mechanisms. The energy loss rate from

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“…The problem has obviously attracted renewed attention with the advent of graphene [21][22][23][24][25][26] . In particular, recent work has solved the problem of the diverging electron/two-phonon scattering processes in σ h -symmetric crystals 27 , explaining the large electron mobility observed in free-standing graphene 28,29 .…”

Section: Introductionmentioning

confidence: 99%

Mermin-Wagner theorem, flexural modes, and degraded carrier mobility in two-dimensional crystals with broken horizontal mirror symmetry

Fischetti¹,

Vandenberghe²

2016

Phys. Rev. B

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We show that the electron mobility in ideal, free-standing two-dimensional 'buckled' crystals with broken horizontal mirror (σ h ) symmetry and Dirac-like dispersion (such as silicene and germanene) is dramatically affected by scattering with the acoustic flexural modes (ZA phonons). This is caused both by the broken σ h symmetry and by the diverging number of long-wavelength ZA phonons, consistent with the MerminWagner theorem. Non-σ h -symmetric, 'gapped' 2D crystals (such as semiconducting transition-metal dichalcogenides with a tetragonal crystal structure) are affected less severely by the broken σ h symmetry, but equally seriously by the large population of the acoustic flexural modes. We speculate that reasonable long-wavelength cutoffs needed to stabilize the structure (finite sample size, grain size, wrinkles, defects) or the anharmonic coupling between flexural and in-plane acoustic modes (shown to be effective in mirror-symmetric crystals, like free-standing graphene) may not be sufficient to raise the electron mobility to satisfactory values. Additional effects (such as clamping and phonon-stiffening by the substrate and/or gate insulator) may be required.

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Long-scale dynamics of crystalline membranes

Cited by 12 publications

References 47 publications

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

Graphene Nanoelectromechanical Systems as Stochastic-Frequency Oscillators

Mermin-Wagner theorem, flexural modes, and degraded carrier mobility in two-dimensional crystals with broken horizontal mirror symmetry

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