Fluctuations and lower critical dimensions of crystalline membranes

Aronovitz, Joseph A.; Golubović, Leonardo; Lubensky, T. C.

doi:10.1051/jphys:01989005006060900

Cited by 107 publications

(201 citation statements)

References 9 publications

Supporting

Mentioning

190

Contrasting

Order By: Relevance

“…The equivalence of two definitions, while quite transparent physically, represents a very non-trivial Ward identity [44,47]. We explicitly verify this identity within the one-loop RG analysis in Appendixes A and D.…”

Section: Formalism a Thermodynamics Of An Elastic Membranementioning

confidence: 72%

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

et al. 2016

View full text Add to dashboard Cite

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.

show abstract

Section: Formalism a Thermodynamics Of An Elastic Membranementioning

confidence: 72%

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

et al. 2016

View full text Add to dashboard Cite

show abstract

“…Unlike long one-dimensional polymers, which perform self-avoiding random walks [24,25], arbitrarily large two-dimensional membranes remain flat at low temperatures because of the strong thermal renormalizations triggered by flexural phonons, which result in strongly scale-dependent enhanced bending rigidities and reduced in-plane elastic constants [26][27][28][29][30][31][32][33][34][35][36][37] (see also books and reviews in Refs. [38][39][40][41]).…”

Section: Introductionmentioning

confidence: 99%

Statistical Mechanics of Thin Spherical Shells

Košmrlj

Nelson

2017

Phys. Rev. X

View full text Add to dashboard Cite

We explore how thermal fluctuations affect the mechanics of thin amorphous spherical shells. In flat membranes with a shear modulus, thermal fluctuations increase the bending rigidity and reduce the inplane elastic moduli in a scale-dependent fashion. This is still true for spherical shells. However, the additional coupling between the shell curvature, the local in-plane stretching modes, and the local out-ofplane undulations leads to novel phenomena. In spherical shells, thermal fluctuations produce a radiusdependent negative effective surface tension, equivalent to applying an inward external pressure. By adapting renormalization group calculations to allow for a spherical background curvature, we show that while small spherical shells are stable, sufficiently large shells are crushed by this thermally generated "pressure." Such shells can be stabilized by an outward osmotic pressure, but the effective shell size grows nonlinearly with increasing outward pressure, with the same universal power-law exponent that characterizes the response of fluctuating flat membranes to a uniform tension.

show abstract

“…As regards these latter quantities, for example, a crude estimate can be obtained from the smallest possible wave vector in a system with a finite size L : q min ϳ 2 / L. 3 In the case of outof-plane phonons, however, the combined effect of fluctuations and anharmonicity yields a strong renormalization of the bending rigidity . 7,25,26 This eventually suppresses outof-plane fluctuations, making it possible the low-temperature flat phase of the sheet. This result can be seen as due to an anharmonicity-induced infrared cutoff, 7 which is the relevant one for large enough samples 26 ͑i.e., in the thermodynamic limit͒.…”

Section: ͑7͒mentioning

confidence: 99%

“…In this case, nonlinear effects make the divergence of local in-plane fluctuations even stronger. 25 In consequence, by employing Eq. ͑10͒ with T 0 ϳ បcq min , one is actually underestimating the Koshino-Taylor effect if the size of the sample is large enough.…”

Section: ͑7͒mentioning

confidence: 99%

Koshino-Taylor effect in graphene

Cano¹

2009

Phys. Rev. B

View full text Add to dashboard Cite

We discuss the phonon-assisted scattering of electrons by defects, i.e., the so-called Koshino-Taylor effect, in graphene. The two-dimensional character of graphene implies that the strength of the Koshino-Taylor effect can be considerably larger than in ordinary metals. We show that at finite temperatures the defect-induced resistivity formally diverges in the thermodynamic limit, having a non-analytic $T\ln T$ component when finite size effects are taken into account.Comment: 4 pages, v2: added reference

show abstract

Fluctuations and lower critical dimensions of crystalline membranes

Cited by 107 publications

References 9 publications

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

Statistical Mechanics of Thin Spherical Shells

Koshino-Taylor effect in graphene

Contact Info

Product

Resources

About