Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

Burmistrov, I. S.; Gornyi, I. V.; Kachorovskii, V. Yu.; Katsnelson, M. I.; Mirlin, A. D.

doi:10.1103/physrevb.94.195430

Cited by 60 publications

(60 citation statements)

References 83 publications

(210 reference statements)

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“…Due to an anharmonic coupling between the in-plane and out-of plane elastic modes, the bending rigidity scales in the universal regime as κ ∝ κ 0 (L/L * ) η , where η is a critical exponent. Although the crumpling transition cannot be observed in a clean graphene, the anomalous power-law scaling of κ leads to highly nontrivial phenomena already verified experimentally, such as anomalous Hooke's law [23,24,[32][33][34]37,51,52], negative thermal expansion coefficient [53][54][55][56][57][58][59], power-law scaling with T of the phonon-limited conductivity [60][61][62], etc.…”

Section: The Modelmentioning

confidence: 99%

Phase diagram of a flexible two-dimensional material

Saykin

Kachorovskii

Burmistrov

2020

Phys. Rev. Research

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Transport and elastic properties of freestanding two-dimensional materials are determined by competition between dynamical and quenched out-of-plane deformations, i.e., between flexural phonons and ripples, respectively. They both tend to crumple the system by overcoming the strong anharmonicity which stabilizes the flat phases. Despite active research, it still remains unclear whether the rippled phase exists in the thermodynamic limit or is destroyed by thermal out-of-plane fluctuations. We demonstrate that a sufficiently strong short-range disorder stabilizes ripples, whereas in the case of a weak disorder the thermal flexural fluctuations dominate in the thermodynamic limit. Therefore the phase diagram of a flexible two-dimensional material with a quenched short-range disorder has four distinct phases. These phases have drastically different elastic and transport properties that are of crucial importance for the emergent field of flexible nanoelectronics.

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Section: The Modelmentioning

confidence: 99%

Phase diagram of a flexible two-dimensional material

Saykin

Kachorovskii

Burmistrov

2020

Phys. Rev. Research

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“…A stretching factor ξ < 1 in general appears due to a 'hidden area' effect: due to transverse fluctuations in the out-of-plane direction, the projected in-plane area is smaller than its curvilinear size. Equivalently, ξ can be viewed as a renormalization of the order parameter for the flat phase: thermal fluctuations reduce the degree of order in the layer [38,40,41,46,51,52].…”

Section: Modelmentioning

confidence: 99%

“…Any term linear in the trace of the strain tensor u αα , in fact, can be removed from the Hamiltonian by a change of variables of the form u α → u α + x α . Physically, the presence of a finite σ 0 describes the 'hidden area' effect, the reduction in projected area due to transverse thermal fluctuations [38,40,41,46,51,51].…”

Section: Feynman Rules Doubly-soft Goldstone Modes and Cancellation O...mentioning

confidence: 99%

Scale without conformal invariance in membrane theory

Mauri,

Katsnelson

2021

Preprint

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We investigate the relation between dilatation and conformal symmetries in the statistical mechanics of flexible crystalline membranes. We analyze, in particular, a well-known model which describes the fluctuations of a continuum elastic medium embedded in a higher-dimensional space. In this theory, the renormalization group flow connects a non-interacting ultraviolet fixed point, where the theory is controlled by linear elasticity, to an interacting infrared fixed point. By studying the structure of correlation functions and of the energy-momentum tensor, we show that, in the infrared, the theory is only scale-invariant: the dilatation symmetry is not enhanced to full conformal invariance. The model is shown to present a non-vanishing virial current which, despite being non-conserved, maintains a scaling dimension exactly equal to D − 1, even in presence of interactions. We attribute the absence of anomalous dimensions to the symmetries of the model under translations and rotations in the embedding space, which are realized as shifts of phonon fields, and which protect the renormalization of several non-invariant operators. We also note that closure of a symmetry algebra with both shift symmetries and conformal invariance would require, in the hypothesis that phonons transform as primary fields, the presence of new shift symmetries which are not expected to hold on physical grounds. We then consider an alternative model, involving only scalar fields, which describes effective phonon-mediated interactions between local Gaussian curvatures. The model is described in the ultraviolet by two copies of the biharmonic theory, which is conformal, but flows in the infrared to a fixed point which we argue to be only dilatation-invariant.

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“…This tension can be eliminated by modifying the reference state about which strain is defined (see Refs. [7,15,65] for a discussion on thermally induced uniform stretching). Such redefinition of the point of expansion implies a small shift in the elastic moduli.…”

Section: B Bilayermentioning

confidence: 99%

Thermal ripples in bilayer graphene

Mauri¹,

Soriano²,

Katsnelson³

2020

Phys. Rev. B

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We study thermal fluctuations of freestanding bilayer graphene subject to vanishing external tension. Within a phenomenological theory, the system is described as a stack of two continuum crystalline membranes, characterized by finite elastic moduli and a nonzero bending rigidity. A nonlinear rotationally invariant model guided by elasticity theory is developed to describe interlayer interactions. After neglection of in-plane phonon nonlinearities and anharmonic interactions involving interlayer shear and compression modes, an effective theory for soft flexural fluctuations of the bilayer is constructed. The resulting model, neglecting anisotropic interactions, has the same form of a well-known effective theory for out-of-plane fluctuations in a single-layer membrane, but with a strongly wave-vector-dependent bare bending rigidity. Focusing on AB-stacked bilayer graphene, parameters governing interlayer interactions in the theory are derived by first-principles calculations. Statistical-mechanical properties of interacting flexural fluctuations are then calculated by a numerical iterative solution of field-theory integral equations within the self-consistent screening approximation. The bare bending rigidity in the considered model exhibits a crossover between a long-wavelength regime governed by in-plane elastic stress and a short wavelength region controlled by monolayer curvature stiffness. Interactions between flexural fluctuations drive a further crossover between a harmonic and a strong-coupling regime, characterized by anomalous scale invariance. The overlap and interplay between these two crossover behaviors is analyzed at varying temperatures.

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Quantum elasticity of graphene: Thermal expansion coefficient and specific heat

Cited by 60 publications

References 83 publications

Phase diagram of a flexible two-dimensional material

Phase diagram of a flexible two-dimensional material

Scale without conformal invariance in membrane theory

Thermal ripples in bilayer graphene

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