Flat phase of quantum polymerized membranes

Coquand, Olivier; Mouhanna, D.

doi:10.1103/physreve.94.032125

Cited by 22 publications

(53 citation statements)

References 103 publications

(290 reference statements)

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“…Our results suggest, in agreement with Ref. [11] that quantum fluctuations leave the membrane flat on the large scale. The interesting logarithmic corrections implied by D = 2 being the upper critical dimension of quantum membranes [11] cannot be addressed here because of computational limitations.…”

supporting

confidence: 93%

“…In anticipation of increasing system size along the Trotter dimension, we start with a smaller membrane of N = 19 440 atoms and proceed by cooling it down. Figure 2 shows the PIMC height correlation function for N = 19 440 (220Å linear size) at T = 300, 50 and 12.5 K. Both T = 50 and 12.5 K data show a clear crossover from classical correlations for q < q T to quantum ones taking place, again in agreement with predictions, for q > q T , where [11,27] q T = ρ κ…”

supporting

confidence: 77%

“…[11] that quantum fluctuations leave the membrane flat on the large scale. The interesting logarithmic corrections implied by D = 2 being the upper critical dimension of quantum membranes [11] cannot be addressed here because of computational limitations. Accessing even lower q requires both larger system size and lower temperatures, which in turn imply higher Trotter number, and such simulations appear at the moment prohibitively expensive.…”

mentioning

confidence: 99%

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Quantum and classical ripples in graphene

2018

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Thermal ripples of graphene are well understood at room temperature, but their quantum counterparts at low temperatures are in need of a realistic quantitative description. Here we present atomistic path-integral Monte Carlo simulations of freestanding graphene, which show upon cooling a striking classical-quantum evolution of height and angular fluctuations. The crossover takes place at ever-decreasing temperatures for ever-increasing wavelengths so that a completely quantum regime is never attained. Zero-temperature quantum graphene is flatter and smoother than classical graphene at large scales, yet rougher at short scales. The angular fluctuation distribution of the normals can be quantitatively described by coexistence of two Gaussians, one classical strongly T-dependent and one quantum about 2 • wide, of zero-point character. The quantum evolution of ripple-induced height and angular spread should be observable in electron diffraction in graphene and other two-dimensional materials, such as MoS2, bilayer graphene, boron nitride, etc.

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supporting

confidence: 93%

supporting

confidence: 77%

mentioning

confidence: 99%

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Quantum and classical ripples in graphene

2018

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“…Recently however, following previous works on disorder-free polymerized membranes [50,52,55,[59][60][61] the present authors [3] have performed a NPRG approach of the model considered within a perturbative framework by Morse et al [57,58] and whose action is given by:…”

Section: Nprg Analysismentioning

confidence: 99%

Universal behaviors in the wrinkling transition of disordered membranes

et al. 2020

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The wrinkling transition experimentally identified by Mutz et al.[1] and then thoroughly studied by Chaieb et al. [2] in partially polymerized lipid membranes is reconsidered. One shows that the features associated with this transition, notably the various scaling behaviors of the height-height correlation functions that have been observed, are qualitatively and quantitatively well described by a recent nonperturbative renormalization group (NPRG) approach to quenched disordered membranes by Coquand et al. [3]. As these behaviors are associated with fixed points of RG transformations they are universal and should also be observed in, e.g., defective graphene and graphene-like materials. :1909.13268v1 [cond-mat.soft] arXiv

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“…We would like to reinforce that even neglecting out-of-plane vibrational modes, our results for the flat membrane are a good reference for first estimates because they resemble the physics of a free-standing graphene monolayer in agreement with experiments. Very recently, PIMC simulation results [48] in agreement with [49] have shown that the crossover between classical and quantum contribution for the out-of-plane vibrational modes should occur around 50K. For lower temperatures quantum fluctuations should leave the membrane flat on the large scale.…”

Section: Numerical Results and Discussionmentioning

confidence: 52%

Strong anharmonicity in pristine graphene

Rabelo

Cândido

2018

J. Phys. Commun.

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The thermodynamic coefficients of a free standing infinite graphene monolayer are calculated using the quasi-classical unsymmetrized self-consistent field method (USF). The basic nonlinear integral equations of this theory are solved numerically in the strong anharmonic approximation. The isothermal and adiabatic elastic bulk moduli, the isochoric and isobaric heat capacities, the thermal expansion, thermal pressure coefficient, and the macroscopic Gruneisen parameter are calculated in terms of the derivatives of a specifically chosen interatomic potential function for different values of stress and for temperatures ranging from below room temperature up to the point of loss of thermodynamic stability. The nearest-neighbor distances vary from 1.4 Å to 1.8 Å for zero stress. Under stress, these distances decrease. At room temperature the molar heat capacities are ∼5.0Jmol −1 K −1 . The elasticity moduli vary from 15.0eV 2 -Å up to zero at the temperature of loss of stability and are increased by stress. The thermal expansion coefficient has a strong dependence on the temperature and is negative for temperatures lower than ∼340K. For high temperatures it monotonically increases and decreases with stress. The macroscopic Gruneisen parameter has a strong nonlinear dependence with temperature and is estimated in about 3.0 3.7;at ∼340K its value decreases to ∼1.0K and for even lower temperature it shows a peak and deep structure similar to what has been earlier reported for fullerene C 60 .The thermodynamic properties of crystals are related to atomic vibrations around their equilibrium positions. The relative displacements are small in comparison with the interatomic distance. Even in quantum crystals, where the zero point vibrations are large, the mean square deviations from the sites are about 30% of interatomic distances while for most of the solids they do not exceed about 10% up to the melting temperatures. This allows for the expansion of the potential energy in a power series of the nuclei displacements in the Born-Oppenheimer approximation [22]. For crystals with strong anharmonicity, perturbative techniques based on harmonic or quasiharmonic approximations do not work. The pseudoharmonic approximation [19][20][21] reduces the study of strong anharmonicity to the analysis of weak interacting phonons and because of that it is more suited to the investigation of the phonon spectrum and related phenomena.The USF has been applied over the years to several types of crystals but mostly with Bravais lattices, and for non Bravais ionic crystals [23,24]. It has been also applied to noncrystalline solids [25]. Recently [26], we have reported on a generalization of the USF to the case of layered structured crystals. In that work though, the thermodynamics of a free standing graphene monolayer was investigated in the weak anharmonic approximation. The anharmonicity has a close relation to the thermal properties of graphene and on-going debates about the contribution of different phonon modes to heat conduction. The...

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Flat phase of quantum polymerized membranes

Cited by 22 publications

References 103 publications

Quantum and classical ripples in graphene

Quantum and classical ripples in graphene

Universal behaviors in the wrinkling transition of disordered membranes

Strong anharmonicity in pristine graphene

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