Thermodynamics of quantum crystalline membranes

Abstract

We investigate the thermodynamic properties and the lattice stability of two-dimensional crystalline membranes, such as graphene and related compounds, in the low temperature quantum regime $T\to 0$. A key role is played by the anharmonic coupling between in-plane and out-of plane lattice modes that, in the quantum limit, has very different consequences than in the classical regime. The role of retardation, namely of the frequency dependence, in the effective anharmonic interactions turns out to be crucial in the quantum regime. We identify a crossover temperature, $T^{\ast }$, between classical and quantum regimes, which is $\sim 70-90$ K for graphene. Below $T^{\ast }$, the heat capacity and thermal expansion coefficient decrease as power laws with decreasing temperature, tending to zero for $T\to 0$ as required by the third law of thermodynamics.

13 pages, 1 figure

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Cited by in corpus (32)

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• Quantum elasticity of graphene: Thermal expansion coefficient and specific heat
• Stress-controlled Poisson ratio of a crystalline membrane: Application to graphene
• Theory of anharmonic phonons in 2D crystals
• Rippling and crumpling in disordered free-standing graphene
• Quantum effects in graphene monolayers: Path-integral simulations
• Anharmonic effects in the optical and acoustic bending modes of graphene
• Quantum and classical ripples in graphene
• Elastic properties and mechanical tension of graphene
• Thermal properties of graphene from path-integral simulations
• Thermodynamic properties of graphene bilayers
• The flat phase of quantum polymerized membranes
• Critical radius and temperature for buckling in graphene
• Bending mode and thermal expansion of graphene
• Thermal properties of graphene under tensile stress
• Anharmonicity of the acoustic modes of graphene
• Ripples in hexagonal lattices of atoms coupled to Glauber spins
• Bending sound in graphene: origin and manifestation
• Bending rigidity, sound propagation and ripples in flat graphene
• Phonon dispersion in two-dimensional solids from atomic probability distributions
• Temperature Dependent Layer Breathing Modes in Two Dimensional Materials
• Rippling transition from electron-induced condensation of curvature field in graphene
• Elastic properties and mechanical stability of bilayer graphene: Molecular dynamics simulations
• Nuclear quantum effects in graphene bilayers
• Infrared Dynamics of Cold Atoms on Hot Graphene Membranes
• Critical behavior in graphene: spinodal instability at room temperature
• Thermal control of graphene morphology: a signature of its intrinsic surface tension
• Comment on "Thermodynamics of quantum crystalline membranes"
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• Perturbative renormalization and thermodynamics of quantum crystalline membranes