Theory of anharmonic phonons in 2D crystals

Abstract

Anharmonic effects in an atomic monolayer thin crystal with honeycomb lattice structure are investigated by analytical and numerical lattice dynamical methods. Starting from a semi-empirical model for anharmonic couplings of third and fourth order, we study the in-plane and out-of-plane (flexural) mode components of the generalized wave vector dependent Grüneisen parameters, the thermal tension and the thermal expansion coefficients as function of temperature and crystal size. From the resonances of the displacement-displacement correlation functions we obtain the renormalization and decay rate of in-plane and flexural phonons as function of temperature, wave vector and crystal size in the classical and in the quantum regime. Quantitative results are presented for graphene. There we find that the transition temperature from negative to positive thermal expansion is lowered with smaller system size and by renormalization of the flexural mode frequency. Extensive numerical analysis throughout the Brillouin zone explores various decay and scattering channels. The relative importance of Normal and Umklapp processes is investigated. The work is complementary to crystalline membrane theory and computational studies of anharmonic effects in two-dimensional crystals.

24 pages, 18 figures

References in corpus (11)

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Cited by in corpus (13)

• Quantum elasticity of graphene: Thermal expansion coefficient and specific heat
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Quantum effects in graphene monolayers: Path-integral simulations
• Anharmonic interatomic force constants and thermal conductivity from Grüneisen parameters: an application to graphene
• Phonon hydrodynamics in crystalline materials
• Ballistic thermophoresis of adsorbates on free-standing graphene
• Bending mode and thermal expansion of graphene
• Anharmonicity of the acoustic modes of graphene
• Phonon hydrodynamics, thermal conductivity and second sound in 2D crystals
• Enhancing (quasi-)long-range order in a two-dimensional driven crystal
• Noncontact friction: Role of phonon damping and its nonuniversality
• Nanotube heat conductors under tensile strain: Reducing the three-phonon scattering strength of acoustic phonons
• Effect of out-of-plane acoustic phonons on the thermal transport properties of graphene