Sound waves and flexural mode dynamics in two-dimensional crystals

Starting from a Hamiltonian with anharmonic coupling between in-plane acoustic displacements and out-of-plane (flexural) modes, we derived coupled equations of motion for in-plane displacements correlations and flexural mode density fluctuations. Linear response theory and time-dependent thermal Gre...

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Bibliographic Details
Published in:Physical review. B 2017-09, Vol.96 (9), Article 094302
Main Authors: Michel, K. H., Scuracchio, P., Peeters, F. M.
Format: Article
Language:English
Subjects:
Acoustic coupling
Anharmonicity
Coupled modes
Density distribution
Displacements (lattice)
Equations of motion
Graphene
Green's functions
Heat sources
Kinetic equations
Lattice vibration
Mathematical analysis
Response functions
Sound waves
Thermal conductivity
Time dependence
Transition metal compounds
Variations
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Summary:Starting from a Hamiltonian with anharmonic coupling between in-plane acoustic displacements and out-of-plane (flexural) modes, we derived coupled equations of motion for in-plane displacements correlations and flexural mode density fluctuations. Linear response theory and time-dependent thermal Green's functions techniques are applied in order to obtain different response functions. As external perturbations we allow for stresses and thermal heat sources. The displacement correlations are described by a Dyson equation where the flexural density distribution enters as an additional perturbation. The flexural density distribution satisfies a kinetic equation where the in-plane lattice displacements act as a perturbation. In the hydrodynamic limit this system of coupled equations is at the basis of a unified description of elastic and thermal phenomena, such as isothermal versus adiabatic sound motion and thermal conductivity versus second sound. The general theory is formulated in view of application to graphene, two-dimensional h-BN, and 2H-transition metal dichalcogenides and oxides.
ISSN:2469-9950
2469-9969
DOI:10.1103/PhysRevB.96.094302