Phonon hydrodynamics, thermal conductivity, and second sound in two-dimensional crystals

Abstract

Starting from our previous work where we have obtained a system of coupled integro-differential equations for acoustic sound waves and phonon density fluctuations in 2D crystals, we derive here the corresponding hydrodynamic equations and study their consequences as function of temperature and frequency. These phenomena encompass propagation and damping of acoustic sound waves, diffusive heat conduction, second sound and Poiseuille heat flow, all of which are characterized by specific transport coefficients. We calculate these coefficients by means of correlation functions without using the concept of relaxation time. Numerical calculations are performed as well in order to show the temperature dependence of the transport coefficients and of the thermal conductivity. As a consequence of thermal tension mechanical and thermal phenomena are coupled. We calculate the dynamic susceptibilities for displacement and temperature fluctuations and study their resonances. Due to the thermo-mechanical coupling the thermal resonances such as Landau-Placzek peak and second sound doublet appear in the displacement susceptibility and conversely the acoustic sound wave doublet appears in the temperature susceptibility, Our analytical results do not only apply to graphene but are also valid for arbitrary 2D crystals with hexagonal symmetry like 2D h-BN, 2H-transition metal dichalcogenides and oxides.