Phonon Hydrodynamics in Fluorides, Alkali Hydrides, and Bilayer Graphene

Abstract

Previous experimental studies have reported wave-like transport of heat in a small number of material systems, such as superfluids like helium II and crystal solids like bismuth. This phenomenon was henceforth referred to as 'second sound'. These rare observations of second sound are partly due to the challenge of obtaining accurate theoretical predictions. In this work, we use an ab-initio framework to study phonon hydrodynamics in 3D crystal fluorides and alkali hydrides, including sodium fluoride (NaF), lithium fluoride (LiF), lithium hydride (LiH), and sodium hydride (NaH). Moreover, we predict the existence of phonon hydrodynamics regime in bilayer graphene systems, including AA-bilayer graphene and AB-bilayer graphene. First, we obtain the second and third-order interatomic force constants using first-principles calculations, which are based on density functional theory (DFT). Secondly, we calculate the lattice thermal conductivity and phonon scattering rates by solving the Boltzmann transport equation (BTE). Thirdly, we apply Guyer's condition to show the phonon hydrodynamics regime based on the average Normal, Umklapp, and Boundary scattering rates. Finally, we examine the effect of different pseudopotentials on the thermal, electronic, and mechanical properties as well as the phonon hydrodynamics regime. In addition, we report the effect of isotopes on the lattice thermal conductivity and phonon hydrodynamics regime. Our calculations predict the existence of the second sound in NaF at 15 K and 8.3 mm characteristic length, consistent with previous experimental work. Based on Guyer's condition, the hydrodynamic window was determined in terms of characteristic lengths (~10² - ~10⁸ nm) and temperatures (up to ~80 K) for fluorides and alkali hydrides. On the other hand, second sound in 2D materials has been predicted to exist at much higher temperatures relative to 3D materials. We report the existence of a second sound for AA-bilayer graphene and AB-bilayer graphene above room temperature at a characteristic length of ~100 nm.