A unified theory of second sound in two dimensional materials

TL;DR

This paper presents a comprehensive theory of second sound in two-dimensional materials, revealing how flexural phonons influence the existence and velocity of drifting and driftless second sound modes, with implications for heat transport.

Contribution

It introduces a unified framework that explains the behavior of second sound modes in 2D materials, accounting for flexural phonons and strain effects, which was not previously understood.

Findings

Drifting second sound does not exist in the thermodynamic limit due to flexural phonons.

The driftless mode remains less affected by flexural phonons.

Tensile strain increases the velocities of both second sound modes.

Abstract

We develop a unified theory for the second sound in two dimensional materials. Previously studied drifting and driftless second sound are two limiting cases of the theory, corresponding to the drift and diffusive part of the energy flux, respectively. We find that due to the presence of quadratic flexural phonons the drifting second sound does not exist in the thermodynamic limit, while the driftless mode is less affected. This is understood as a result of infinite effective inertia of flexual phonons, due to their constant density states and divergent Bose-Einstein distribution in the long wave length limit. Consequently, the group velocity of the drifting mode is smaller than that of the driftless mode. However, upon tensile strain, the velocity of drifting mode becomes larger. Both of them increase with tensile strain due to the linearization of the flexural phonon dispersion. Our results clarify several puzzles encountered previously and pave the way for exploring wave-like heat transport beyond hydrodynamic regime.