What is the coherence time of phonons?

Publication in Physical Review Letters!

Understanding and quantifying the fundamental physical property of coherence of thermal excitations is a long-standing and general problem in physics. The conventional theory, i.e., the phonon gas model, fails to describe coherence and its impact on thermal transport.

In this work, we propose a general heat conduction formalism supported by theoretical arguments and direct atomic simulations, which takes into account both the conventional phonon gas model and the wave nature of thermal phonons.

By naturally introducing wave packets in the heat flux from fundamental concepts, we derive an original thermal conductivity expression including coherence times and lifetimes. Our theory and simulations reveal two distinct types of coherence, i.e., intrinsic and mutual, appearing in two different temperature ranges.

This contribution establishes a fundamental frame for understanding and quantifying the coherence of thermal phonons, which should have a general impact on the estimation of the thermal properties of solids.

Fig. 1: (a) The conventional lattice of Tl3VSe4. (b) The phonon dispersion of Tl3VSe4 from lattice dynamic calculations (white lines) and room-temperature spectral energy density calculations (contour) for the conventional cell along Γ (0; 0; 0) → M (0.5; 0; 0). The lattice constant is denoted by a. The symbols in (b) indicate the modes being analyzed, 0.25 THz (square) and 0.93 THz (circle). (c) Evolution-time- and coherence-time dependent phonon number (contour) of Tl3VSe4 for the 0.93 THz mode at 100 and 300 K. (d) Phonon decay (correlation) versus correlation time in Tl3VSe4 for the 0.25 and 0.93 THz modes at 100 and 300 K. The dash-dotted lines (p + w) show the fitting by Eq. (5). The dotted line (p) shows the fitting by the conventional exponential decay. The inset of (d) shows the realistic wave packet of the mode 0.93 THz resulting from the combination of shorter wave packets at 300 K.

Ref : Z. Zhang, Y. Guo, M. Bescond, J. Chen, M. Nomura and S. Volz, “Heat Conduction Theory Including Phonon Coherence,” Phys. Rev. Lett. 128, 015901 (2022). https://doi.org/10.1103/PhysRevLett.128.015901