Experimental Observation of Quasi-ballistic Thermal Transport and Extraction of Phonon Mean Free Paths in Graphite

In nonmetallic crystals, heat is predominantly carried by the lattice vibrations called phonons. While carrying heat, these phonons may scatter among themselves or with the boundary and the impurities present in the crystal, resulting in resistance to heat flow. The average distance traveled by phonons between consecutive scattering events, called the phonon mean free path (MFP), is an important quantity used to classify different thermal transport regimes such as diffusive, ballistic and quasi-ballistic heat flow. At length scales significantly longer than the MFP, phonons will undergo multiple scatterings, leading to diffusive thermal transport as described by the Fourier's law. However, when the length scale is reduced to the order of the MFP, the thermal transport becomes quasi-ballistic. This transport regime has enabled experimental measurement of the contribution of phonons to the thermal conductivity as function of their MFP for low thermal conductivity materials like silicon, by defining an inverse problem using a suppression function with experimental measurements from transient grating (TG) as input [1]. However, this suppression function was obtained under the single-mode relaxation time approximation (RTA) to the linearized Peierls-Boltzmann equation (LPBE) [2], which does not hold for the ultrahigh thermal conductivity materials [3].

Here we report the experimentally extracted phonon mode-resolved dynamical thermal conductivity of graphite, an ultrahigh thermal conductivity material, by processing TG experimental measurements with the solution of the complete LPBE without the RTA. To perform the fitting of the experimental data with the computational expensive LPBE solution in realtime, we have developed numerical efficiencies driven by the symmetries of the phonon collision operator.

By comparing the experimentally extracted mode-resolved thermal conductivity with first-principles computation, we observe that the experimental interpretation of the contribution of individual phonon modes to the overall thermal conductivity is captured well by the full LPBE solution, but the RTA-based suppression function fails dramatically, particularly at cryogenic temperatures.

This work is supported by the Prime Minister's Research Fellowship (02-01036), the Science and Engineering Research Board's Core Research Grant No. CRG/2020/006166 and the Mathematical Research Impact Centric Support Grant No. MTR/2022/001043.

References:

[1] A. J. Minnich, Phys. Rev. Lett. 109, 205901 (2012).

[2] A. A. Maznev, Jeremy A. Johnson, and Keith A. Nelson, Phys. Rev. B 84, 195206 (2011).

[3] N. Malviya and N. K. Ravichandran, Phys. Rev. B 108, 155201 (2023).