Experimental Extraction of Phonon Scattering Lifetimes in MoS₂ Using Transient Grating

In crystalline semiconductors, heat is predominantly transported via the collective vibrations of lattice atoms, and the quanta of the normal modes of these lattice vibrations are called phonons. The resistance to thermal transport in a crystal is caused by the scattering of phonons among themselves, which is driven by the anharmonic crystal potential in pristine semiconductors. During these scattering events, phonons tend to attain equilibrium, and the corresponding time involved, called the phonon lifetime, is an important quantity to determine phonon-specific thermal properties, for example, the distribution of heat-carrying phonons. The transient grating (TG) is a well-established non-contact optical pump-probe technique that is often used experimentally probe the phonon specific mean free paths, and hence the phonon lifetimes [1,2]. Here, we probe the phonon lifetimes for van der Waals materials like layered MoS₂ using the TG setup. For MoS₂, by comparing our measurements with the predictions from the complete solution of the governing equation for phonon transport, the Peierls-Boltzmann equation (PBE), from first principles, we uncover a significant contribution of momentum conserving Normal scattering as well as the higher-order scattering among four phonons to the total phonon lifetimes. We also discuss the suitability of the computationally inexpensive approximation to the PBE - Callaway model for MoS₂, motivated by its widespread success for several ultrahigh thermal conductivity materials uncovered recently [3].<br/><br/>In the TG technique used in this work, two short pump lasers are made to interfere and get absorbed into the sample, resulting in a spatially sinusoidal temperature grating, with a characteristic period Λ. The decay of this impulsive temperature profile is probed using another probe laser beam. By comparing the observed temperature decay with that calculated from the PBE, the effective thermal conductivity of the sample as a function of Λ can be obtained, from which phonon-specific properties, such as the phonon lifetimes, can be extracted [1,2]. Our experimental measurements highlight the significant contribution of four-phonon scattering to thermal resistance in MoS₂ around and beyond room temperature. By comparing our experimental measurements on phonon lifetimes with the first-principles predictions, we conclude that the Normal processes dominate the total scattering rates at low phonon frequencies in MoS₂, particularly around and below room temperature. Interestingly, we find that four-phonon Normal scattering rates are much stronger than the three-phonon Umklapp scattering rates, which is quite unusual compared to several other materials studied earlier [4]. The comparison of our experimental measurements with first principles predictions also reveal strong anharmonic renormalization of phonon frequencies in MoS₂, even at room temperature, thus significantly affecting its thermal conductivity. We believe that our experimental findings, with insights from predictive first principles calculations, will provide clarity on the nature of phonon-phonon interactions in layered and low-dimensional materials.<br/><br/>This work is supported by the Prime Minister's Research Fellowship (02-01036) and 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.<br/><br/>References:<br/>[1] J. A. Johnson, A. A. Maznev, J. Cuffe, J. K. Eliason, A. J. Minnich, T. Kehoe, C. M. Torres, G. Chen, and K. A. Nelson, Phys. Rev. Lett. 110, 025901 (2013).<br/>[2] N. K. Ravichandran, H. Zhang, and A. J. Minnich, Phys. Rev. X 8, 041004 (2018).<br/>[3] N. Malviya and N. K. Ravichandran, Phys. Rev. B 108, 155201 (2023).<br/>[4] N. K. Ravichandran and D. Broido, Phys. Rev. X 10, 021063 (2020).