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Previous multitemperature model (MTM) resolving phonon temperatures at the polarization level and measurements have uncovered remarkable nonequilibrium among different phonon polarizations in laser irradiated graphene and metals. Here, we develop a semiconductor-specific MTM (SC-MTM) by including electron-hole pair generation, diffusion, and recombination, and show that a phonon polarization-level model does not yield observable polarization-based nonequilibrium in laser-irradiated molybdenum disulfide (MoS$_2$). In contrast, appreciable nonequilibrium is predicted between zone-center optical phonons and the other modes. The momentum-based nonequilibrium ratio is found to increase with decreasing laser spot size and interaction with a substrate. This finding is relevant to the understanding of the energy relaxation process in two-dimensional optoelectronic devices and Raman measurements of thermal transport.

The Raman peak position and linewidth provide insight into phonon anharmonicity and electron-phonon interactions in materials. For monolayer graphene, prior first-principles calculations have yielded decreasing linewidth with increasing temperature, which is opposite to measurement results. Here, we explicitly consider four-phonon anharmonicity, phonon renormalization, and electron-phonon coupling, and find all to be important to successfully explain both the G peak frequency shift and linewidths in our suspended graphene sample over a wide temperature range. Four-phonon scattering contributes a prominent linewidth that increases with temperature, while temperature dependence from electron-phonon interactions is found to be reversed above a doping threshold (ℏω_{G}/2, with ω_{G} being the frequency of the G phonon).

Micro-Raman spectroscopy has become an important tool in probing thermophysical behavior in emerging functional materials such as two-dimensional (2D) layered structures. Localized heating by the focused Raman excitation laser beam is expected to produce both stress and nonequilibrium temperature distributions in the material. Here we investigate the effects of hot optical phonons in the Raman spectra of molybdenum disulphide (MoS2) and distinguish them from those caused by thermally-induced compressive stress, which causes a Raman frequency blue shift in the focused Raman laser spot. With the stress effect accounted for in micro-Raman measurements, the degree of nonequilibrium between the hot optical phonons and the acoustic phonon bath is found to be much smaller than those observed in prior micro-Raman measurements of suspended graphene. The observation agrees with a first-principles based theoretical prediction of overpopulated zone-center optical phonons compared to other optical phonons in the Brillouin zone and acoustic phonons. The findings provide detailed insight into the energy relaxation processes in this emerging 2D transition metal dichalcogenide (TMD) electronic and optoelectronic material and clarify an important question in micro-Raman measurements of thermal transport in this and other 2D materials., Comment: 19 pages. 4 figures

FourPhonon is a computational package that can calculate four-phonon scattering rates in crystals. It is built within ShengBTE framework, which is a well-recognized lattice thermal conductivity solver based on Boltzmann transport equation . An adaptive energy broadening scheme is implemented for the calculation of four-phonon scattering rates. In analogy with thirdorder.py in ShengBTE , we also provide a separate python script , Fourthorder.py , to calculate fourth-order interatomic force constants. The extension module preserves all the nice features of the well-recognized lattice thermal conductivity solver ShengBTE , including good parallelism and straightforward workflow. In this paper, we discuss the general theory, program design, and example calculations on Si, BAs and LiCo O 2 . Program summary Program Title: FourPhonon CPC Library link to program files: https://doi.org/10.17632/jjcwt5436h.1 Developer's repository link: https://github.com/FourPhonon Licensing provisions: GNU General Public License version 3 Programming language: Fortran 90, MPI Nature of problem: Calculation of lattice thermal conductivity and related quantities, determination of both three-phonon and four-phonon scattering rates Solution method: Four-phonon scattering rates at RTA level, adaptive broadening scheme Additional comments including restrictions and unusual features: For a productive run, one needs to use High Performance Computing facilities and it takes several hours to several days to finish calculations