Verification of the phonon relaxation time approximation by probing the relaxation process of a single excited mode

T Hori, PHYSICAL REVIEW B, 100, 214116 (2019).

DOI: 10.1103/PhysRevB.100.214116

The relaxation process of the single-phonon modes excited in an argon crystal is simulated to investigate whether the perturbation theory still works when a phonon mode is subject to a large excitation. The excited modes are attained by adding the displacements and velocities according to the contribution of the modes to those of equilibrium states. The relaxation curves exhibit exponential decay, which agrees with the perturbation theory of phonon scattering. The scattering rates obtained from the relaxation curves increase with the temperature of the excited modes. However, the difference between the scattering rates is less than that of the excited mode temperature; the typical rate of increase is 20% even when the temperature of the excited mode is 50 times larger than that of the equilibrium state. This tendency is also found in a silicon crystal, which is a more realistic and complex material. From these results, it is revealed that the relaxation time approximation is also valid even under large nonequilibrium condition. The results also show that the scattering rates of the other phonon modes increase when one mode is excited to a high temperature. The relaxation at extremely low equilibrium state temperature is also investigated. The temporal variation of the energies shows exponential- like decay and oscillation that is lacking at high temperature. The influence of the temperature of the equilibrium state and the excited mode on the oscillation amplitude and frequency is evaluated. The results indicate that the amplitude of the oscillation depends on the temperature of both, whereas the frequency is only affected by the temperature of the excitation mode.

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