Dynamics and lifetimes of resonant phonons in the quasiparticle and nonquasiparticle regimes

Abstract

The dynamics and lifetimes of a phonon with model resonant interactions from the quasiparticle to nonquasiparticle regime were investigated employing Green's function and the Green-Kubo method. In the weak-coupling case, the dynamics of the resonant phonon are analogous to a damped harmonic oscillator and its lifetime $\ensuremath{\tau}$ is in accordance with the standard phonon transport theory $\ensuremath{\tau}=\frac{1}{2\mathrm{\ensuremath{\Gamma}}}$ ($\mathrm{\ensuremath{\Gamma}}$ being the imaginary part of phonon self-energy). In the strong-coupling nonquasiparticle regime, however, the resonant phonon ``propagates'' in a complex form of wave packets and the actual phonon lifetime ${\ensuremath{\tau}}_{\mathrm{GK}}$ as determined from the Green-Kubo formula significantly deviates from the standard $\ensuremath{\tau}=\frac{1}{2\mathrm{\ensuremath{\Gamma}}}$ relation. Taking the four-phonon resonant ${\mathrm{AgCrSe}}_{2}$ and three-phonon resonant PbSe model systems as examples, the phonon nonquasiparticle dynamics and their lifetimes in real materials are further investigated by first-principle calculations. Substantial discrepancies between ${\ensuremath{\tau}}_{\mathrm{GK}}$ and $\ensuremath{\tau}$ are found for the strongly resonant phonons at high-symmetrical points in both materials. Meanwhile, the lifetime ${\ensuremath{\tau}}_{\mathrm{GK}}$ of the phonons that are not subjected to resonant phonon interactions almost recovers to the conventional theoretical result $\ensuremath{\tau}$ despite the non-Lorentzian spectral feature of these phonons. It is suggested that $\ensuremath{\omega}{\ensuremath{\tau}}_{\mathrm{GK}}$, instead of the conventional $\ensuremath{\omega}\ensuremath{\tau}$, can be applied as a criterion to distinguish phonon quasiparticles and nonquasiparticles in addition to the phonon spectral functions.