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

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 $\tau$ is in accordance with the standard phonon transport theory $\tau =\frac{1}{2\mathrm{\Gamma }}$ ($\mathrm{\Gamma }$ 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 ${\tau }_{\mathrm{GK}}$ as determined from the Green-Kubo formula significantly deviates from the standard $\tau =\frac{1}{2\mathrm{\Gamma }}$ 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 ${\tau }_{\mathrm{GK}}$ and $\tau$ are found for the strongly resonant phonons at high-symmetrical points in both materials. Meanwhile, the lifetime ${\tau }_{\mathrm{GK}}$ of the phonons that are not subjected to resonant phonon interactions almost recovers to the conventional theoretical result $\tau$ despite the non-Lorentzian spectral feature of these phonons. It is suggested that $\omega {\tau }_{\mathrm{GK}}$, instead of the conventional $\omega \tau$, can be applied as a criterion to distinguish phonon quasiparticles and nonquasiparticles in addition to the phonon spectral functions.

Figure 1

Schematic diagrams of the phonon dispersion for (a) three phonon resonance and (b) four phonon resonance. (c) The real part and imaginary part of phonon self-energy calculated with ${\omega }_0=3\mathrm{THz}$, ${\gamma }_0=0.5\mathrm{THz}$, $A={10}^{-5}\mathrm{T}{\mathrm{Hz}}^3{\mathrm{K}}^{-2}$, and $n=2$ at $T=474.3\mathrm{K}$ for the resonant phonon interactions [Eqs. (6) and (7)].

Figure 2

(a) Spectral functions and (b) time-correlation functions of the resonant phonon [Eq. (3)] (red solid lines) and the DHO [Eq. (4)] (black solid lines) at different temperatures (or interaction strength), calculated with ${\omega }_0=3\mathrm{THz}$, $\gamma =0.5\mathrm{THz}$, $A={10}^{-5}\mathrm{T}{\mathrm{Hz}}^3{\mathrm{K}}^{-2}$, and $n=2$.

Figure 3

Phonon lifetime ${\tau }_{\mathrm{GK}}$ as a function of temperature, calculated by the Green-Kubo method [Eq. (8)] for the resonant phonon [Eq. (3)] (red circles) and the DHO [Eq. (4)] (black rectangles), respectively. The green dashed line indicates the critical phonon lifetime that leads to $\omega \tau =1$ according to standard theory.

Figure 4

Theoretical phonon dispersions of (a) ${\mathrm{AgCrSe}}_2$ and (b) PbSe at 300 K.

Figure 5

(a) Spectral functions and (b) time-correlation functions of the transverse acoustic and longitudinal acoustic phonons of ${\mathrm{AgCrSe}}_2$ at the high-symmetrical $F$ point, calculated at 100, 200, and 300 K, respectively.

Figure 6

(a) Spectral functions and (b) time-correlation functions of the transverse acoustic and longitudinal acoustic phonons of ${\mathrm{AgCrSe}}_2$ at the high-symmetrical $L$ point, calculated at 100, 200, and 300 K, respectively.

Figure 7

Theoretical phonon lifetimes ${\tau }_{\mathrm{GK}}$ (solid circles), as calculated by Green-Kubo method [Eq. (8)], and $\tau ={\left(2\mathrm{\Gamma }\right)}^{-1}$ (open circles), as calculated by the standard theory, of the transverse acoustic and longitudinal acoustic phonons of ${\mathrm{AgCrSe}}_2$ at the high-symmetrical (a) $F$ and (b) $L$ point at 100, 200, and 300 K. The lines are spline interpolated for better visualization.

Figure 8

(a) Spectral functions and (b) time-correlation functions of the transverse optical phonons of PbSe at the zone center Γ point, calculated at 100, 200, and 300 K, respectively.

Figure 9

Theoretical phonon lifetime ${\tau }_{\mathrm{GK}}$ (solid circles), as calculated by Green-Kubo method [Eq. (8)], and $\tau ={\left(2\mathrm{\Gamma }\right)}^{-1}$ (open circles), as calculated by the standard theory, of the optical phonons of PbSe at the zone center Γ point at 100, 200, and 300 K. The lines are spline interpolated for better visualization.