Correlation Matrix Method for Phonon Quasiparticles

Abstract

Phonon anharmonicity is ubiquitous in real materials and is crucial for understanding thermal properties and phase stability. In this work, we show that anharmonic phonon modes can be obtained by maximizing their vibration stability during fitting the atomic trajectory. We prove that all information about these quasiparticles is contained in two small correlation matrices $\mathcal{S}$ and $\mathcal{Q}$, which can be constructed directly from molecular dynamics simulations. Based on these matrices, we proposed an optimization scheme, which allows us to efficiently determine temperature-dependent phonon modes along with their frequencies and lifetimes. We verified this method by applying it to silicon and cubic CaSiO$_3$, where it successfully captured their temperature-dependent phonon behaviors and the well-known phonon softening in cubic CaSiO$_3$. This theory provides a convenient tool for investigating phonon quasiparticles and can be extended to study other quasiparticles, such as electrons, holes, and magnons.

Figures (3)

• Figure 1: Optimization process and ACF for silicon phonons. (a) $\Delta C_v$ obtained using mass-weighted velocities for different initial modes. (b) $\Delta C_r$ obtained using mass-weighted trajectories. In both panels, $\Delta C$ represents the difference between $C$ and its optimal value. (c) Normalized ACF of an optical phonon. (d) Normalized ACF of an acoustic phonon. All calculations performed at $\vec{k}=(1/5,1/5,1/5)$ at 500K.
• Figure 2: Phonon dispersions for silicon at (a) 500 K and (b) 1000 K. The linewidths are represented by the thickness of the curves. The corresponding phonon spectral functions are presented in panels (c) and (d).
• Figure 3: Phonon dispersions and modes for CaSiO$_3$ at (a)400 K and (b) 1000 K. The linewidths are represented by the line thickness. Panels (d, e) display the corresponding phonon spectral functions. Panels (c, f) show the lowest phonon modes ML and RL at 1000 K.