Breaking Rayleigh’s Law with Spatially Correlated Disorder to Control Phonon Transport

Controlling thermal transport in insulators and semiconductors is crucial for many technological fields such as thermoelectrics and thermal insulation, for which a low thermal conductivity ($\kappa$) is desirable. A major obstacle for realizing low $\kappa$ materials is Rayleigh’s law, which implies that acoustic phonons, which carry most of the heat, are insensitive to scattering by point defects at low energy. We demonstrate, with large scale simulations on tens of millions of atoms, that isotropic long-range spatial correlations in the defect distribution can dramatically reduce phonon lifetimes of important low-frequency heat-carrying modes, leading to a large reduction of $\kappa$—potentially an order of magnitude at room temperature. We propose a general and quantitative framework for controlling thermal transport in complex functional materials through structural spatial correlations, and we establish the optimal functional form of spatial correlations that minimize $\kappa$. We end by briefly discussing experimental realizations of various correlated structures.

Figure 1

The ${\omega }^4$ Rayleigh’s law for phonon-disorder inverse lifetimes. Inset: low-$\omega$ phonons are insensitive to randomly distributed point defects, contrary to high-$\omega$ phonons.

Figure 2

Top: 2D cuts of the mass distribution in supercells of size $200\times 200\times 200$ atoms (each pixel representing an atom) with several power-law decaying correlations $C(\mathit{r})\propto 1/r^{\alpha }$ with $\alpha =\infty$ (uncorrelated) and $\alpha =2$, 1, and 0.5. The color scale denotes the discrete relative difference from the average mass, with five atomic species present in the supercell. Bottom: the phonon spectral function $A(\mathit{k},\omega )$ calculated by the CPGF method, together with the VCA dispersion (dashed blue line).

Figure 3

Phonon-disorder inverse lifetimes extracted from the width of the CPGF-calculated spectral peaks for several power-law decaying correlations.

Figure 4

The thermal conductivities for several power-law decaying correlations evaluated through Green-Kubo CPGF calculations above 10 rad THz, with second-order perturbation theory below 10 rad THz (dots) and through perturbation theory only (dashed lines).