Anderson Localization Quenches Thermal Transport in Aperiodic Superlattices

We show that aperiodic superlattices exhibit intriguing interplay between phononic coherent wave interference effects and incoherent transport. In particular, broadband Anderson localization results in a drastic thermal conductivity reduction of 98% at room temperature, providing an ultralow value of $1.3\mathrm{W}{\mathrm{m}}^{-1}{\mathrm{K}}^{-1}$, and further yields an anomalously large thermal anisotropy ratio of $\sim {10}^2$ in aperiodic $\mathrm{Si}/\mathrm{Ge}$ superlattices. A maximum in the thermal conductivity emerges as an unambiguous consequence of phonon Anderson localization at a system length scale bridging the extended and localized transport regimes. The frequency-resolved picture, combined with our lattice dynamical description of Anderson localization, elucidates the rich transport characteristics in these systems and the potential of correlated disorder for sub- to few-THz phononic engineering of heat transport in thermoelectric applications.

Figure 1

Schematic images of $\mathrm{Si}/\mathrm{Ge}$ (a) p-SL and (b) ap-SL, and the associated atom displacement fields for extended and localized phonon modes, respectively. (c) Room-temperature thermal conductivities of p-SL and ap-SL in the absence and presence of interfacial mixing as a function of system size. Dashed line represents the bulk alloy of ${\mathrm{Si}}_{0.5}{\mathrm{Ge}}_{0.5}$. (d) Emergence of thermal conductivity maximum as disorder increases. Solid lines represent analytic reproductions from the spectral analysis.

Figure 2

Frequency-resolved phonon transmission at different system sizes of (a),(b) p-SL and (c),(d) ap-SL with sharp and mixed interfaces, respectively. (e) Phonon MFPs and localization lengths at 300 K. Dashed lines represent fits to power law $\sim {\omega }^{\alpha }$, with $\alpha =-2$ and $-4$ indicating phonon-phonon and impurity scattering, respectively. (f) Normalized thermal conductivity accumulation ($L=354.4\mathrm{nm}$).

Figure 3

Low-frequency cross-plane phonon dispersion of p-SL (thick line) and five ap-SL system configurations (thin lines) for (a) longitudinal and (b) transverse phonons with $N_{\mathrm{p}}=4$. (c) Phonon density of states. The maximum frequencies of the vibrational spectra of Ge and Si are indicated by dashed lines. (d) Group velocity weighted phonon density of states for p-SL and ap-SL with $N_{\mathrm{p}}=2–16$.