Enhancement and reduction of one-dimensional heat conduction with correlated mass disorder

Abstract

Short-range order in strongly disordered structures plays an important role in their heat conduction property. Using numerical and analytical methods, we show that short-range spatial correlation (with a correlation length of $\Lambda_{m}$) in the mass distribution of the one-dimensional (1D) alloy-like random binary lattice leads to a dramatic enhancement of the high-frequency phonon transmittance but also increases the low-frequency phonon opacity. High-frequency semi-extended states are formed while low-frequency modes become more localized. This results in ballistic heat conduction at finite lengths but also paradoxically higher thermal resistance that scale as $\sqrt{\Lambda_{m}}$ in the $L\rightarrow\infty$ limit. We identify an emergent crossover length ($L_{c}$) below which the onset of thermal transparency appears. The crossover length is linearly dependent on but is two orders of magnitude larger than $\Lambda_{m}$. Our results suggest that the phonon transmittance spectrum and heat conduction in a disordered 1D lattice can be controlled via statistical clustering of the constituent component atoms into domains. They also imply that the detection of ballistic heat conduction in disordered 1D structures may be a signature of the intrinsic mass correlation at a much smaller length scale.