Controlling thermal conductivity in harmonic chains with correlated mass and bond disorder: Analytical approach

TL;DR

The paper addresses how heat propagates in one-dimensional harmonic chains with correlated mass disorder and weak bond disorder, showing that the asymptotic scaling of thermal conductivity with system size $N$ is dictated solely by either mass or bond disorder, independent of cross-correlations. A second-order perturbative expression for the inverse localization length involves the spectra $W_1$, $W_2$, and $W_3$ of the correlators, revealing how disorder statistics control localization and transport. The authors derive explicit scaling laws, $G∼N^{α}$ with $α=-1/(2+β)$ and $κ∼N^{α'}$ with $α'=(1+β)/(2+β)$ where $β= ext{min}(β_1,β_2)$, and confirm these via transfer-matrix simulations with colored noise sequences, demonstrating that cross-correlations do not affect the scaling. The results provide a practical framework for tailoring thermal transport in nanoscale systems and have potential applications in thermoelectrics and thermal insulation by designing correlated mass and bond disorder sequences.

Abstract

We investigate heat transport in one-dimensional harmonic chains with mass disorder and weak bond disorder, coupled at both ends to oscillator heat baths through weak impedance mismatches. The model incorporates correlations in mass disorder, in bond disorder, and between the two. We find that the scaling of thermal conductivity $κ$ with system size $N$ is determined solely by either mass disorder or bond disorder. This indicates that cross-correlations between the two types of disorder play no important role in the scaling behavior of $κ$. Consequently, by tuning the self-correlations, it is possible to control how the thermal conductivity scales with the system size. Such control could have potential applications in thermoelectric devices and thermal insulation technologies.

Figures (1)

• Figure 1: Dimensionless thermal conductance as a function of the system size. Different point styles represent numerical data for different values of $\delta$: circles ($\delta=\pi/4$), squares ($\delta=0$), triangles ($\delta=-\pi/4$). Filled points (empty points) correspond to numerical data with $\beta_1=3$ ($\beta_1=1$) and $\beta_2=-0.5$ ($\beta_2=4$) . Continuous line (dashed line) depicts the best fit of the numerical data to the function $f(N) = aN^\alpha$ with $\alpha=-0.66\pm 0.01$ ($\alpha=-0.33\pm 0.01$). The size of the error bars are less than the point size