Recovery of normal heat conduction in harmonic chains with correlated disorder

TL;DR

This paper investigates how long-range correlations in isotopic disorder within one-dimensional harmonic chains influence heat conduction, demonstrating that specific correlations can restore size-independent conductivity.

Contribution

It reveals that disorder correlations can control the scaling of heat conductivity with chain length, enabling recovery of normal conduction in disordered harmonic chains.

Findings

Long-range correlations alter low-frequency extended states.

Proper correlations can achieve size-independent conductivity.

Disorder correlations can produce near-normal conduction in free boundary conditions.

Abstract

We consider heat transport in one-dimensional harmonic chains with isotopic disorder, focussing our attention mainly on how disorder correlations affect heat conduction. Our approach reveals that long-range correlations can change the number of low-frequency extended states. As a result, with a proper choice of correlations one can control how the conductivity $\kappa$ scales with the chain length $N$. We present a detailed analysis of the role of specific long-range correlations for which a size-independent conductivity is exactly recovered in the case of fixed boundary conditions. As for free boundary conditions, we show that disorder correlations can lead to a conductivity scaling as $\kappa \sim N^{\varepsilon}$, with the scaling exponent $\varepsilon$ being arbitrarily small (although not strictly zero), so that normal conduction is almost recovered even in this case.