Origin of negative differential thermal resistance in a chain of two weakly coupled nonlinear lattices

TL;DR

This paper investigates the origin of negative differential thermal resistance (NDTR) in a chain of two weakly coupled nonlinear lattices, revealing how nonlinearity influences NDTR and identifying the transition conditions.

Contribution

It introduces an analytical approach using a classical Landauer formula combined with self-consistent phonon theory to explain NDTR in nonlinear lattice chains.

Findings

Nonlinearity significantly affects the occurrence of NDTR.

A transition from no NDTR to NDTR is observed as nonlinearity varies.

Analytical results align well with numerical simulations.

Abstract

Negative differential resistance in electronic conduction has been extensively studied, but it is not the case for its thermal counterpart, namely, negative differential thermal resistance (NDTR). We present a classical Landauer formula in which the nonlinearity is incorporated by the self-consistent phonon theory in order to study the heat flux across a chain consisting of two weakly coupled lattices. Two typical nonlinear models of hard and soft on-site potentials are discussed, respectively. It is shown that the nonlinearity has strong impacts on the occurring of NDTR. As a result, a transition from the absence to the presence of NDTR is observed. The origin of NDTR consists in the competition between the temperature difference, which acts as an external field, and the temperature-dependent thermal boundary conductance. Finally, the onset of the transition is clearly illustrated for this model. Our analytical calculation agrees reasonably well with numerical simulations.