Crossover behavior of the thermal conductance and Kramers' transition rate theory.

Kirill A Velizhanin,Michael Zwolak,Chih-Chun Chien,Subin Sahu,Yonatan Dubi

doi:10.1038/srep17506

Abstract

Kramers’ theory frames chemical reaction rates in solution as reactants overcoming a barrier in the presence of friction and noise. For weak coupling to the solution, the reaction rate is limited by the rate at which the solution can restore equilibrium after a subset of reactants have surmounted the barrier to become products. For strong coupling, there are always sufficiently energetic reactants. However, the solution returns many of the intermediate states back to the reactants before the product fully forms. Here, we demonstrate that the thermal conductance displays an analogous physical response to the friction and noise that drive the heat current through a material or structure. A crossover behavior emerges where the thermal reservoirs dominate the conductance at the extremes and only in the intermediate region are the intrinsic properties of the lattice manifest. Not only does this shed new light on Kramers’ classic turnover problem, this result is significant for the design of devices for thermal management and other applications, as well as the proper simulation of transport at the nanoscale.

Highlights

Thermal transport is an important process in micro- and nano-scale technologies
We demonstrate that thermal transport goes through three physically distinct regimes as the coupling to the surrounding environment – the reservoir that supplies the heat – changes
To investigate the crossover behavior in an anharmonic lattice we examine the thermal conductance in a paradigmatic nonlinear lattice – the Peyrard-Bishop-Dauxois (PBD) model[25,26,27]

Summary

Introduction

Thermal transport is an important process in micro- and nano-scale technologies. It is often in a precarious position: On the one hand, thermal management strategies, including the engineering of low-resistance interfaces, become increasingly important as elements in electronic devices approach the atomic level. The dependence of the thermal conductance on the coupling strength to the reservoirs is physically analogous to the friction-induced turnover in Kramers’ reaction rate problem for chemical reactions in solution.

Results

Conclusion