Analytical results for a minimalist thermal diode

Nonequilibrium thermal rectification at the junction of harmonic chains

A thermal diode or rectifier is a system that transmits heat or energy in one direction better than in the opposite direction. We investigate the influence of the distribution of energy among wave numbers on the diode effect for the junction of two dissimilar harmonic chains. An analytical expression for the diode coefficient, characterizing the difference between heat fluxes through the junction in two directions, is derived. It is shown that the diode coefficient depends on the distribution of energy among wave numbers. For an equilibrium energy distribution, the diode effect is absent, while for non-equilibrium energy distributions the diode effect is observed even though the system is harmonic. We show that the diode effect can be maximized by varying the energy distribution and relative position of spectra of the two harmonic chains. Conditions are formulated under which the system acts as an ideal thermal rectifier, i.e., transmits heat only in one direction. The results obtained are important for understanding the heat transfer in heterogeneous low-dimensional nanomaterials.

Approaching the perfect diode limit through a nonlinear interface

We consider a system formed by two different segments of particles, coupled to thermal baths, one at each end, modeled by Langevin thermostats. The particles in each segment interact harmonically and are subject to an on-site potential for which three different types are considered, namely, harmonic, ϕ^{4}, and Frenkel-Kontorova. The two segments are nonlinearly coupled, between interfacial particles, by means of a power-law potential with exponent μ, which we vary, scanning from subharmonic to superharmonic potentials, up to the infinite-square-well limit (μ→∞). Thermal rectification is investigated by integrating the equations of motion and computing the heat fluxes. As a measure of rectification, we use the difference of the currents, resulting from the interchange of the baths, divided by their average (all quantities taken in absolute value). We find that rectification can be optimized by a given value of μ that depends on the bath temperatures and details of the chains. But, regardless of the type of on-site potential considered, the interfacial potential that produces maximal rectification approaches the infinite square well (μ→∞) when reducing the average temperature of the baths. Our analysis of thermal rectification focuses on this regime, for which we complement numerical results with heuristic considerations.

Heat rectification, heat fluxes, and spectral matching

Heat rectifiers would facilitate energy management operations such as cooling or energy harvesting, but devices of practical interest are still missing. Understanding heat rectification at a fundamental level is key to helping us find or design such devices. The match or mismatch of the phonon band spectrum of device segments for forward or reverse temperature bias of the thermal baths at device boundaries was proposed as the mechanism behind rectification. However, no explicit theoretical relation derived from first principles had been found so far between heat fluxes and spectral matching. We study heat rectification in a minimalistic chain of two coupled ions. The fluxes and rectification can be calculated analytically. We propose a definition of the matching that sets an upper bound for the heat flux. In a regime where the device rectifies optimally, matching and flux ratios for forward and reverse configurations are found to be proportional. The results can be extended to a system of N particles in arbitrary traps with nearest-neighbor linear interactions.