Approaching the perfect diode limit through a nonlinear interface

TL;DR

The paper addresses thermal rectification in a two-segment one-dimensional chain connected to Langevin baths, where a nonlinear interfacial potential $V_μ$ with exponent $μ$ couples interfacial particles. By sweeping $μ$ from $1$ to $μ \to ∞$ across left-right segments with on-site potentials that are harmonic, $φ^4$, or FK, the study derives heat currents and a rectification measure $R$, revealing that the optimal $μ$ increases as the average temperature $T_m$ decreases and that the infinite-square-well limit ($μ \to ∞$) can realize near-perfect diode behavior ($R \approx 2$) at low $T_m$. A heuristic infinite-square-well analysis shows that rectification arises from collision-driven energy exchange with rate $ρ$, and asymmetries in fluctuations between opposite baths explain the large $R$ in the rare-collision regime, with the exact behavior depending on the on-site potential (e.g., inversion of preferred direction in FK). Overall, the work demonstrates a practical route to highly efficient thermal diodes via a tunable nonlinear interface, offering insights for nanoscale thermal management and device design.

Abstract

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 ($μ\to\infty$). 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 baths inversion, divided by their average. 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 ($μ\to\infty$), 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.

Figures (7)

• Figure 1: Schematic representation of the system formed by two different segments nonlinearly coupled and subject to thermal baths at the ends, producing rectification under flux inversion.
• Figure 2: (a) Rectification factor $R$ and (b) corresponding heat currents $J_{LR}$ and $J_{RL}$, vs. $1/\mu$, for the $\phi^4$ on-site potential, and different values of $T_m$. Lines are a guide to the eye. $J_{LR}$ and $J_{RL}$ are plotted by filled and hollow symbols, joined by solid and dashed lines, respectively, and correspond to the time average over $10^3$ samples. We include the outcomes for the infinite-square-well ($1/\mu=0$), obtained through a different integration algorithm. For this limit, in the inset of panel (a), $R$ is plotted vs. $T_m$, for all the on-site potentials considered. In all cases, $k_\mu = 0.5$, $\Delta_{rel}= 1.5$, and $N = 20$.
• Figure 3: Currents for a harmonic system with two particles ($N=2$) as a function of the width $\ell$ of the infinite-square-well interface. The inset shows the rectification factor and the dashed horizontal line refers to the perfect diode effect, nearly attained for $\ell \gtrsim 1$. The histogram of $\rho \Delta T$, where $\rho$ is the the number of stretches per unit time, is also shown in the main plot. $T_m = 0.05$ and $\Delta_{rel} = 1$. In this case, since $N=2$, we set $k_L = k_R = 0$.
• Figure 4: Heat flux vs. $\Delta_{rel} \equiv \Delta T/T_m$ for different values of $\mu$, setting $N=20$, $k_\mu=0.5$, $T_m=0.05$ and the $\phi^4$ model. The inset shows the corresponding rectification factor.
• Figure 5: Size effects. Rectification and corresponding heat fluxes vs. $N$, for the $\phi^4$ on-site potential, and interface with $\mu=10$, in the cases: $(k_\mu,\Delta_{rel})=$ (0.5,1.0),(0.5,1.5), (0.2,1.5), with $T_m=0.05$.