Coexisting Ballistic and Diffusive Heat Transport in Micrometer-Long Molecular Junctions

TL;DR

This study reveals that in micrometer-long molecular junctions, heat transport exhibits coexisting ballistic and diffusive regimes, with thermal conductivity diverging as length increases, challenging traditional Fourier law assumptions.

Contribution

It demonstrates that real molecular systems can sustain coexisting ballistic and diffusive heat transport over micrometer scales, with conductivity diverging as a power law, contrary to standard theories.

Findings

Thermal conductivity does not converge in long molecular junctions.

Low-frequency acoustic modes remain ballistic regardless of length.

Conductivity diverges as L^{1/3} due to coexisting transport regimes.

Abstract

Boltzmann transport theory, the standard framework for predicting thermal conductivity, assumes that every vibrational mode eventually scatters, acquiring a finite lifetime that yields a convergent, length-independent thermal conductivity: Fourier's law. Here we show that this assumption fails in a real molecular system. Through atomistic simulations of Au-alkane-Au single-molecule junctions spanning five orders of magnitude in length (0.5 nm to 4 $\mu$m), we find that thermal conductivity never converges. Transport is ballistic for up to one hundred nanometers at room temperature, extending nearly two orders of magnitude beyond existing single-molecule measurements. Past this window, conductivity diverges as $L^{1/3}$, the scaling predicted by the Kardar-Parisi-Zhang universality class for momentum-conserving systems. Frequency-resolved decomposition of the heat current reveals the mechanism behind the divergence. Low-frequency acoustic modes never thermalize: protected by momentum conservation, they remain ballistic at every chain length, still carrying 50% of the total heat current at $L = 2 \mu$m. All other modes thermalize collectively as discrete vibrational states merge into scattering-active phonon bands with increasing length. Hence, the diverging conductivity emerges from the boundary between these coexisting transport regimes: as $L$ grows, the onset of scattering shifts progressively toward lower frequencies, suppressing the ballistic channel at a rate that sustains the $L^{1/3}$ divergence, leaving a finite contribution at every length. This coexistence of permanent ballistic and well-behaved diffusive transport, anticipated in abstract one-dimensional lattice models, survives the structural and chemical complexity of real micrometer-sized junctions.