First demonstration of a classic paradox effect bodes well for semiconductor development

Nearly 70 years ago, the unexpected result of a numerical simulation sparked a chaos theory revolution in modern science and launched the study of nonlinear systems.

In 1953, Fermi, Pasta, Ulam, and Tsingou discovered an apparent paradox when investigating thermalization of mechanical vibration along a single atomic chain. Now, a research team led by Deyu Li, professor of mechanical engineering, and a former graduate student, has produced the first experimental evidence of divergent thermal conductivity of aligned atomic chains, a direct consequence of that legendary numerical modeling, which is known as the FPUT paradox.

Professor Deyu Li for the Mechanical Engineering departmental brochure. (John Russell/Vanderbilt University)

The groundbreaking work has significant implications for the development of more powerful electronics and other devices where relentless pressure for higher performance comes with a relentless escalation in heat loads. It points to a new route of creating a type of thermal superconductors with thermal conductivity values higher than that of any known materials.

Li and Lin Yang, PhD ’19, now a postdoctoral research fellow at the Lawrence Berkeley National Laboratory, demonstrated experimentally that the thermal conductivity of a special kind of ultra-thin nanowires becomes divergent with the wire length. Their work, “Observation of superdiffusive phonon transport in aligned atomic chains,” was published in the journal Nature Nanotechnology.

According to the FPUT paradox, the thermal conductivity of one-dimensional atomic chains would keep increasing with the chain length, which has been further demonstrated by numerous theoretical studies. However, until now, no experimental data had been obtained to prove the concept. In fact, the divergent thermal conductivity of one-dimensional atomic chains had been thought to be limited to academic interest because, in reality, achieving isolated single atomic chains of sufficient length has been almost impossible.

In their paper, Yang, Li and co-workers discovered that when the size of a quasi-one-dimensional NbSe3 nanowire hits 26 nanometers, its thermal conductivity starts to increase sharply as the wire diameter further reduces. Such behavior is exactly opposite to the so-called classical size effect. They further showed that the thermal conductivity of diameter wires of less than 10nm becomes divergent with the wire length following a 1/3 power law length dependence, consistent with numerous theoretical predictions. The behavior violates the well-known Fourier heat conduction law and serves as the first observation of superdiffusive transport of one-dimensional phonons, which are discrete units or quantums of vibrational mechanical energy, in one-dimensional van der Waals crystal nanowires.

“The results are what I have dreamed to obtain since I worked on thermal transport through nanowires when I was a Ph.D. student over 20 years ago,” Li said.