Watching heat flow through diamond nanobeams: theorists team up with experimentalists

This was published on March 27, 2026

An accurate description of how heat flows through diamond at the nanoscale is challenging for both theorists and experimentalists. A new article in Physical Review Letters addresses both challenges presents a joint effort involving MARVEL members from the THEOS lab at EPFL. Experimentalists fabricated long suspended diamond cantilevers with a triangular section less than a micrometer in width, and used some luminescent defects in the diamond as nano-thermometers to measure changes in temperature. Theorists then applied viscous heat equations to explain that transport arises in the cantilever from the interplay between different types of phonon interactions – “hydrodynamic” events that conserve the momentum of the crystal - and extrinsic effects determined by sample size and geometry.

By Nicola Nosengo/NCCR MARVEL

Experimental and theoretical condensed-matter physicists and materials scientists have joined forces to explain and measure – with spatial resolution below a micrometer - how heat is transported in diamond nanostructures, highlighting an unexpected dependence of the heat flow on the size of the diamond structure.

Thanks to its unique heat transport properties, diamond finds more and more applications in advanced technologies like high-power and ultrafast electronics, nonlinear optics, quantum sensing, and quantum nanophotonics. But making an accurate description of how heat flows in it at the nanoscale is challenging for both theorists and experimentalists. For theorists, the problem is that in carbon-based materials like diamond (as well as graphene and graphite), heat can travel in a nondiffusive way, which is quite different from the more common diffusive transport seen in other materials. For experimentalists, a huge challenge is finding sensors that can measure temperature changes on sufficiently small scales and with high accuracy.

A new article in Physical Review Letters addresses both challenges, starting with an elegant solution to the experimental problem. Scientists in Christophe Galland’s group at EPFL fabricated long suspended diamond cantilevers with a triangular section less than a micrometer in width. They designed small metal patches on their tips to apply heat with a focused laser beam. Then, to measure the resulting temperature profile, they scanned a second laser across the cantilever to excite negatively charged nitrogen vacancy (NV) centers, which are luminescent defects in the diamond, introduced here on purpose during the material synthesis. Their spin resonance frequency is temperature- dependent, so NVs can be used as optically addressable nano-thermometers. This makes it possible to image temperature variations inside the device and to study heat transport in nanostructures with unprecedented detail.

Artistic representation of the diamond cantilever used for the experiments. 

“The method offers several advantages over existing approaches”, says Galland. “It provides high spatial resolution, temperature sensitivity better than 0.15 K, and it is non-contact and non-perturbative, meaning that no additional transducers need to be attached to the device. This allows us to access local temperature inhomogeneities and investigate nanoscale heat transport in a way that was previously difficult to achieve with conventional techniques”.

The authors analyzed cantilevers with different cross sections, ranging from about 0.2 to 2.6 square micrometers, finding a strong reduction in conductivity as the width decreased, which is a signature of nondiffusive heat transport mediated by phonons, which are collective oscillations in the crystal structure.

To explain the experimental results, Enrico Di Lucente and Michele Simoncelli applied the viscous heat equations (VHEs) to the diamond cantilevers studied in the experiments. The VHEs were introduced in 2020 by Michele Simoncelli (then at the THEOS lab at EPFL, and now at Columbia University), Andrea Cepellotti, and THEOS leader Nicola Marzari, to coarse-grain the microscopic Boltzmann transport equation (describing the evolution of the populations of the vibrational modes) into a set of macroscopic equations for the temperature and the viscosity that are able to describe simultaneously both the diffusive (Fourier) behavior and the hydrodynamic one.

The results of the simulations were in good agreement with the experimental measures. From a theory standpoint, the authors explain that transport arises in the cantilever from the interplay between different types of phonon interactions – “hydrodynamic” events that conserve the momentum of the crystal - and extrinsic effects determined by sample size and geometry.

“We demonstrated the need for a multiscale approach combining microscopic and mesoscopic theories of phonon transport,” says Enrico Di Lucente, a former THEOS member now at Columbia University. “In doing so, we accounted not only for the intrinsic phonon scattering mechanisms underlying phonon hydrodynamics, but also for extrinsic effects, such as device boundaries and instrument-induced impurities”. In particular, the model allowed for rationalizing the anomalous trends in diamond size-dependent thermal conductivity. These trends would be inaccessible to other state-of-the-art microscopic approaches, due to the number of degrees of freedom of 3D diamond nanostructures. “In fact, we show clear evidence of purely non-diffusive behavior, manifested as a marked reduction of the thermal conductivity as the width of the device decreases”, says Di Lucente. Fully microscopic simulations cannot realistically handle such complexity, he explains. “Our mesoscopic model, however, while retaining quantum-level accuracy and remaining firmly grounded in first-principles ab initio calculations, can capture these effects and provide genuine predictive insight”.

The authors say that this combination of theory and experiment could be applied to the study of hydrodynamic heat transport in 3D materials (so far, it has mostly been studied in bidimensional ones like graphite), or could be pushed at even smaller scales to probe quantum effects in phonon heat transport.

Reference

Goblot, V., Wu, K., Di Lucente, E., Zhu, Y., Losero, E., Jobert, Q., Jaramillo Concha, C., Quack, N., Marzari, N., Simoncelli, M., Galland, C., Imaging Heat Transport in Suspended Diamond Nanostructures with Integrated Spin Defect Thermometers, Phys. Rev. Lett. 136, 12, 2026, doi: https://doi.org/10.1103/3s96-7ghm

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