The interference between phonons and its effects on heat propagation

Thermal management is a major societal challenge, since the ability of controlling heat transport allows us reducing heat dissipation, as well as to recycle wasted heat into usable forms of energy, such as electricity. Indeed, the most of the energy produced in the world is lost as heat, so that controlling heat transport and conversion can greatly help in solving the energy crisis. In insulating and semiconductive materials, heat is mainly transported by collective atomic vibrations, called phonons, which propagate across materials as waves. Recently, materials with a periodic nanostructure have been proposed for controlling the propagation of these waves, and thus that of heat, in the same way as acoustic metamaterials can focus, filter or stop the sound waves. Phonons with wavelengths comparable to the nanostructure length scale can be specularly reflected by periodic interfaces and interfere with each other, leading to a phenomenology analogous to the diffraction of light. This modifies phonon energies and velocities, thus impacting on the thermal transport. Recently, simulations have shown that the nature itself of the phonon is modified in presence of such coherent effects, changing from propagative to diffusive to localized. Following the latest theories, a new energy transport mechanism could arise, which can be described as a tunneling of energy between phonon waves that coherently interfere. Unfortunately, no experimental proofs of all this have been provided up to now, due to the technical difficulty of accessing phonons with wavelengths comparable to the nanostructure length scale, which can be as short as tens of nanometers.

Figure 1: TEM images of our sample, with indicated the relevant geometrical parameters: period A=377 nm, holes’ diameter D=124 nm and inter-holes distance N=253 nm.

In this work, we have employed the Extreme Ultraviolet Transient Grating (EUV-TG) technique available at the TIMER beamline of FERMI, to measure phonons with wavelengths comparable to the nanostructure lengthscale in a nanophononic membrane of amorphous SiN, patterned with a square lattice of holes, with period A=377 nm and diameter D=124 nm (see Figure 1). EUV TG measurements have allowed us to confirm the expected modifications of the phonon energies, but also to reveal the existence of a new attenuation mechanism for phonons in nanophononic materials. Namely, by combining finite element simulations and our experimental results, we have showed that the specular reflections at the interfaces reduce the phonon lifetime, due to two mechanisms: one, active at the shortest wavelengths, is related to deviations (due to reflections) with respect to the original propagation direction; the second one, unexpected, is the effect of the interference between a given phonon and its reflections. Specifically, when the phonon wavelength increases, interference becomes more and more important and, simultaneously, phonon lifetime decreases more strongly, until a minimum is reached for phonon wavelengths equal to the inter-holes distance (N), as shown in Figure 2. At longer wave lengths, phonon lifetime increases again, in agreement with the expectation that, when the wavelength becomes much longer than the nanostructure lengthscale, the phonon is no longer efficiently scattered by the interfaces. Most interestingly, our simulations show that, while the phonon propagation is inhibited, energy flux takes place by the hopping of energy between phonon reflections, which is promoted by interference.

Figure 2: Coherent contribution to phonon lifetime as obtained by simulations at the experimental wavelengths (in red) and in a larger wavelength range (in blue). The dashed line is a guide to the eye, whlie N and A are the values of the neck and the periodicity, respectively. The green solid line represents the calculated phonon lifetime if no coherent effects are present, i.e., the lifetime due to incoherent scattering of the phonon from the roughness of the boundaries of the membrane and the holes’ walls.

Our work represents the first experimental evidence of a coherent phonon attenuation mechanism. These findings are relevant for a variety of fundamental and application fields, as they represent a first step towards a deeper understanding of the wave behavior of phonons, whose manipulation may be crucial for developing efficient phononic devices. First of all, this will allow us tailoring thermal properties for specific applications, such as thermoelectricity. Tailoring phonon-mediated electronic and magnetic properties can also enable the control of piezoelectricity, piezomagnetism or optomechanics, as well as the development of new information technologies based on phonons for encoding logic functions.

Mohammad Hadi^1,∗, Haoming Luo^1,2,3,∗, Stéphane Pailhès¹, Anne Tanguy², Anthony Gravouil², Flavio Capotondi⁴, Dario De Angelis⁴, Danny Fainozzi⁴, Laura Foglia⁴, Riccardo Mincigrucci⁴, Ettore Paltanin⁴, Emanuele Pedersoli⁴, Jacopo S. Pelli-Cresi⁴, Filippo Bencivenga^4, and Valentina M. Giordano^1,†

¹ Institute of Light and Matter, Université de Lyon, Villeurbanne cedex, France.
² LaMCos, INSA-Lyon, CNRS UMR5259, Université de Lyon, Villeurbanne Cedex, France.
³ LMS, CNRS, École Polytechnique, Institut Polytechnique de Paris, Palaiseau, France.
⁴ Elettra - Sincrotrone Trieste S.c.P.A., Trieste, Italy.

Contact persons email: 

Local contact person emails: