Percolation is the basis for understanding a wide range of critically important and very different phenomena, such as how fires spread, desertification, the spread of an infection, or the propagation of brain activity.

This model allows the researchers to understand various phenomena (as systems) qualitatively and make quantitative predictions. It allows us to describe in statistical terms the long-distance connections between systems containing numerous objects (connected by short-distance random relationships) and define their behaviour.

In solids, such as crystals, percolation is thought to be the basic mechanism regulating the transition from one macroscopic state to another, like a kind of domino effect. To date, this has been observed directly in planar systems but never within a three-dimensional medium.

A team of researchers from the Department of Physics at Sapienza University of Rome and the Department of Applied Physics at the Hebrew University of Jerusalem (the group of Prof. Aharon J. Agranat) has observed, using orthographic imaging techniques with laser light, percolation phenomena within a ferroelectric supercrystal. The results of the study have been published in the journal Physical Review Letters.

The transparent crystal used by the researchers has peculiar physical properties: only a giant refractive index would allow the beam of white light to propagate inside it without diffraction and dispersion, that is, without a progressive loss of the information initially encoded in the wave.

"At the heart of the observed percolation – says the study coordinator Eugenio Del Re of the Department of Physics of Sapienza University - there is a behaviour governed by fractal dimensions, i.e. characterised by objects that repeat themselves in the same way on different scales of magnification, such as the self-replicating shape of the cauliflower. Within the supercrystal, diffusion occurs in a self-similar manner."

The analysis makes it possible to predict when a specific system will reach the so-called percolation threshold, i.e. when the transmission of a phase becomes diffuse and can no longer be controlled. The study results thus open up new scenarios for information and energy storage in the fields of photonics and electronics.

References:

Direct Observation of Fractal-Dimensional Percolation in the 3D Cluster Dynamics of a Ferroelectric Supercrystal - Ludovica Falsi, Marco Aversa, Fabrizio Di Mei, Davide Pierangeli, FeiFei Xin, Aharon J. Agranat and Eugenio DelRe – Phys. Rev. Lett. 126, 037601 (2021) https://doi.org/10.1103/PhysRevLett.126.037601

Further Information:

Ludovica Falsi
Department of Physics
ludovica.falsi@uniroma1.it

Eugenio Del Re
Department of Physics
eugenio.delre@uniroma1.it