When an intense magnetic field is applied perpendicularly to a two-dimensional electron gas, the ensemble of electrons adopts a short-distance circular trajectory (the quantum Hall effect). Deprived of any long-distance propagation, the electron gas becomes an insulator. However, one-dimensional channels open along the edges of the gas, allowing electrons to propagate in a single direction as dictated by the orientation of the field. Physicists are looking to use these theoretically independent channels as "optical fibers" as a way to transport single electrons amidst a "Fermi Sea" of electrons.

These edge channels are actually coupled via electrostatic interactions. Consequently, a single electron propagating along a channel should then be described by a coherent superposition of collective excitations distributed throughout all of the channels. The electrostatic interactions between these excitations promote the decoherence of the initial quantum state, accompanied by a relaxation of energy.

The researchers conducted an experiment to highlight these phenomena. For this, single electrons were emitted by a quantum dot (a highly constricted region of the sample, acting as an energy filter) and propagated over a length of 480 or 750 nm. They were then analyzed in a second quantum dot acting as an energy filter.

For the first time, the researchers have observed the proportion of charges that remain at their initial energy after propagation along an edge channel. There is a sharp decrease when the injected electron energy or the length of propagation is increased; remarkably, the researcher have observed that this proportion can rebound slightly. This indicates that, under certain conditions, the collective excitations shared between the edge channels can partially reconstruct the initial excitation, as a result of additive interference.

Moreover, comparing the experimental data with a theoretical model made it possible to identify an additional energy loss, the detailed mechanisms of which still need to be studied.

This work was conducted in collaboration with the Centre for Nanoscience and Nanotechnology (C2N) of Paris-Saclay University and the University of Genoa (Italy).