In three-dimensional space, all interactions can be divided into two types – bosonic and fermionic, depending on changes in the properties of the system. The wave function of the bosonic system does not change its phase when the particles are rearranged, while the wave function of the fermion system changes its phase by π.
In two-dimensional systems, the phase change can be different from 0 or π – this means that there is a different type of particles that have fractional statistics. In theory, such particles are called anions and represent a generalization of the concepts of fermion and boson.
A group of physicists from France, led by Gwendal Thebes, was the first to experimentally confirm the existence of enions and measure their statistics. They carried out a collision of quasiparticles on quantum conductors with a two-dimensional GaAs/AlGaAS electron gas. Fractional statistics of colliding quasiparticles were revealed by measuring the current correlations taken from the scatterer.