It is well known that a wave function of two identical bosons is symmetric upon their exchange, while it is antisymmetric for two fermions. However, particles confined to two dimensions arent limited to obeying the exchange rules of bosons and fermions. In two dimensions, swapping the positions of two particles in a clockwise manner is distinct from doing it counterclockwise. In three or more dimensions, one could continuously deform such trajectories into each other, rendering the two operations identical. Experimentally, when you confine electrons to an atomically thin layer by essentially electrostatic means, the low-energy collective excitations of the system now behave as two-dimensional particles (although the higher-energy excitations are still conventional electrons). In particular, they can act as anyons - particles whose braiding statistics is neither bosonic nor fermionic. Naturally, one has to go to very low temperatures in search of such quasiparticles, and this is exactly the regime in which the fractional quantum Hall effect - the primary playground for finding anyons - is observed. Read more