Self-Interacting Anyons on 2D Sheets

http://physics.aps.org/articles/v3/93

"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 aren’t 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.
Writing in Physical Review B, Robert Willett and colleagues from Bell Laboratories in the US present experiments that demonstrate the existence of a very special kind of “non-Abelian” anyons [1]. “Conventional” Abelian anyons have been conjectured to exist in a number of fractional quantum Hall states, yet despite several attempts, their braiding statistics have never been established conclusively. The reason they are called Abelian is because the exchange of two such anyons leads to a nontrivial phase acquired by their wave function, and a series of exchanges merely results in multiple phase factors whose order is irrelevant. Unfortunately, the relative simplicity of their statistics is also the reason why they are so difficult to detect experimentally. The problem is that the phase factors may arise from other sources such as the Aharonov-Bohm effect, the dynamical phase, etc. Hence distilling the statistical phase contribution from the overall phase is quite difficult [2]."