Anyons in the fractional quantum Hall effect

A basic tenet of quantum theory is that all elementary particles are either bosons or fermions. Ensembles of bosons or fermions behave differently due to differences in their underlying quantum statistics. Starting in the early 1980’s it was theoretically conjectured that excitations that are neither bosons nor fermions may exist under special conditions in two-dimensional interacting electron systems. These unusual excitations were dubbed “anyons”. Anyons possess fractional charge and fractional statistics, however directly probing these properties presents experimental challenges. This lecture will focus on the development of electronic Fabry-Perot interferometers that resulted in the first direct observation of anyonic braiding statistics in the fractional quantum Hall state at ν=1/3. These experiments have now been extended to the more fragile multi-edge-mode hierarchy state at ν=2/5. Application of interferometry to the putative non-abelian state at ν=5/2 will be discussed.