| Particles other than bosons and fermions can exist in two dimensions. One possibility is that when one particle makes a circle around another particle the total many-particle wave function acquires a non-trivial phase factor. Such particles are called Abelian anyons. In a more exotic situation, the action of moving one particle around other particles or in other words, particle braiding, is represented by a unitary matrix acting on the quantum-state vector. If the braiding matrices do not commute with each other, the particles are called non-Abelian anyons.;The existence of both Abelian and non-Abelian anyons has been predicted in Fractional Quantum Hall systems. Quasiparticles in the Laughlin states with filling factor nu = 1/(2m+1) are Abelian anyons. On the other hand, quasiparticles in the Moore-Read and Read-Rezayi states with filling factors nu = 5/2 and nu = 12/5, respectively, are proposed to be non-Abelian anyons. However, no experimental observation of the exchange statistics of identical anyons has been reported so far.;In this thesis we demonstrate that the current and shot noise in the topologically nontrivially set-up of the electronic Mach-Zehnder interferometer can be used to detect anyonic statistics. The transport is not sensitive to the fluctuations of the topological charge inside the interferometer and hence the interference picture is not destroyed by the tunneling of low-energy neutral excitations between the edges and localized states in the interferometer. The current and noise exhibit non-Analytic dependences on small tunneling amplitudes. The low-temperature Fano factor is always below 1 for Abelian anyons and can greatly exceed 1 for non-Abelian statistics. |
