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 operations of braiding a particle around another are represented by unitary matrices 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 Abelian and non-Abelian anyons has been predicted in Fractional Quantum Hall systems but no experimental observation of anyonic statistics has been reported so far. We show that transport measurements in the non-trivial topology of the electronic Mach-Zehnder interferometer can be used to probe anyonic statistics.
1. K.T. Law, D.E. Feldman, Y. Gefen, Phys. Rev. B 74, 045319 (2006).
2. D. E. Feldman, Y. Gefen, A. Kitaev, K. T. Law, and A. Stern, Phys. Rev. B 76 085333 (2007)
3. K.T. Law, arXiv: 0707.3995.