Negative excess shot noise by ayon braiding

Abstract

Anyon is a type of quasiparticle that occur only in two-dimensional systems, with properties much less restricted than fermions and bosons. It obeys the fractional exchange statistics. Abelian anyons are theoretically expected to appear in fractional quantum Hall (FQH) systems of filling factor $\nu$ = 1 / (2n+1), $n = 1,2,\cdots$. They gain the phase $\pm \pi \nu$ when their positions are adiabatically exchanged, and $\pm 2 \pi \nu$ when one braids around the other. Yet, the unambiguous experimental detection of this fundamental property has remained an open challenge. Shot noise is a form of noise in electric current that arises because of the discrete nature of charges carried by charge carriers. Shot noise S, zero-frequency nonequilibrium fluctuation of electrical current I, has valuable information. Its Poisson value S = 2qI in the tunneling regime of a quantum point contact (QPC) was used to detect the charge $q$ of current carriers. The fractional charge $e^* = \nu e$ of anyons was measured from the ratio S/I = $2 e^*$ at a QPC between FQH edges

e is the electron charge. The Poisson value originates from uncorrelated transfer of discrete charges. In this thesis, we theoretically study shot noise in a FQH system. In this particular FQH system, we expect that the shot noise gives the information about not only the charge but also the fractional exchange statistics of anyon. We calculate the shot noise and find its unusual behavior originating from the Abelian fractional statistics of Laughlin anyons. Experimental realization of this work will give a fingerprint of fractional statistics.