Signatures of Fractional Statistics in Noise Experiments in Quantum Hall Fluids

The elementary excitations of fractional quantum Hall (FQH) fluids are vortices with fractional statistics. Yet, this fundamental prediction has remained an open experimental challenge. Here we show that the cross-current noise in a three-terminal tunneling experiment of a two dimensional electron gas in the FQH regime can be used to detect directly the statistical angle of the excitations of these topological quantum fluids. We show that the noise also reveals signatures of exclusion statistics and of fractional charge. The vortices of Laughlin states should exhibit a bunching effect, while for higher states in the Jain sequences they should exhibit an “antibunching” effect.

Figure 1

The proposed $T$ junction [32] and virtual processes for currents in the same ($S$) and opposite ($O$) orientations. Blue lines represent edge states where the edge state 0 is held at potential $V$ relative to edges 1 and 2, i.e., $V_0-V_1=V_0-V_2=V$. Red solid lines show paths of two quasiparticles tunneling through a FQH liquid from one edge state to two others and magenta dashed lines represent virtual tunneling events.

Figure 2

The temperature dependence of the direct term ${\tilde{A}}_0$ (orange dashed line) and the exchange term ${\tilde{B}}_0$ (green solid line) defined in the text, for $\nu =2/5$ with $T_0\sim 80\mathrm{mK}$ ($V=40\mu \mathrm{V}$). This qualitative behavior is generic to all fractions.

Figure 3

(a) $\tilde{S}(\omega /{\omega }_0)$ for $\nu =1/5,2/5$, for $T=20\mathrm{mK}$, 40 mK, respectively, with $V\sim 40\mu \mathrm{V}$. $\tilde{S}(\omega /{\omega }_0=1)$ is positive for the Laughlin state $\nu =1/5$ and negative for the Jain state $\nu =2/5$. (b) The effective charge $\overline{e}(T)$ in units of $e$ is determined by the crossing points of (a) for $\nu =1/5$ and $\nu =2/5$.