Universal Anyon Tunneling in a Chiral Luttinger Liquid

Abstract

The edge modes of fractional quantum Hall liquids are described by chiral Luttinger liquid theory. Despite many years of experimental investigation fractional quantum Hall edge modes remain enigmatic with significant discrepancies between experimental observations and detailed predictions of chiral Luttinger liquid theory. Here we report measurements of tunneling conductance between counterpropagating edge modes at $\nu=1/3$ across a quantum point contact fabricated on an AlGaAs/GaAs heterostructure designed to promote a sharp confinement potential. We present evidence for tunneling of anyons through a $\nu=1/3$ incompressible liquid that exhibits universal scaling behavior with respect to temperature, source-drain bias, and barrier transmission, as originally proposed by Wen [1, 2]. For transmission $t\geq0.800$, we measured the tunneling exponent $\bar{g} = 0.333 \pm 0.005$ averaged over 29 independent data sets, consistent with the scaling dimension $\Delta = g/2 = 1/6$ for a Laughlin quasiparticle at the edge. When combined with measurements of the fractional charge $e^*=e/3$ and the recently observed anyonic statistical angle $\theta_a=\frac{2\pi}{3}$, the measured tunneling exponent fully characterizes the topological order of the primary Laughlin state at $\nu=1/3$.