Topological Robustness of Anyon Tunneling at $ν= 1/3$
The scaling exponent $g$ of the quasiparticle propagator for incompressible fractional quantum Hall states in the Laughlin sequence is expected to be robust against perturbations that do not close the gap. Here we probe the topological robustness of the chiral Luttinger liquid at the boundary of the $ν=1/3$ state by measuring the tunneling conductance between counterpropagating edge modes as a function of quantum point contact transmission. We demonstrate that for transmission $t\geq 0.7$ the tunneling conductance is well-described by the first two terms of a perturbative series expansion corresponding to $g=1/3$. We further demonstrate that the measured scaling exponent is robustly pinned to $g=1/3$ across the plateau, only deviating as the bulk state becomes compressible. Finally we examine the impact of weak disorder on the scaling exponent, finding it insensitive. These measurements firmly establish the topological robustness of anyon tunneling at $ν=1/3$ and substantiate the chiral Luttinger liquid description of the edge mode.