Plateau Behavior in the Chiral Luttinger Liquid Exponent

The current-voltage power law exponent, $\alpha$, for electron tunneling into chiral Luttinger liquids at the fractional quantum Hall edge is found to exhibit a plateaulike structure at $\alpha$ close to 3 as the filling factor, $\nu$, is varied. The presence of a plateau near $\alpha =3\mathrm{}$ strongly suggests a fundamental connection between $\alpha$ and the structure of the underlying quantum ground states associated with the robust incompressible $\nu =1\mathrm{}/3$ Hall fluid. However, the position in the inverse filling factor where the plateau occurs can vary between samples and appears shifted to values higher than expected from theory.