Continuum of Chiral Luttinger Liquids at the Fractional Quantum Hall Edge

We study current versus voltage $\left(I-V\right)$ when tunneling into the edge of the fractional quantum Hall effect over a continuum of filling factors $\left(\nu \right)$ from 1/4 to 1. Our devices manifest the power law $I-V$ behavior previously observed by Chang et al. at discrete fillings, but now with as many as six decades in current and over the whole range of filling factor suggesting the existence of a continuum of chiral Luttinger liquids. Surprisingly the exponent behaves approximately as $1/\nu$ and does not exhibit the strong plateau features predicted in recent theoretical works based on the intermixing of copropagating and counterpropagating multiple edge modes.