Incidence of the boundary shape in the tunnelling exponent of electrons into fractional quantum Hall edges

Experiments on tunneling into fractional quantum Hall droplets systematically found tunneling exponents smaller than those predicted by the ordinary chiral Luttinger liquid theory. In this note, by considering the effects of a smooth boundary, we propose a modification of the theory that predicts a reduced exponent, in qualitative agreement with experiments. Such modification consists on a self-interaction cubic term, containing higher derivatives of the chiral boson field, that provides a non-universal one loop correction to the propagator.