Tunneling into the Edge of a Compressible Quantum Hall State

We present a composite-fermion theory of tunneling into the edge of a compressible quantum Hall system. The tunneling conductance is non-Ohmic, due to slow relaxation of electromagnetic and Chern-Simons field disturbances caused by the tunneling electron. Universal results are obtained in the limit of a large number of channels involved in the relaxation. The tunneling exponent is found to be a continuous function of the Hall resistivity ${\rho }_{\mathrm{xy}}$, with a slope that is discontinuous at filling factor $\nu =1\mathrm{}/2$, in the limit of vanishing bulk resistivity ${\rho }_{\mathrm{xx}}$. When $\nu$ corresponds to a principal fractional quantized Hall state, our results agree with the chiral Luttinger liquid theories of Wen and Kane, Fisher, and Polchinski.