Effective action of a compressible quantum Hall state edge: Application totunneling - art. no. 075322

The electrodynamical response of the edge of a compressible quantum Hall sy stem affects tunneling into the edge. Using composite Fermi liquid theory, we derive an effective action for the edge modes interacting with tunneling charge. This action generalizes the chiral Luttinger liquid theory of the quantum Hall edge to compressible systems in which transport is characteriz ed by a finite Hall angle. In addition to the standard terms, the action co ntains a dissipative term. The tunneling exponent is calculated as a functi on of the filling fraction for several models, including screened and unscr eened Iona-range Coulomb interaction, as well as a short-range interaction. We find that tunneling exponents are robust and to a large extent insensit ive to the particular model. We discuss recent tunneling measurements in ov ergrown cleaved edge systems, and demonstrate that the profile of charge de nsity near the edge is very sensitive to the parameters of the system. In g eneral, the density is nonmonotonic, and can deviate from the bulk value by up to 30%. Implications for the correspondence to chiral Luttinger edge th eories are discussed.