Tunneling into the Edge of a Compressible Quantum Hall State

Phys. Rev. Lett. 80, 141 – Published 5 January 1998
A. V. Shytov, L. S. Levitov, and B. I. Halperin


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 ρxy, with a slope that is discontinuous at filling factor ν=1/2, in the limit of vanishing bulk resistivity ρxx. When ν corresponds to a principal fractional quantized Hall state, our results agree with the chiral Luttinger liquid theories of Wen and Kane, Fisher, and Polchinski.

DOI: http://dx.doi.org/10.1103/PhysRevLett.80.141

  • Received 21 March 1997
  • Published in the issue dated 5 January 1998

© 1998 The American Physical Society

Authors & Affiliations

A. V. Shytov1, L. S. Levitov1, and B. I. Halperin2,3

  • 112-112, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • 2Physics Department, Harvard University, Cambridge, Massachusetts 02138
  • 3Institute for Advanced Study, Princeton, New Jersey 08540

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