Tunneling into the Edge of a Compressible Quantum Hall State

1997/03/31 by A. V. Shytov, Leonid Levitov, L. S. Levitov +2 · 3 citations
Physics and Astronomy · #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #Topological Materials and Phenomena #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.80.141

published as Phys. Rev. Lett. 80, 141 (1998) · 5 pages, 1 EPS figure, RevTeX, epsfig

arxiv created 1997/03/31 · openalex publication_date 1998/01/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \ensuremathρ_xy, with a slope that is discontinuous at filling factor \ensuremathν\phantom\rule0ex0ex=\phantom\rule0ex0ex1/2, in the limit of vanishing bulk resistivity \ensuremathρ_xx. When \ensuremathν corresponds to a principal fractional quantized Hall state, our results agree with the chiral Luttinger liquid theories of Wen and Kane, Fisher, and Polchinski.

Citations

• Dynamics of compressible edge and bosonization
• Semiclassical theory of the Coulomb anomaly
• Collective modes and electronic spectral function in smooth edges of quantum hall systems

Cited by

• How universal is the fractional-quantum-Hall edge Luttinger liquid?
• The gauge-invariant Green function in 3+1 dimensional QED (QCD) and 2+1 dimensional Abelian (non-Abelian) Chern–Simon theory
• Nonequilibrium tunneling into general quantum Hall edge states