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arXiv:cond-mat/9304010 · Physical Review Letters

Resonant tunneling between quantum Hall edge states

Kyungsun Moon, Hangmo Yi, C. L. Kane, S. M. Girvin, Matthew P. A. Fisher

Published Dec 27, 1993• 204 citations
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Abstract

Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the \ensuremath{\nu}=1/3 Laughlin parent state, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for \ensuremath{\nu}=1/3 which confirm this picture and provide a parameter-free prediction for the line shape.

DOI
10.1103/physrevlett.71.4381

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Resonant tunneling between fractional quantum Hall edge states is studied in the Luttinger liquid picture. For the \ensuremath{\nu}=1/3 Laughlin parent state, the resonance line shape is a universal function whose width scales to zero at zero temperature. Extensive quantum Monte Carlo simulations are presented for \ensuremath{\nu}=1/3 which confirm this picture and provide a parameter-free prediction for the line shape.
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We have recently calculated exact nonequilibrium quantum transport properties through a point contact in a Luttinger liquid. Using a particular quasiparticle basis of the Hilbert space dictated by integrability, we here compute explicitly the exact I(V) characteristic and conductance out of equilibrium as a function of driving voltage V and temperature T. These are described by universal scaling functions of two variables, the scaled point-contact interaction strength, and V/T. The differential-conductance curve as a function of the interaction strength broadens significantly as V/T is increased, and develops a pronounced maximum at a (universal) critical value (eV/kB{\mathit{k}}_{\mathit{B}}kB​T)=7.188 68. . .. In addition, we derive an exact duality between strong and weak backscattering. The theory presented here has recently been realized experimentally in resonant tunneling-transport experiments between edge states in fractional quantum Hall effect devices. In this context the exact duality is between electron tunneling and Laughlin-quasiparticle tunneling.
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In a microscopic model of fractional quantum Hall liquids with electron-electron interactions and confinement, we calculate the edge Green's function via exact diagonalization. Our results for nu=1/3 and 2/3 suggest that, in the presence of Coulomb interaction, "external" parameters such as the sharpness of the edge and the strength of the edge confining potential, which can lead to edge reconstruction, may cause deviations from universality in the edge-tunneling I-V exponent. In particular, we do not find any direct dependence of this exponent on the range of the interaction potential as suggested by recent calculations in contradiction to the topological nature of the edge.