Strong-coupling branching between edges of fractional quantum Hall liquids

Abstract

We have developed a theory of quasiparticle backscattering in a system of point contacts formed between single-mode edges of several Fractional Quantum Hall Liquids (FQHLs) with in general different filling factors νj and one common single-mode edge ν0 of another FQHL. In the strongtunneling limit, the model of quasiparticle backscattering is obtained by the duality transformation of the electron tunneling model. The new physics introduced by the multi-point-contact geometry of the system is coherent splitting of backscattered quasiparticles at the point contacts in the course of propagation along the common edge ν0. The "branching ratios" characterizing the splitting determine the charge and exchange statistics of the edge quasiparticles that can be different from those of Laughlin's quasiparticles in the bulk of FQHLs. Accounting for the edge statistics is essential for the system of more than one point contact and requires the proper description of the flux attachement to tunneling electrons.

Antidot tunneling between quantum Hall liquids with different filling factors

“…In the simplest case of FQHL with the filling factor ν = 1/odd, the quasiparticles that tunnel through the liquid between its edges coincide with the quasiparticles in the bulk [3] and their fractional charge νe can be measured experimentally [4,5]. So far, fractional statistics of quasiparticle has not been directly observed in experiments, although there is experimental [6] and theoretical [7] interest to manifestations of this statistics in the noise correlators of the tunnel currents.Strong tunneling between edges of FQHLs with different filling factors should create quasiparticles which are different from those in the bulk of the liquids but still have fractional charge and statistics [8,9]. Untill now, such tunneling has been considered only in the geometry of a single point contact [8] or multiple contacts [9] for which the interference between different contacts is not important (i.e., the edges do not form closed loops).…”

“…Strong tunneling between edges of FQHLs with different filling factors should create quasiparticles which are different from those in the bulk of the liquids but still have fractional charge and statistics [8,9]. Untill now, such tunneling has been considered only in the geometry of a single point contact [8] or multiple contacts [9] for which the interference between different contacts is not important (i.e., the edges do not form closed loops).…”

“…Untill now, such tunneling has been considered only in the geometry of a single point contact [8] or multiple contacts [9] for which the interference between different contacts is not important (i.e., the edges do not form closed loops). The purpose of this work is to study an "antidot" tunnel junction: two separate point contacts at points x 1 , x 2 along the x-axis between two single-mode edges of QHLs with different filling factors ν 0,1 = 1/(2m 0,1 + 1) with m 0 > m 1 ≥ 0 -see Fig.…”

“…This discussion assumes that large tunnel amplitudes U j completely suppress quantum fluctuations of the fields ϕ j . For large but finite U j , the fields can tunnel between different minima n j of the strong-coupling solution (6), the process that represents quasiparticle backscattering and can be described quantitatively in terms of the instanton expansion [9]. The operators (W j D/2π) exp{±i2θ j /λ}, where θ j are dual to ϕ j : [θ j , ϕ k ] = iπ(−1) j δ jk , generate the jumps of ϕ j changing n j by ∓(−1) j .…”

“…Bosonic fields φ l have the standard quadratic Lagrangian defined by the Fourier transform of the imaginary-time-ordered correlators (see, e.g., [9]…”