Antidot tunneling between quantum Hall liquids with different filling factors

Abstract

We consider tunneling through two point contacts between two edges of Quantum Hall liquids of different filling factors ν0,1 = 1/(2m0,1 + 1) with m0 − m1 ≡ m > 0. Properties of the antidot formed between the point contacts in the strong-tunneling limit are shown to be very different from the ν0 = ν1 case, and include vanishing average total current in the two contacts and quasiparticles of charge e/m. For m > 1, quasiparticle tunneling leads to non-trivial m-state dynamics of effective flux through the antidot which restores the regular "electron" periodicity of the current in flux despite the fractional charge and statistics of quasiparticles. [2]. Although the quasiparticles are defined most simply in the incompressible bulk of the FQHL, in the lowenergy transport experiments, quasiparticles are created typically at the liquid edges, e.g. by tunneling between them. 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). 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. 1. In this geometry, the tunneling processes at two point contacts interfere and statistics of tunneling quasiparticles directly affects the dc current.If the two filling factors are equal, ν 0 = ν 1 ≡ ν, as in experiments [4], strong tunneling leads to formation of a closed edge between the points x 1 and x 2 encircling the antidot and separated from external edges of the surrounding uniform QHL [10]. Quasiparticles of charge νe can then tunnel between the external edges * on leave from St. Petersburg State Polytechnical University, Center for Advanced Studies, St. Petersburg 195251, Russia. through the antidot. As shown below, the situation is very different for ν 0 = ν 1 , and the antidot formed between the point contacts does not decouple completely from external edges even in the limit of strong tunneling. As a result, the total tunnel current between the two QHLs vanishes in this limit. Also, interference between the two contacts produces the quasiparticles of charge e...

Comment on “Strongly Correlated Fractional Quantum Hall Line Junctions”

“…(1), and changing the transfer matrix T (2) into the scattering matrix P which relates incoming and outgoing fields φ, one can immediately see that P coincides with the scattering matrix of a point contact [4] (or in fact any odd number of successive point contacts [8]) in the strong-coupling limit. In this case the junction conductance is G = G m contrary to the result obtained in [1] (see Eqs.…”

Mach-Zehnder Interferometer in the Fractional Quantum Hall Regime

“…The current associated with the quasiparticle tunneling is expressed as usual in terms of the transfer operators: I q = (i/m) j=1,2 ± ±T ± j e ∓iV t/m . The model (15) with the Klein factors (14) for quasiparticle tunneling between the edges of the MZI is a direct analogue of the quasiparticle model we derived earlier for the antidot [7]. At ν 0 = ν 1 it coincides with the postulated quasiparticle model of [3] for a special choice of matricesF j .…”

“…This implies that the quasiparticles have to carry the charge e/m and coincide with the quasiparticles e * = 2eν 0 ν 1 /(ν 0 +ν 1 ) = e/m in one point contact [6]. (Flux dynamics in the MZI is similar to that in the antidot tunneling [7], where, however, m = m 0 − m 1 , and the e/m quasiparticles are different from those in individual contacts.) The quasiparticle Lagrangian for MZI derived below is a mathematical expression of the flux-induced electron-quasiparticle transmutation.…”

“…This expression coincides (up to redefinition of the phase κ V = κ(V )−Vt) with the interference current in the antidot geometry [7,10]. One can evaluate the integral (5) for integer 1/ν l by residues, and find the visibility Vis ≡ (max κ I −min κ I)/(max κ I + min κ I).…”

“…1) formed by two single-mode edges with filling factors ν l = 1/(2m l + 1), l = 0, 1, which differ from the model studied in [7] only by the direction of propagation of one edge. In the standard bosonization approach [8], Lagrangian of weak electron tunneling in the two contacts [3] can be expressed through two bosonic fields φ l related to the correspondent edge density ρ l (x, τ ) = ( √ ν l /2π)∂ x φ l (x, τ ) as follows: where D is a common energy cut-off of the edge modes, U j and κ j are the absolute values and the phases of the dimensionless tunneling amplitudes.…”