Mach-Zehnder Interferometer in the Fractional Quantum Hall Regime

Abstract

We consider tunneling between two edges of Quantum Hall liquids (QHL) of filling factors ν0,1 = 1/(2m0,1 +1), with m0 ≥ m1 ≥ 0, through two point contacts forming Mach-Zehnder interferometer. Quasiparticle description of the interferometer is derived explicitly through the instanton duality transformation of the initial electron model. For m0 +m1 +1 ≡ m > 1, tunneling of quasiparticles of charge e/m leads to non-trivial m-state dynamics of effective flux through the interferometer, which restores the regular "electron" periodicity of the current in flux. The exact solution available for equal propagation times between the contacts of interferometer shows that the interference pattern depends in this case on voltage and temperature only through a common amplitude. The main qualitative elements of our approach can be summarized as follows. The phase difference between the two point contacts expressed in terms of the effective flux Φ through the MZI contains, in addition to the external flux Φ ex , a statistical contribution. This contribution emerges, since each electron coherently tunneling at different contacts changes Φ by ±mΦ 0 , where m = m 0 + m 1 + 1 and Φ 0 is the flux quantum. As a result, the system has m quantum states which differ by number of flux quanta modulo m which are not mixed * also at St. Petersburg State Polytechnical University, Center for Advanced Studies, St. Petersburg 195251, Russia. by perturbative electron tunneling. However, in the nonperturbative regime of strong tunneling, the states are mixed as Φ is changed by ±Φ 0 by tunneling of individual quasiparticles. 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. If the times t 0 and t 1 of propagation between the contacts along the two edges of the interferometer are equal: ∆t ≡ t 0 − t 1 = 0, the quasiparticle Lagrangian can be solved by methods of the exactly solvable models. The resultant expression for the tunneling current shows the crossover from the quasiparticle tunneling at large voltages to the electron tunneling at low voltages. Our results correct Ref. 2 by showing that the quasiparticle model used in that work does not correspond in the weak-tunneling limit to electron tunneling at two separate point contacts, and also restrict the validity of the quasiparticle current found in [3] to the leading term in the large-V asymptotics.In details, we start with the electronic model of MZI (Fig.

Influence of device geometry on tunneling in theν=52quantum Hall liquid

“…3, with metal. Other methods that could show unique signatures of Abelian and nonAbelian states include thermopower measurements 28,37 and Mach-Zehnder interferometry 18,52,[58][59][60][61][62][63][64] . The nonequilibrium fluctuation-dissipation theorem 65,66 would provide an independent test of the existence of upstream modes.…”

Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

“…First, the thermal Hall conductance κ = π 2 k 2 B T /6h in the PH-Pfaffian state differs from all other proposed topological orders. A more striking manifestation of the PH-Pfaffian state comes from Mach-Zehnder interferometry [46][47][48][49][50][51][52][53] which we address below. We discover two unique signatures of the PH-Pfaffian order: the current through the interferometer does not depend on the magnetic field; the Fano factor for the current noise diverges at some values of the magnetic field.…”

Mesoscopic Quantum Hall Effect

“…Moreover, it is interesting to find out how charging and size effects discussed here may influence the interferometry at other filling factors, where quite similar processes can take place [66]. Although the first theoretical steps have already been taken [67,68,69] the experiment, as usual, may bring new surprises.…”

“…As we have seen above, at the lowest Landau level, the angular behavior determines the radial behavior as well. Therefore, the wave functions of two electrons 68) where m is the relative angular momentum and M is the center of mass momentum, are the eigenfunctions for arbitrary interaction potential, once we neglect mixing of Landau levels.…”