Abstract
We investigate a Fabry-Pérot interferometer in the integer Hall regime in which only one edge channel is transmitted and nn channels are trapped into the interferometer loop. Addressing recent experimental observations, we assume that Coulomb blockade effects are completely suppressed due to screening, while keeping track of a residual strong short range electron-electron interaction between the co-propagating edge channels trapped into the interferometer loop. This kind of interaction can be completely described in the framework of the edge-magnetoplasmon scattering matrix theory allowing us to evaluate the backscattering current and the associated differential conductance as a function of the bias voltage. The remarkable features of these quantities are discussed as a function of the number of trapped channels. The developed formalism reveals very general and provides also a simple way to model the experimentally relevant geometry in which some of the trapped channels are absorbed into an Ohmic contact, leading to energy dissipation.
Highlights
The interacting cases strongly deviate from this linearity at higher voltages (ω0τσ ≈ π) and show a remarkable oscillating behavior. This is even more evident for what it concerns the differential conductance which is constant in the free case, but oscillates and decay quite fast by increasing the number of trapped channels. Notice that this phenomenology is reminiscent of what derived in literature for a Fabry-Pérot interferometer (FPI) in the integer and fractional quantum Hall regime [27] or for the topological insulators in presence of interaction [28]
In the present paper we have discussed the physics of a FPI in the integer quantum Hall regime
Motivated by very recent experiments, we focused on a system at filling factor ν = n + 1 (n ∈ ) where only one edge channel is transmitted across the sample, while the other n are trapped into the interferometer loop
Summary
In the last few years various accurate experimental observations shed new light on the remarkable physics associated to the Fabry-Pérot interferometer (FPI) of integer and fractional quantum Hall edge channels [1,2,3]. When only one channel is transmitted throughout the FPI, by increasing the number of channels trapped in the loop (namely the integer filling factor of the system), one moves from the standard Aharonov-Bohm effect of electrons (at filling factor 1 ≤ ν ≤ 2) to a more puzzling situation in which a pair of electrons seems to interfere (at filling factor 3 ≤ ν ≤ 4) This phenomenology has been deduced from both the halving of the periodicity of the conductance with respect to the Aharonov-Bohm flux and the doubling of the effective outgoing charge measured through shot noise. The classical and quantum contributions to the current and the associated differential conductance are derived in Section 3 by means of the Kubo formula The plots of these quantities, as well as the relevant comments concerning the behavior of the system as a function of the number of trapped channels are reported, in view of a possible interpretation of the experimental observations.
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