| Interference of fractionally charged quasi-particles should lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem an arbitrary observable of an electronic system is invariant under the adiabatic insertion of the quantum of singular flux. To resolve this paradox we consider a microscopic model of an electronic Mach-Zehnder interferometer based on a quantum Hall system at filling factor 1/m. These interferometers have a shape of a Corbino disk and utilize quantum Hall edge states in place of optical beams, and quantum point contacts as beam splitters, to partition edge channels. The ground state of the interferometer is described by a Laughlin type wave-function, while low-energy excitations are incompressible deformations of this state. We construct the low-energy effective theory by projecting on the space of such incompressible deformations and show that so defined theory is a generalization of the chiral conformal theory of the quantum Hall edge. Amplitudes of quasi-particle tunneling in this theory are found to be insensitive to the singular magnetic flux inserted through the hole in the Corbino disk. This behavior results from topological screening of the singular flux by the quantum Hall system. We describe strong coupling to Ohmic contacts and the quasi-particles current through the interferometer with the help of a master equation. The current as a function of the singular magnetic flux oscillates with the electronic period, i.e. our theory conforms the Byers-Yang theorem. These oscillations, originating from the Coulomb blockade effect, are suppressed with the system size. In contrast, if the magnetic flux through the interferometer is varied with the modulation gate, then the oscillations have m times larger quasi-particle period and survives in thermodynamic limit. |
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