Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2010-05-31
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
24 pages, 9 figures
Scientific paper
Interference of fractionally charged quasi-particles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum. However, according to the Byers-Yang theorem, observables of an electronic system are invariant under adiabatic insertion of a quantum of singular flux. We resolve this seeming paradox by considering a microscopic model of an electronic Mach-Zehnder interferometer made from a quantum Hall liquid at filling factor 1/m. An approximate ground state of such an interferometer is described by a Laughlin type wave function, and low-energy excitations are incompressible deformations of this state. We construct a low-energy effective theory by projecting the state space of the liquid onto the space of such incompressible deformations and show that the theory of the quantum Hall edge so obtained is a generalization of a chiral conformal field theory. Amplitudes of quasi-particle tunneling in this theory are found to be insensitive to the magnetic flux threading through the hole in the Corbino disk. This behavior is a consequence of topological screening of the singular flux by the quantum Hall liquid. We describe strong coupling of the edges of the liquid to Ohmic contacts and the resulting quasi-particle current through the interferometer with the help of a master equation. As a function of the singular magnetic flux, the current oscillates with the electronic period, i.e., our theory conforms to the Byers-Yang theorem. These oscillations, which originate from the Coulomb blockade effect, are suppressed with increasing system size. In contrast, when the magnetic flux through the interferometer is varied with a modulation gate, current oscillations have the quasi-particle period and survive in the thermodynamic limit.
Froehlich Juerg
Levkivskyi Ivan P.
Sukhorukov Eugene V.
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