Topological screening and interference of fractionally charged quasi-particles

Interference of fractionally charged quasi-particles is expected to lead to Aharonov-Bohm oscillations with periods larger than the flux quantum $\Phi_0$. However, according to the Byers-Yang theorem, observables of an electronic system are invariant under insertion of a quantum of singular flux. We resolve this paradox by considering a {\em microscopic} model of an electronic interferometer made from quantum Hall edges at filling factor $\nu=1/m$. 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 onto the space of such deformations. Amplitudes of quasi-particle tunneling in this theory are found to be insensitive to the singular flux. This behavior is a consequence of {\em topological screening} of the flux by the quantum Hall liquid. We describe strong coupling of the edges 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 period $\Phi_0$. These oscillations are suppressed with increasing system size. When the magnetic flux is varied with a modulation gate, current oscillations have the quasi-particle period $m\Phi_0$ and survive in the thermodynamic limit.