Resonant dephasing of the electronic Mach-Zehnder interferometer

We address the recently observed unexpected behavior of Aharonov-Bohm oscillations in the electronic Mach-Zehnder interferometer experimentally realized in a quantum Hall system [1]. We argue that the measured lobe-like structure in the visibility of oscillations and the phase rigidity result from a long-range {\em local} interaction between two adjacent counter-propagating edge states, which leads to a resonant scattering of bosonic charge excitations. The visibility and phase shift, expressed in terms of the transmission coefficient for bosons, provide the tool for investigating the nature of quantum Hall edge states. [1] I. Neder {\em et al}., Phys. Rev. Lett. {\bf 96}, 016804 (2006).