Time dependent electronic transport in chiral edge channels

• We discuss Coulomb interaction effects on charge propagation along quantum Hall edge channels.
• Various experimental works are connected and analyzed in a unified theoretical framework.
• Low frequency transport is described by a lumped element model.
• High frequency transport is described by edge magnetoplasmon propagation.
• Interchannel magnetoplasmon scattering leads to electron fractionalization and decoherence.

We study time dependent electronic transport along the chiral edge channels of the quantum Hall regime, focusing on the role of Coulomb interaction. In the low frequency regime, the a.c. conductance can be derived from a lumped element description of the circuit. At higher frequencies, the propagation equations of the Coulomb coupled edge channels need to be solved. As a consequence of the interchannel coupling, a charge pulse emitted in a given channel fractionalized in several pulses. In particular, Coulomb interaction between channels leads to the fractionalization of a charge pulse emitted in a given channel in several pulses. We finally study how the Coulomb interaction, and in particular the fractionalization process, affects the propagation of a single electron in the circuit. All the above-mentioned topics are illustrated by experimental realizations.