Coherent electron splitting in interacting chiral edge channels

This paper theoretically studies the quantum coherence of an electronic state on an artificial chiral Tomonaga-Luttinger (TL) liquid. Coulomb interaction between copropagating integer quantum Hall edge channels causes the TL liquid nature of charge excitations, resulting in the splitting of an electronic state into bosonic eigenmodes. We investigate the single-electron coherence under the splitting process by calculating the Aharonov-Bohm (AB) oscillations in an electronic Mach-Zehnder interferometer employing copropagating spin-up and spin-down edge channels as the interference paths. We investigate the voltage bias dependence of the AB oscillations at zero temperature, taking the inter-channel interaction into account using the bosonization technique. The calculation results of the visibility and the phase of the AB oscillations show non-monotonical bias dependence when the copropagating channels are electrostatically asymmetric. These observations are interpreted as the signatures of the second-order interference between the fractionalized spin excitations with different phase evolutions. We also report finite entanglement entropy between the bosonic eigenmodes split from an electron, which presents an analogy between the `electron splitting' in a TL liquid and the Cooper-pair splitting at a superconducting junction.