Relaxation of an electron wave packet at the quantum Hall edge at filling factor 2

Artur O. Slobodeniuk, Edvin G. Idrisov, Eugene V. Sukhorukov

Published 2015-06-27Version 1

In this work, we address the recent experiment [S. Tewari et al., arXiv:1503.05057v1], where the suppression of the phase coherence of the single-electron wave packet created at the edge of a quantum Hall (QH) system at filling factor 2 has been investigated. The authors of the experiment have observed an unexpected behavior that the degree of the phase coherence saturates at high energies, instead of vanishing, and suggested that this phenomenon may be explained using the model of edge states [I.P. Levkivskyi, E.V. Sukhorukov, Phys. Rev. B 78, 045322 (2008)], which accounts for the strong Coulomb interaction between the two electron channels at the edge of the QH system, presumably leading to the relaxation of the wave packet to the ground state. Here, we theoretically investigate the problem of the relaxation of the electron wave packet at the QH edge and conclude that the observed phenomenon cannot be explained within the mentioned above model for the following reason: Under the assumption of the linearity of the electron spectrum at low energies, the system remains integrable in terms of the collective charge excitations, and thus full relaxation to the ground state is not possible, despite strong interactions. We complete our study by finding the energy distribution and the Wigner function of the outgoing non-equilibrium state of the single-electron wave packet.