Collision of two interacting electrons on a mesoscopic beam splitter
Exact solution in the classical limit
 authored by
 Elina Pavlovska, Peter G. Silvestrov, Patrik Recher, Girts Barinovs, Vyacheslavs Kashcheyevs
 Abstract
Experiments on collisions of isolated electrons guided along the edges in quantum Hall setups can mimic mixing of photons with the important distinction that electrons are charged fermions. In the socalled electronic HongOuMandel (HOM) setup uncorrelated pairs of electrons are injected toward a beam splitter. If the two electron wave packets were identical, then Fermi statistics would force the electrons to scatter to different detectors, yet this quantum antibunching may be confounded by Coulomb repulsion. Here we model an electronic HOM experiment using a quadratic twodimensional saddle point potential for the beam splitter and unscreened Coulomb interaction between the two injected electrons subjected to a strong outofplane magnetic field. We show that classical equations of motion for the drift dynamics of electrons' guiding centers take on the form of Hamilton equations for canonically conjugated variables subject to the saddle point potential and the Coulomb potential where the dynamics of the centerofmass coordinate and the relative coordinate separate. We use these equations to determine collision outcomes in terms of a few experimentally tuneable parameters: the initial energies of the uncorrelated electrons, relative time delay of injection, and the shape of the saddle point potential. A universal phase diagram of deterministic bunching and antibunching scattering outcomes is presented with a single energy scale characterizing the increase of the effective barrier height due to interaction of coincident electrons. We suggest clearcut experimental strategies to detect the predicted effects and give analytical estimates of conditions when the classical dynamics is expected to dominate over quantum effects.
 External Organisation(s)

University of Latvia
Technische Universität Braunschweig
Laboratory for Emerging Nanometrology Braunschweig (LENA)
 Type
 Article
 Journal
 Physical Review B
 Volume
 107
 ISSN
 24699950
 Publication date
 07.04.2023
 Publication status
 Published
 Peer reviewed
 Yes
 ASJC Scopus subject areas
 Electronic, Optical and Magnetic Materials, Condensed Matter Physics
 Electronic version(s)

https://doi.org/10.1103/PhysRevB.107.165304 (Access:
Unknown)