Berlin 2015 – scientific programme
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TT: Fachverband Tiefe Temperaturen
TT 109: Transport: Majorana Fermions (jointly with DS, HL, MA, O)
TT 109.3: Talk
Friday, March 20, 2015, 10:00–10:15, H 0104
Localization length and non-adiabaticity - braiding errors in Majorana quantum wires — •Michael Sekania1,3, Martin Greiter1, Ronny Thomale1, and Peter Schmitteckert2 — 1Institute for Theoretical Physics and Astrophysics, Julius-Maximilian University of Würzburg, Am Hubland, D-97074 Würzburg, Germany — 2Institute of Nanotechnology, Karlsruhe Institute of Technology, D-76344 Eggenstein-Leopoldshafen, Germany — 3Theoretical Physics III, Center for Electronic Correlations and Magnetism, Institute of Physics, University of Augsburg, D-86135 Augsburg, Germany
Majorana fermions have been attracting substantial interest in recent years. Several experimental groups have already reported tentative observation of Majorana zero modes in quantum nanowires that are proximity-coupled to a bulk superconductor. The unambiguous detection of Majorana quasi-particles, however, has so far remained elusive. One of the ultimate experimental checks for the existence of Majorana zero modes would be a braiding experiment, that reveals the non-trivial braiding statistics of the Majorana fermions. We present numerical studies of the braiding of Majorana bound states (MBS) in presence of a quasi-particle background, and show braiding errors due to non-adiabaticity -- which is a realistic scenario for experiments -- and due to system sizes which are comparable to the localization length of the MBS. The latter seems to be the case for certain experimental realizations reported recently. We further address the influence of finite-range interactions on the braiding process.