Riding a wild horse: Majorana fermions interacting with solitons of fast bosonic fields
Department of Condensed Matter Physics and Materials Science, Brookhaven National Laboratory Upton, NY 11973-5000, USA
Accepted: 25 November 2011
I consider a class of one-dimensional models where Majorana fermions interact with bosonic fields. Contrary to a more familiar situation where bosonic degrees of freedom are phonons and as such form a slow subsystem, I consider fast bosons. Such situation exists when the bosonic modes appear as collective excitations of interacting electrons as, for instance, in superconductors or carbon nanotubes. It is shown that an entire new class of excitations emerge, namely bound states of solitons and Majorana fermions. The latter bound states are not topological and their existence and number depend on the interactions and the soliton's velocity. Intriguingly the number of bound states increases with the soliton's velocity.
PACS: 73.21.-b – Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems / 71.10.Pm – Fermions in reduced dimensions (anyons, composite fermions, Luttinger liquid, etc.)
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