Riding a wild horse: Majorana fermions interacting with solitons of fast bosonic fields

TL;DR

This paper explores a novel class of excitations in one-dimensional systems where fast bosonic fields interact with Majorana fermions, revealing bound states that depend on interactions and soliton velocity, with potential implications for superconductors and nanotubes.

Contribution

It introduces a new class of non-topological bound states formed by Majorana fermions and solitons in systems with fast bosonic modes, expanding understanding of excitations in such models.

Findings

Bound states of Majorana fermions and solitons exist in these models.

Number of bound states increases with soliton velocity.

Bound states depend on interactions and are not topological.

Abstract

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.