Traveling Majorana solitons in a one-dimensional spin-orbit coupled Fermi superfluid

TL;DR

This paper studies traveling solitons in a one-dimensional spin-orbit coupled Fermi superfluid, revealing a critical velocity affected by spin-orbit coupling and discovering Majorana solitons with potential applications in quantum computing.

Contribution

It introduces the concept of Majorana solitons in a topological superfluid and analyzes their properties and stability, which is a novel finding in the field.

Findings

Critical velocity for solitons is lower than Landau prediction due to spin-orbit coupling.

Traveling solitons decay by sound radiation above the critical velocity.

Majorana solitons host two Majorana fermions with a phase jump of π, independent of velocity.

Abstract

We investigate traveling solitons of a one-dimensional spin-orbit coupled Fermi superfluid in both topologically trivial and non-trivial regimes by solving the static and time-dependent Bogoliubov-de Gennes equations. We find a critical velocity $v_{h}$ for traveling solitons that is much smaller than the value predicted using the Landau criterion due to the presence of spin-orbit coupling, which strongly upshifts the energy level of the soliton-induced Andreev bound states towards the quasi-particle scattering continuum. Above $v_{h}$, our time-dependent simulations in harmonic traps indicate that traveling solitons decay by radiating sound waves. In the topological phase, we predict the existence of peculiar Majorana solitons, which host two Majorana fermions and feature a phase jump of $\pi$ across the soliton, irrespective of the velocity of travel. These unusual properties of Majorana solitons may open an alternative way to manipulate Majorana fermions for fault-tolerant topological quantum computations.