Chiral Majorana edge states in the vortex core of a $p+ip$ Fermi superfluid

TL;DR

This paper investigates how a vortex in a two-dimensional $p+ip$ Fermi superfluid interacts with a Bose-Einstein condensate, revealing conditions under which chiral Majorana edge states emerge and how they can be controlled.

Contribution

It demonstrates the emergence and control of chiral Majorana edge states at vortex interfaces in a $p+ip$ Fermi superfluid interacting with a BEC, highlighting a transition mechanism based on bosonic density.

Findings

Fermions are depleted from the vortex core at high bosonic densities.

Chiral Majorana edge states form along the fermion-boson interface.

A first-order transition occurs in the vortex core states depending on vortex chirality.

Abstract

We study a single vortex in a two-dimensional $p+ip$ Fermi superfluid interacting with a Bose-Einstein condensate. The Fermi superfluid is topologically non-trivial and hosts a zero-energy Majorana bound state at the vortex core. Assuming a repulsive $s$-wave contact interaction between fermions and bosons, we find that fermions are depleted from the vortex core when the bosonic density becomes sufficiently large. In this case, a dynamically-driven local interface emerges between fermions and bosons, along which chiral Majorana edge states should appear.We examine in detail the variation of vortex-core structures as well as the formation of chiral Majorana edge states with increasing bosonic density. In particular, when the angular momentum of the vortex matches the chirality of the Fermi superfluid, the Majorana zero mode and normal bound states within the core continuously evolve into chiral Majorana edge states. Otherwise, a first-order transition occurs in the lowest excited state within the core, due to the competition between counter-rotating normal bound states in forming chiral Majorana edge states. Such a transition is manifested as a sharp peak in the excitation gap above the Majorana zero mode, at which point the Majorana zero mode is protected by a large excitation gap.Our study presents an illuminating example on how topological defects can be dynamically controlled in the context of cold atomic gases.