Effect of Particle Number Conservation on the Berry Phase Resulting from Transport of a Bound Quasiparticle around a Superfluid Vortex

TL;DR

This paper investigates how particle number conservation influences the Berry phase in superfluid systems with bound quasiparticles, revealing that standard non-conserving methods miss key physics relevant to Majorana modes.

Contribution

It demonstrates the importance of particle number conservation for accurately calculating the Berry phase and shows that superfluid condensate effects are beyond the standard BdG framework.

Findings

Particle number conservation alters the Berry phase values.

Superfluid condensate impacts the Berry phase beyond BdG predictions.

Bound quasiparticles deform the superfluid ground state in a particle-number conserving context.

Abstract

Motivated by understanding Majorana zero modes in topological superfluids in particle-number conserving framework beyond the present framework, we study the effect of particle number conservation on the Berry phase resulting from transport of a bound quasiparticle around a superfluid vortex. We find that particle-number non-conserving calculations based on Bogoliubov-de Gennes (BdG) equations are unable to capture the correct physics when the quasiparticle is within the penetration depth of the vortex core where the superfluid velocity is non-zero. Particle number conservation is crucial for deriving the correct Berry phase in this context, and the Berry phase takes non-universal values depending on the system parameters and the external trap imposed to bind the quasiparticle. Of particular relevance to Majorana physics are the findings that superfluid condensate affects the part of the Berry phase not accounted for in the standard BdG framework, and that the superfluid many-body ground state of odd number of fermions involves superfluid condensate deformation due to the presence of the bound quasiparticle - an effect which is beyond the description of the BdG equations.