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