  A topological superfluid phase characterized by an emergent chiral-p-wave
pair potential is expected to form in a two-dimensional Fermi superfluid
subject to s-wave pairing, spin-orbit coupling and a large-enough Zeeman
splitting. Andreev bound states appear at phase boundaries, including Majorana
zero modes whose existence is assured by the bulk-boundary correspondence
principle. Here we study the physical properties of these subgap-energy bound
states at step-like interfaces using the spin-resolved Bogoliubov-deGennes
mean-field formalism and assuming small spin-orbit coupling. Extending a
recently developed spin-projection technique based on Feshbach partitioning
[SciPost Phys. 5, 016 (2018)] combined with the Andreev approximation allows us
to obtain remarkably simple analytical expressions for the bound-state energies
as well as the majority and minority spin components of their wave functions.
Besides the vacuum boundary, where a majority-spin Majorana excitation is
encountered, we also consider the boundary between the topological and a
nontopological superfluid phase that can appear in a coexistence scenario due
to the first-order topological phase transition predicted for this system. At
this superfluid-superfluid interface, we find a localized chiral Majorana mode
hosted by the minority-spin sector. Our theory further predicts majority-spin
subgap-energy bound states similar to those found at a Josephson junction
between same-chirality p-wave superfluids. Their presence affects the Majorana
mode due to a coupling of minority and majority spin sectors only in the small
energy range where their spectra overlap. Our results may inform experimental
efforts aimed at realizing and characterizing unconventional Majorana
quasiparticles.
