  We investigate how the vortex-vortex separation changes Majorana zero modes
in the vicinity of the BCS-BEC (Bose-Einstein condensation) topological phase
transition of p-wave resonant Fermi gases. By analytically and numerically
solving the Bogoliubov-de Gennes equation for spinless p-wave superfluids with
plural vortices, it is demonstrated that the quasiparticle tunneling between
neighboring vortices gives rise to the quantum oscillation of the low-lying
spectra on the scale of the Fermi wavelength in addition to the exponential
splitting. This rapid oscillation, which appears in the weak coupling regime as
a consequence of quantum oscillations of quasiparticle wave functions,
disappears in the vicinity of the BCS-BEC topological phase transition. This is
understandable from that the wave function of the Majorana zero modes is
described by the modified Bessel function in the strong coupling regime and
thus it becomes spread over the vortex core region. Due to the exponential
divergence of the modified Bessel function, the concrete realization of the
Majorana zero modes near the topological phase transition requires the
neighboring vortices to be separated beyond the length scale defined by the
coherence length and the dimensionless coupling constant. All these behaviors
are also confirmed by carrying out the full numerical diagonalization of the
non-local Bogoliubov-de Gennes equation in a two dimensional geometry.
Furthermore, this argument is expanded into the case of three-vortex systems,
where a pair of core-bound and edge-bound Majorana states survive at zero
energy state regardless of the vortex separation.
