We study Majorana modes in the vortex core of a two-dimensional
p+ip Fermi superfluid interacting with a Bose-Einstein condensate. Under a repulsive
s-wave contact interaction between fermions and bosons, fermions are depleted from the vortex core when the bosonic density becomes sufficiently high. This gives rise to a dynamically driven local interface that 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, where the circulation of the vortex plays an important role. Whereas both the Majorana modes and the vortex-core structures can be controlled and manipulated by tuning the bosonic density and the Bose-Fermi interaction strength, our study presents an illuminating example of how topological defects can be dynamically controlled in the context of cold-atomic gases.
Multiply quantized vortices in the BCS-to-BEC (Bose-Einstein condensation) evolution of
p-wave resonant Fermi gases are investigated theoretically. The vortex structure and the low-energy quasiparticle states are discussed, based on the self-consistent calculations of the Bogoliubov-de Gennes and gap equations. We reveal the direct relation between the macroscopic structure of vortices, such as particle densities, and the low-lying quasiparticle state. In addition, the net angular momentum for multiply quantized vortices with a vorticity $\ensuremath{\kappa}$ is found to be expressed by a simple equation, which reflects the chirality of the Cooper pairing. Hence, the observation of the particle density depletion and the measurement of the angular momentum will provide the information on the core-bound state and
p-wave superfluidity. Moreover, the details on the zero energy Majorana state are discussed in the vicinity of the BCS-to-BEC evolution. It is demonstrated numerically that the zero energy Majorana state appears in the weak coupling BCS limit only when the vortex winding number is odd. The $\ensuremath{\kappa}$ branches of the core-bound states for a vortex state with vorticity $\ensuremath{\kappa}$ exist; however, only one of them can be the zero energy. This zero energy state vanishes at the BCS-BEC topological phase transition because of interference between the core-bound and edge-bound states.
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 nonlocal 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.
Two-dimensional spin-orbit-coupled Fermi gases subject to
s-wave pairing can be driven into a topological phase by increasing the Zeeman spin splitting beyond a critical value. In the topological phase, the system exhibits the hallmarks of chiral
p-wave superfluidity, including exotic Majorana excitations. Previous theoretical studies of this realization of a two-dimensional topological Fermi superfluid have focused on the BCS regime where the
s-wave Cooper pairs are only weakly bound and, hence, the induced chiral
p-wave order parameter has a small magnitude. Motivated by the goal to identify potential new ways for the experimental realization of robust topological superfluids in ultracold-atom gases, we study the BCS-to-BEC crossover driven by increasing the Cooper-pair binding energy for this system. In particular, we obtain phase diagrams in the parameter space of two-particle bound-state energy and Zeeman spin-splitting energy. Ordinary characteristics of the BCS-to-BEC crossover, in particular the shrinking and eventual disappearance of the Fermi surface, are observed in the nontopological phase. In contrast, the topological phase retains all features of chiral
p-wave superfluidity, including a well-defined underlying Fermi surface, even for large
s-wave pair-binding energies. Compared to the BCS limit, the topological superfluid in the BEC regime turns out to be better realizable even for only moderate magnitude of spin-orbit coupling because the chiral
p-wave order parameter is generally larger and remnants of
s-wave pairing are suppressed. We identify optimal parameter ranges that can aid further experimental investigations and elucidate the underlying physical reason for the persistence of the chiral
p-wave superfluid.
In order to clarify the structure of a singly quantized vortex in a superfluid fermion gas near the Feshbach resonance, we numerically solve the generalized Bogoliubov-de Gennes equation in the boson-fermion model. The superfluid gap, which contains contributions from both condensed fermion pairs and condensed bosons, is self-consistently determined, and the quasiparticle excitation levels bound in the vortex core are explicitly shown. We find that the boson condensate contributes to enhance the matter density depletion and the discreteness of localized quasiparticle spectrum inside the core. It is predicted that the matter density depletion and the discrete core levels are detectable in the vicinity of the BCS-Bose-Einstein condensation crossover point.
We consider a single vortex in a superfluid Fermi gas in the BCS-BEC crossover regime near a Feshbach resonance. The effect of the molecular Bose-Einstein condensate upon the vortex structure is discussed within the mean field approximation at zero temperature. Using the self-consistent Bogoliubov-de Gennes equation of the fermion-boson coupled model, we calculate density distributions of atoms and molecules. As the number of the molecules increases, both atomic and molecular density changes from BCS-like distribution to BEC-like. We also study the change of the vortex core size in the crossover regime.