Vortex structures and zero energy states in the BCS-to-BEC evolution of p-wave resonant Fermi gases

TL;DR

This paper theoretically investigates vortex structures and zero energy Majorana states in p-wave resonant Fermi gases during the BCS-to-BEC evolution, revealing their relation to superfluid properties and topological phase transitions.

Contribution

It provides a self-consistent analysis of vortex structures, quasiparticle states, and Majorana zero modes, highlighting their dependence on vorticity and coupling strength.

Findings

Zero energy Majorana states appear only in the weak coupling BCS limit with odd vorticity.

Vortex core bound states have multiple branches, with only one potentially at zero energy.

Zero energy states disappear at the topological phase transition due to state interference.

Abstract

Multiply quantized vortices in the BCS-to-BEC 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 $\kappa$ 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. There exist the $\kappa$ branches of the core bound states for a vortex state with vorticity $\kappa$, whereas 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.