Stable semivortex solitons in a fermionic condensate

In the present work, we numerically show the existence of semivortex solitons in a two-dimensional fermionic spinor. This soliton is free of two-dimensional potentials and includes a Rashba-type spin-orbit coupling. The theoretical framework consists of a mean-field theory applied to a Fermi superfluid. We obtain the gap solitons using an ansatz of semivortex type. This approach allows us to reduce the two-dimensional equations to a system of radial equations determined numerically for a parameter space given by the chemical potential and the cross-interaction between the spinors. To test the stability of the soliton solutions, we performed real-time computational simulations using finite differences with the Runge-Kutta 4 method. Our results show that the soliton stability zone only partially coincides with the Vakhitov-Kolokolov linear stability criterion. Interestingly, we have found stable solitons for times much larger than the simulations observed in similar works for bosonic systems. Moreover, this stability was tested by inducing oscillations of a soliton due to a step-like change of the Zeeman parameter. We compute the resulting fluctuations in the spin state of the soliton induced by the transfer of particles between the spinors.