Stable semivortex gap solitons in a spin-orbit-coupled Fermi gas

We demonstrate the existence of semivortex (SV) solitons, with vorticities $0$ and $1$ in the two components, in a two-dimensional (2D) fermionic spinor system under the action of the Rashba-type spin-orbit coupling in the combination with the Zeeman splitting (ZS). In the ``heavy-atom" approximation, which was previously elaborated for the bosonic system, the usual kinetic energy is neglected, which gives rise to a linear spectrum with a bandgap. The model includes the effective Pauli self-repulsion with power $7/3$, as produced by the density-functional theory of Fermi superfluids. In the general case, the inter-component contact repulsion is included too. We construct a family of gap solitons of the SV type populating the spectral bandgap. A stability region is identified for the SV solitons, by means of systematic simulations, in the parameter plane of the cross-repulsion strength and chemical potential. The stability region agrees with the prediction of the anti-Vakhitov-Kolokolov criterion, which is a relevant necessary stability condition for systems with self-repulsive nonlinearities. We also test the stability of the SV solitons against a sudden change of the ZS strength, which initiates robust oscillations in the spin state of the soliton due to transfer of particles between the system's components.