Spin polarized Majorana zero modes in penta-silicene nanoribbons

In the present work, we study the possibility of obtaining Majorana zero modes (MZMs) in penta-silicene nanoribbons (p-SINRs) [R. Pawlak et al. Proceedings of the National Academy of Sciences 117, 228 (2020)], following the same procedure as our previous work [R. C. Bento Ribeiro et al. Phys. Rev. B 105, 205115 (2022)]. The spinless and spin full p-SINR with p-wave superconducting pairing reveals the emergence of topologically protected MZMs at opposite edges of the p-SINR. We consider an external magnetic field perpendicularly applied to the nanoribbon plane and an extrinsic Rashba spin-orbit coupling (RSOC), besides the first nearest neighbor hopping term and p-wave superconducting pairing. The dispersion relation profiles show the closing and reopening of the superconducting gap for only one spin component, suggesting a spin-polarized topological phase transition (TPT). Associated with these TPTs, the energy spectrum as a function of the p-SINR chemical potential exhibits zero-energy states and preferential spin direction. It is associated with nonoverlapping wave functions well-localized at opposite edges of the superconducting p-SINR. Our findings strongly suggest the emergence of topologically protected and spin-polarized MZMs at the p-SINR ends.