“…However, the spin splitting that could facilitate the creation of polarized currents cannot, in principle, be produced by the unique action of SOC, because the system possess states with opposite spins and the same energy due to Kramer's degeneracy [16], a result of time reversal symmetry [9]. Magnetic fields, magnetic materials, and the injection of spin-polarized currents [17][18][19][20][21][22][23][24][25][26][27] or time-dependent Hamiltonians [28] have been used to break this symmetry and generate or manipulate spin-polarized currents. To obtain this result in non-magnetic materials, or without applying an external magnetic field, several systems have been proposed, such as point contact [29,30], graphene nanostructures [31], planar systems with SOC and corrugated graphene nanoribbons [32][33][34], or even creating spin-dependent chemical potentials by microwave irradiation [35].…”