Floquet states of Valley-Polarized Metal with One-way Spin or Charge Transport in Zigzag Nanoribbons

Two-dimensional Floquet systems consisting of irradiated valley-polarized metal are investigated. For the corresponding static systems, we consider two graphene models of valley-polarized metal with either a staggered sublattice or uniform intrinsic spin-orbital coupling, whose Dirac point energies are different from the intrinsic Fermi level. If the frequency of irradiation is appropriately designed, the largest dynamical gap (first-order dynamical gap) opens around the intrinsic Fermi level. In the presence of the irradiation, two types of edge state appear at the zigzag edge of semi-infinite sheet with energy within the first-order dynamical gap: the Floquet edge states and the strongly localized edge states. In narrow zigzag nanoribbons, the Floquet edge states are gapped out by the finite size effect, and the strongly localized edge states remain gapless. As a result, the conducting channels of the nanoribbons consist of the strongly localized edge states. Under the first and second model, the strongly localized edge states carry one-way spin polarized and one-way charge current around the intrinsic Fermi level, respectively. Thus, the narrow zigzag nanoribbons of the first and second model have asymmetric spin and charge transmission rates, respectively. Quantum-transport calculations predict sizable pumped currents of charge and spin, which could be controlled by the Fermi level.