We investigate alternating response of the spin current in a quantum dot system coupled to a normal metal electrode, to which an alternating driving voltage and a pumping rotating magnetic field are applied. The expression of the time-averaged spin current and its differential is obtained based on a non-equilibrium Green＇s function method. We find that for a given rotating frequency, the spin current increases rapidly and appears to have small steps when the driven frequency increases. As the driven frequency is further increasing, the spin current can be significantly enhanced and approaches a stable value. The photon-assisted processes bring about interesting features of spin current. The influence of the gate voltage and temperature on the spin current is examined in detail.
By using a model Hamiltonian with competing antiferromagnetic （AFM） spin density wave （SDW） and d-wave superconductivity orders, the effect of next-nearest-neighbour （nnn） hopping on spin and charge structures in high-temperature superconductors is investigated at finite temperatures. For an optimally doped sample, we find that the AFM order magnitude in the vortex core is firstly enhanced and then suppressed, accompanied with a positively → negatively → positively＂ charged vortex structure transition with increasing nnn hopping strength, which implies that the AFM order is unnecessarily bounded to an electron-rich vortex core. In addition, a charge ordering pattern with four negatively charged peaks localized in a small region is also found around the vortex core centre without net charge. Recent scanning-tunneling-microscopy experimental observations of the checkerboard structure are hopefully understood.
