Abstract
Based on the scattering matrix theory and non-equilibrium green function method, we have investigated the fluctuations of charge and spin current of the systems which consists of a quantum dot (QD) with a resonant level coupled to two semiconductor contacts within in alternative site (AS) and alternative bond (AB) framework, where two transverse (B_x) and longitudinal (B_z) magnetic fields are applied to the QD. It is only necessary to use the auto-correlation function to characterize the fluctuations of charge current for a two-terminal system because of the relation which is defined as Σ_α^e S_αβ = Σ_β^e S_αβ=0. Our result shows that both auto-shot noise (S_LL) and cross-shot noise (S_LR) are essential to characterize the fluctuations of spin current when B_x is present. Moreover, our model calculations show that the sign of the cross-shot noise of spin current is negative for all surface states of AS/QD/AS junctions, while it oscillates between positive and negative values for two surface states of AB/QD/AB junctions as we sweep the gate voltage.