Time-Dependent Perturbation in Two-Dimensional Disordered Symplectic Systems: Dephasing and Scaling

The effect of time-dependent perturbations on transport phenomena in disordered systems has been studied in various context, such as the destruction of localization, the suppression of the interference effect, and the effect of temperature. In general, timedependent perturbations destroy the phase coherence. In fact, a numerical study of the dephasing effect by a time-dependent perturbation in two-dimensional disordered systems has been performed by Nakanishi et al. They have investigated the effect of the timedependent on-site potential oscillating with a frequency ω and demonstrated that the ω-dependent correction to the conductivity takes an universal form in the metallic regime. In the present work, we study a different type of time-dependent perturbation, namely the timedependent transfer-integrals. It is expected that this type of perturbation is more representative for the effect of temperature. We consider a two-dimensional disordered system with spin-orbit interaction, which belongs to the symplectic universality class. The system exhibits the Anderson transition even in two dimensions. We numerically evaluate the conductivity as a function of the frequency of the perturbation using the equation of motion method. In the metallic regime, it is examined whether the universal ω-dependent correction to the conductivity can be observed also for the present type of perturbation. For the critical regime, we find that the frequency dependence of the conductivity can be described by the one-parameter scaling. The model we adopt is the Ando model extend to the case where transfer-integrals oscillate with a frequency ω. The Hamiltonian is given by