Transport properties for a quantum dot coupled to normal leads with pseudogap

We study transport properties for a quantum dot coupled to normal leads with a pseudogap density of states at zero temperature, using the second-order perturbation theory based on the Keldysh formalism. We clarify that the hybridization function $\Gamma(\omega)\propto |\omega|^r\; (0 \le r < 1) $ induces the cusp or dip structure in the density of states in the dot when finite bias voltage is applied to the interacting quantum dot system. It is found that the current-voltage characteristics and differential conductance are drastically changed at $r=1/2$.