The effect of charge fluctuation on a normal-superconducting-normal single-electron transistor

We theoretically investigate quantum fluctuation of charge between even and odd states of a normal-superconducting-normal single-electron tunneling transistor. It is shown that due to the superconducting gap, the charge fluctuation in the Coulomb blockade regime for even state is larger than that for odd state. We show that large energy correction in the former regime caused by charge fluctuation can be explained by considering the charging energy renormalization.