Influence of the Environment on Charge Quantization in Small Superconducting Islands

F. Neumann, G.-L. Ingold, and H. Grabert

Phys. Rev. B 50, 12811–12819 (1994) DOI: 10.1103/PhysRevB.50.12811

The number of Cooper pairs on a small superconducting island coupled to superconducting leads by a Josephson junction fluctuates due to tunneling of Cooper pairs through the junction. On the other hand, the impedance of the circuit surrounding the island tends to suppress these fluctuations and to restore charge quantization. We consider the influence of the electromagnetic environment within a two state approximation for the charge on the island. The average charge and the slope of the steps of the Coulomb staircase are calculated for a realistic environmental impedance and finite temperatures in the range of current experimental studies. It is shown that even a low frequency environment may lead to a considerable reduction of charge fluctuations provided the integrated total impedance is large enough.