Masters Defense: Nikoline Lyk Pedersen

Coulomb blockade in nearly open superconducting islands

Using WKB approximation and degenerate perturbation theory the energy splitting of the ground state fora system containing two superconductors connected with a nearly open Josephson junction in the adiabaticlimit has been found. This has been done with the goal of investigating Coulomb blockade in such a system, when reflection is nearly zero. The calculations have been done for both systems with equal superconducting gap on the two superconductors and with very different gap size. As expected Coulomb blockade in such asystem is repressed as T→1, also when the two superconducting gaps are not equal.

The bound state energies and ground state eigenfunctions for these systems have been found as well. There are some difference in these properties between the ∆L = ∆R case and the ∆L = ∆R case, where ∆L/R is the superconducting gap on either the left or right side of the junction. In general the system with ∆L = ∆R has more complicated bound state energy, bound states and ground states, but similar energysplitting to the ∆L = ∆R system.