Flux-dependent phase shift and periodicity crossover in superconducting nanoloops containing impurity layers

The flux-dependent phase shift can be effectively realized in a superconducting nanoloop by embedding a single Josephson junction with impurity scattering into the system. The current-flux relation exhibits an alternation between 0-like and π-like states strongly depending on the impurity characters and the width of the magnetic impurity layers. The current evolution with doubled flux periodicity for both nonmagnetic and magnetic impurity cases is also accompanied in square loops. Moreover, a reverse crossover from hc/e - toward nearly hc/2e - periodic oscillations can be obtained in a rectangular loop system. Such a sample may be important for superconducting electronics and can serve as a basic element for quantum qubits.