Effects of a concentric superconducting nanocylinder insertion on the electrodynamic response of a two-junction quantum interferometer

The dynamical equations of a circular superconducting quantum interferometer containing two equal conventional overdamped Josephson junctions on its two symmetric arms and a concentric nanocylinder, which entraps a quantized finite value of magnetic flux, are derived. It is shown that, for given values of the quantum interferometer and nanocylinder self-inductance and of the mutual induction coefficient between these concentric superconducting loops, the conventional quantum interference device behaves like a π-SQUID.