Field Tuned Superconductor to Insulator Transitions in an Amorphous Film with an Imposed Multiply Connected Geometry

We have observed multiple magnetic field driven superconductor to insulator transitions (SIT) in amorphous Bi films perforated with a nano-honeycomb (NHC) array of holes. The period of the magneto-resistance, H=H_M=h/2eS where S is the area of a unit cell of holes, indicates the field driven transitions are boson dominated. The field-dependent resistance follows R(T)=R_0(H)exp(T_0(H)/T) on both sides of the transition so that the evolution between these states is controlled by the vanishing of T_0 to0. We compare our results to the thickness driven transition in NHC films and the field driven transitions in unpatterned Bi films, other materials, and Josephson junction arrays. Our results suggest a structural source for similar behavior found in some materials and that despite the clear bosonic nature of the SITs, quasiparticle degrees of freedom likely also play an important part in the evolution of the SIT.