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Unusual transport properties of superconducting (SC) materials, such as theunder doped cuprates, low dimensional superconductors in strong magneticfields, and insulating films near the Insulator Superconductor Transition(IST), have been attributed to the formation of inhomogeneous phases.Difficulty correlating the behaviors with observations of the inhomogeneitiesmake these connections uncertain. Of primary interest here are proposals thatinsulating films near the IST, which show an activated resistance and giantpositive magnetoresistance, contain islands of Cooper Pairs (CPs). Here wepresent evidence that these types of inhomogeneities are essential to such aninsulating phase in amorphous Bi (a-Bi) films deposited on substrates patternedwith nanometer-sized holes. The patterning induces film thickness variations,and corresponding coupling constant variations, that transform the compositionof the insulator from localized electrons to CPs. Analyses near thethickness-tuned ISTs of films on nine different substrates show that weak linksbetween SC islands dominate the transport. In particular, the ISTs all occurwhen the link resistance approaches the resistance quantum for pairs. Theseobservations lead to a detailed picture of CPs localized by spatial variationsof the superconducting coupling constant.

Cooper pair insulator in amorphous films induced by nanometer-scale thickness variations