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Spatial disorder has been shown to drive two-dimensional (2D) superconductors to an insulating phase through a superconductor-insulator transition (SIT). Numerical calculations predict that with increasing disorder, emergent electronic granularity is expected in these materials-a phenomenon where superconducting (SC) domains on the scale of the material's coherence length are embedded in an insulating matrix and coherently coupled by Josephson tunneling. Here, we present spatially resolved scanning tunneling spectroscopy (STS) measurements of the three-dimensional (3D) superconductor BaPb 1- x  Bi  x  O 3 (BPBO), which surprisingly demonstrate three key signatures of emergent electronic granularity, having only been previously conjectured and observed in 2D thin-film systems. These signatures include the observation of emergent SC domains on the scale of the coherence length, finite energy gap over all space, and strong enhancement of spatial anticorrelation between pairing amplitude and gap magnitude as the SIT is approached. These observations are suggestive of 2D SC behavior embedded within a conventional 3D s -wave host, an intriguing but still unexplained interdimensional phenomenon, which has been hinted at by previous experiments in which critical scaling exponents in the vicinity of a putative 3D quantum phase transition are consistent only with dimensionality d = 2.

Signatures of two-dimensional superconductivity emerging within a three-dimensional host superconductor