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

Abstract

Significance We report signatures of a new phenomenon wherein a hidden “interdimensional” order emerges from a bulk three-dimensional superconductor tuned to approach a phase transition to an insulator. Prior electrical transport measurements found that the superconductor–insulator transition of BaPb1−xBixO3 demonstrated critical scaling behavior but inexplicably required parameters consistent only with two dimensions. Here, we directly image the three-dimensional superconducting state as it approaches an insulating phase and discover that signatures of a two-dimensional granular superconducting phase spontaneously emerge at the transition. Moreover, the properties of this phase precisely match the theory of emergent electronic granularity specific to two-dimensional materials. These findings posit that a three-dimensional superconductor electronically reorganizes itself into a two-dimensional granular superconductor before ultimately transforming to an insulator. 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 BaPb1−xBixO3 (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.