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−xBi_xO₃ (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.

空间无序已被证明通过超导体 - 绝缘体转变（SIT）将二维（2D）超导体驱动到绝缘相。数值计算预测，随着无序度的增加，预计这些材料中会出现电子粒度——这种现象，即材料相干长度尺度上的超导 (SC) 域嵌入绝缘矩阵中，并通过约瑟夫森隧道相干耦合。在这里，我们展示了三维 (3D) 超导体 BaPb _{1− x} Bi _x O _{3 的}空间分辨扫描隧道光谱 (STS) 测量（BPBO），它令人惊讶地展示了涌现电子粒度的三个关键特征，之前仅在二维薄膜系统中推测和观察到。这些特征包括在相干长度、整个空间的有限能隙以及接近 SIT 时配对幅度和间隙幅度之间的空间反相关性的强烈增强。这些观察结果暗示了嵌入在传统 3D s波宿主中的 2D SC 行为，这是一种有趣但仍然无法解释的多维现象，之前的实验已经暗示了这一点，其中假定的 3D 量子相变附近的关键标度指数是仅与维数d = 2一致。