Visualization of spatial inhomogeneity in the superconducting gap using micro-ARPES

Electronic inhomogeneity arises ubiquitously as a consequence of adjacent and/or competing multiple phases or orders in strongly correlated electron systems. Gap inhomogeneity in high-Tc$\mathit{Tc}$$\mathit{Tc}$ cuprate superconductors has been widely observed using scanning tunneling microscopy/spectroscopy. However, it has yet to be evaluated by angle-resolved photoemission spectroscopy (ARPES) due to the difficulty in achieving both high energy and spatial resolutions. Here, we employ high-resolution spatially-resolved ARPES with a micrometric beam (micro-ARPES) to reveal the spatial dependence of the antinodal electronic states in optimally-doped Bi2$2$$2$Sr2$2$$2$CaCu2$2$$2$O8+δ$8+\mathit{\delta }$$8+\mathit{\delta }$. Detailed spectral lineshape analysis was extended to the spatial mapping dataset, enabling the identification of the spatial inhomogeneity of the superconducting gap and single-particle scattering rate at the micro-scale. Moreover, these physical parameters and their correlations were statistically evaluated. Our results suggest that high-resolution spatially-resolved ARPES holds promise for facilitating a data-driven approach to unraveling complexity and uncovering key parameters for the formulation of various physical properties of materials.