Imaging how fluctuations destroy superconductivity in two dimensions
Two-dimensional superconductors test our understanding of quantum phases. Low-temperature "anomalous metal" states are widely observed where conventional theories predict only superconducting or insulating ground states. In model systems based on proximity-coupled Josephson junction arrays, the critical temperature falls far faster with decreasing normal-state conductance than predicted by existing models. Whether these observations indicate a new quantum phase, a need to refine models of disorder and fluctuations, or both remains unresolved. Using scanning magnetic susceptometry, we image the local superfluid phase stiffness $ρ_s$ in gate-tunable Josephson junction arrays consisting of epitaxial Al islands on an InAs quantum well. Across six arrays and more than two orders of magnitude in the zero-temperature phase stiffness $ρ_{s0}$, the diamagnetic critical temperature $T_{c,φ}$ is suppressed more strongly than can be explained solely by thermal phase fluctuations, scaling approximately as $T_{c,φ}\proptoρ_{s0}^{0.3}$. While $ρ_s$ is remarkably uniform at high carrier densities, at low carrier densities we find that anomalous metal transport emerges together with large-scale inhomogeneity that transport alone cannot directly detect. These results are inconsistent with a classical XY description within standard junction models, instead pointing to quantum fluctuations that suppress superconductivity throughout the superconducting phase and amplify inhomogeneity near the superconductor-insulator transition, producing anomalous metal behavior.