Reentrant superconductivity in a naturally occurring Josephson junction array tuned by radio-frequency power.

Superconductivity, characterized by dissipationless current flow with flux expulsion or quantization, is usually suppressed when the magnetic field or the temperature is sufficiently high. However, in rare instances, superconductivity can reappear upon increasing the temperature or magnetic field, a phenomenon known as reentrant superconductivity. It usually emerges from competing orders in strongly correlated materials. Here we demonstrate reentrant superconductivity as a function of both temperature and magnetic field, tuned by radio-frequency power in a relatively simple system: granular aluminum, which exhibits the properties of a naturally occurring Josephson junction array. At low temperatures, giant Shapiro steps emerge, exhibiting characteristics of a single Josephson junction. Coherent phase locking across the array's multiple junctions amplifies the quantized voltage, enabling tunability at radio frequencies, as observed in artificially designed Josephson arrays. We show that our system can be tuned from a coherent superconducting (stiff-phase) to an insulating (phase-fluctuating) state using radio-frequency power. We propose that radio-frequency power modulates the Josephson coupling energy, . Remarkably, at elevated temperatures, the screening of the electron charge suppresses the charging energy, causing superconductivity to reappear. This many-body effect cannot be described within a single junction framework and involves many-body correlations. Our system can therefore be tuned to observe both the single-junction regime and many-body correlation effects, serving as a quantum simulator for complex phenomena in condensed matter physics.