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After decades of explorations, suffering from low critical temperature andsubtle nature, whether a metallic ground state exists in a two-dimensionalsystem beyond Anderson localization is still a mystery. Supremely, phasecoherence could be the key that unlocks its intriguing nature. This workreveals how quantum phase coherence evolves across bosonicsuperconductor-metal-insulator transitions via magneto-conductance quantumoscillations in high-Tc superconducting films. A robust intervening anomalousmetallic state characterized by both resistance and oscillation amplitudesaturations in the low temperature regime is detected. By contrast, withdecreasing temperature the oscillation amplitude monotonically grows on thesuperconducting side, but decreases at low temperatures on the insulating side.It suggests that the saturation of phase coherence plays a prominent role inthe formation of this anomalous metallic state.

Quantum coherence across bosonic superconductor-anomalous metal-insulator transitions