The Meissner effect and the associated perfect bulk diamagnetism together with zero resistance and gap opening are characteristic features of the superconducting state. In the pseudogap state of cuprates unusual diamagnetic signals as well as anomalous proximity effects have been detected but a Meissner effect has never been observed. Here we have probed the local diamagnetic response in the normal state of an underdoped La1.94Sr0.06CuO4 layer (up to 46 nm thick, critical temperature Tc < 5 K) which was brought into close contact with two nearly optimally doped La1.84Sr0.16CuO4 layers (Tc approx 32 K). We show that the entire barrier layer of thickness much larger than the typical c axis coherence lengths of cuprates exhibits a Meissner effect at temperatures well above Tc but below Tc. The temperature dependence of the effective penetration depth and superfluid density in different layers indicates that superfluidity with long-range phase coherence is induced in the underdoped layer by the proximity to optimally doped layers; however, this induced order is very sensitive to thermal excitation.
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