Strong doping dependence of the interlayer superconducting coherence in Bi2(Sr,La)2CaCu2O8+y

Microscopic electronic inhomogeneity in underdoped cuprate superconductors has been recently suggested by the scanning tunneling spectroscopy measurements. An important question is how superconducting coherence develops with doping in the bulk. We evaluate the interlayer Josephson current density jc in superconducting Bi2(Sr,La)2CaCu2O8+y from the Josephson plasma resonance experiments. We find that jc shows an exponential doping dependence in a wide doping range, which is found to be much stronger dependence than expected in the d-wave coherent tunneling theory. This result implies the inhomogeneous superconducting state in each CuO2 planes inside the bulk, where the fraction of non-superconducting regions gradually shrinks with doping and disappears in the overdoped regime.