Abstract
Interlayer tunneling spectra, the Josephson critical current density ${J}_{\mathrm{c}}$, and the normal tunneling resistance have been measured simultaneously for intrinsic Josephson junctions in Bi${}_{2}$Sr${}_{2}$CaCu${}_{2}$O${}_{8+\ensuremath{\delta}}$ over a wide range of doping using a small mesa structure and a short-pulse technique. It is found that ${J}_{\mathrm{c}}$ decreases by nearly two orders of magnitude in the underdoped region. Experimental ${J}_{\mathrm{c}}$ is found to show a significant deviation from the theoretical estimates. In order to interpret the result, we propose a model in which the superconducting order parameter is inhomogeneous in $\mathbf{k}$ space rather than in real space. Based on this model, quasiparticle current-voltage characteristics are calculated, giving a qualitative agreement with the experiment.
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