Abstract
We studied the $c$-axis transport of ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ (Bi2212) cross-whisker junctions formed by annealing ``naturally'' formed whisker crosses. These frequently appear during growth when the $ab$ faces of neighboring whiskers come in contact. We obtained Fraunhofer patterns of the cross-junction critical currents in a parallel magnetic field, and found a sharp increase in the quasiparticle tunneling conductance at ${V}_{g}=50--60\phantom{\rule{0.3em}{0ex}}\mathrm{mV}$, indicating high junction quality. For our weak junctions, the interface critical current density is about 3% of the critical current density across the stack of bulk intrinsic junctions, as is the room-temperature conductivity, and both are independent of the twist angle, in contrast to most of the data reported on ``artificial'' cross-whisker junctions [Y. Takano et al., Phys. Rev. B65, 140513(R) (2002)]. As a minimum, our results provide strong evidence for incoherent tunneling at least at the interface, and for at least a small $s$-wave order-parameter component in the bulk of Bi2212 for $T\ensuremath{\leqslant}{T}_{c}$. They are also consistent with the bicrystal twist experiments of Li et al. [Phys. Rev. Lett. 83, 4160 (1999)].
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