Abstract
We have investigated the effect of midgap bound states on the Josephson properties of symmetric 45\ifmmode^\circ\else\textdegree\fi{} [001] tilt bicrystal grain-boundary junctions (GBJ's) characterized by different junction widths. GBJ's, $1\phantom{\rule{0.3em}{0ex}}\ensuremath{\mu}\mathrm{m}$ wide, show a monotonic temperature dependence of the Josephson current with a slight upwards curvature, the result of the competition between midgap states and the opposite-sign continuous current. In some junctions, an increasing contribution of the midgap-state-mediated current is observed at low temperatures, leading to an anomalous nonmonotonic temperature dependence of the critical current. This behavior is more evident for junctions smaller than $500\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$, where, in some cases, a 0- to $\ensuremath{\pi}$-junction transition is clearly observed. Experimental results agree qualitatively with theoretical models taking into account midgap states in strongly nonuniform barrier interfaces.
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