We investigate the dc current-voltage characteristics of d-wave Josephson junctions, where the barrier at the interface may have arbitrary strength. Dividing the current into n-particle currents I_n (n integer), we can explicitly show which physical processes are responsible for the subharmonic gap structure (SGS). For orientations where midgap states (MGS) ezist, the resonances in the n-particle processes are drastically changed, giving rise to a strongly modified SGS. Introducing broadening in a phenomenological way, we show that MGS may produce a current peak near zero bias and we explain which physical processes are contributing to this peak. The agreement of our theory with recent experiments is discussed.
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