Resonant transport through midgap states in voltage-biased Josephson junctions of d-wave superconductors

We study theoretically the ac Josephson effect in voltage-biased planar jun ctions of d-wave superconductors. For some orientations of the superconduct ors a current peak is found at finite voltage in the current-voltage charac teristics. We pick out the relevant physical processes and write down an an alytical formula for the current which clearly shows how the midgap state a cts as a resonance and produces the peak. We present a possible explanation for the zero-bias conductance peak, recently found in experiments on grain boundary junctions of high-temperature superconductors, in terms of resona nt transmission through midgap state of quasiparticles undergoing multiple Andreev reflections. We note that within our framework the zero-bias conduc tance peak appears in rather transparent Josephson junctions of d-wave supe rconductors. (C) 1999 Academic Press.