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 junctions of d-wave superconductors. For some orientations of the superconductors a current peak is found at finite voltage in the current-voltage characteristics. We pick out the relevant physical processes and write down an analytical formula for the current which clearly shows how the midgap state acts 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 resonant transmission through midgap state of quasiparticles undergoing multiple Andreev reflections. We note that within our framework the zero-bias conductance peak appears in rather transparent Josephson junctions of d-wave superconductors. 
T. Lofwander, G. Johansson, V. S. Shumeiko, G. Wendin, and M. Hurd