Coherent quasiparticle tunneling in d-wave superconductor SIS junctions

Coherent quasiparticle tunneling characteristics are numerically calculated for a superconductor/insulator/superconductor (SIS) tunnel junction with a d-wave order parameter. It is found that in coherent tunneling the differential conductance $dI/dV$ exhibits a very sharp peak at the superconducting gap voltage, showing a sharp contrast to the case of incoherent tunneling, where the $dI/dV$ peak is very broad. The sharp $dI/dV$ peak is in good agreement with experimental results for intrinsic Josephson junctions of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{8+\delta }.$ It is also found that when a small amount of incoherent tunneling is involved, the tunneling characteristics change abruptly to those of incoherent tunneling. These results imply that the tunneling in the intrinsic Josephson junctions is mostly coherent.