Conductance oscillation of a mesoscopic normal metal spanning unconventional and conventional superconductors

We present a theory for the conductance of a mesoscopic normal metal spanning two superconductors, in which an analytical expression of the conductance is formulated. It is found that the conductance oscillates with the phase difference of two superconductors periodically. When one of the superconductors has a $d$-wave symmetry, the 2π-period component of the conductance oscillation decays with the misorientation angle α and vanishes at $\alpha =\pi /4\mathrm{}$ in contradiction to the $s$-wave case, from which a method is proposed to identify unambiguously the pairing symmetry of the high-$T_c$ superconductors.