Reflectionless Tunneling Through a Double-Barrier NS Junction

The resistance is computed of an ${\rm NI}_{1}{\rm NI}_{2}{\rm S}$ junction, where N = normal metal, S = superconductor, and ${\rm I}_{i}$ = insulator or tunnel barrier (transmission probability per mode $\Gamma_{i}$). The ballistic case is considered, as well as the case that the region between the two barriers contains disorder (mean free path $l$, barrier separation $L$). It is found that the resistance at fixed $\Gamma_{2}$ shows a {\em minimum} as a function of $\Gamma_{1}$, when $\Gamma_{1}\approx\sqrt{2}\Gamma_{2}$, provided $l\gtrsim\Gamma_2 L$. The minimum is explained in terms of the appearance of transmission eigenvalues close to one, analogous to the ``reflectionless tunneling'' through a NIS junction with a disordered normal region. The theory is supported by numerical simulations. ***Submitted to Physica B.***