Macroscopic Resonant Tunneling through Andreev Interferometers

We investigate the conductance through and the spectrum of ballistic {\it Andreev interferometers}, chaotic quantum dots attached to two $s$-wave superconductors, as a function of the phase difference $\phi$ between the two order parameters. A combination of analytical techniques -- random matrix theory, Nazarov's circuit theory and the trajectory-based semiclassical theory -- allows us to explore the quantum-to-classical crossover in detail. When the superconductors are not phase-biased, $\phi=0$, we recover known results that the spectrum of the quantum dot exhibits an excitation gap, while the conductance across two normal leads carrying $N_{\rm N}$ channels and connected to the dot via tunnel contacts of transparency $\Gamma_{\rm N}$ is $\propto \Gamma_{\rm N}^2 N_{\rm N}$. In contrast, when $\phi=\pi$, the excitation gap closes and the conductance becomes $G \propto \Gamma_{\rm N} N_{\rm N}$ in the universal regime. In the tunneling regime, $\Gamma_{\rm N} \ll 1$, resonant contributions induce an order-of-magnitude enhancement of the conductance towards $G \propto N_{\rm N}$ in the short-wavelength limit. We relate this to the emergence of a giant peak in the density of states at the Fermi level. Our predictions are corroborated by numerical simulations.