Macroscopic resonant tunnelling through Andreev interferometers

We investigate the conductance through and the spectrum of ballistic 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(N) channels and connected to the dot via tunnel contacts of transparency Gamma(N) is alpha Gamma(2)(N) N(N). In contrast, when phi= pi, the excitation gap closes and the conductance becomes G alpha Gamma(N)N(N) in the universal regime. For Gamma(N) << 1, we observe an order-of-magnitude enhancement of the conductance towards G alpha N(N) in the short-wavelength limit. We relate this enhancement to resonant tunnelling through a macroscopic number of levels close to the Fermi energy. Our predictions are corroborated by numerical simulations.