Macroscopic Resonant Tunneling through Andreev Interferometers

TL;DR

This paper studies how the conductance and energy spectrum of ballistic chaotic quantum dots connected to two superconductors change with the phase difference, revealing a transition from an excitation gap to resonant tunneling as the phase varies.

Contribution

It combines multiple analytical techniques to analyze the quantum-to-classical crossover and identifies a phase-dependent transition in conductance and spectrum in Andreev interferometers.

Findings

At phase difference zero, the spectrum has an excitation gap.

At phase difference pi, the gap closes and conductance increases.

Resonant tunneling enhances conductance near the Fermi energy.

Abstract

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 $N_{\rm N}$ 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. For $\Gamma_{\rm N} \ll 1$, we observe an order-of-magnitude enhancement of the conductance towards $G \propto N_{\rm N}$ in the short-wavelength limit. We relate this enhancement to resonant tunneling through a macroscopic number of levels close to the Fermi energy. Our predictions are corroborated by numerical simulations.