Macroscopic Resonant Tunneling through Andreev Interferometers

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 $\varphi$ 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, $\varphi =0$, we recover known results that the spectrum of the quantum dot exhibits an excitation gap, while the conductance across two normal leads carrying $N_{\mathrm{N}}$ channels and connected to the dot via tunnel contacts of transparency ${\Gamma }_{\mathrm{N}}$ is $\propto {\Gamma }_{\mathrm{N}}^2{N}_{\mathrm{N}}$. In contrast, when $\varphi =\pi$, the excitation gap closes and the conductance becomes $G\propto {\Gamma }_{\mathrm{N}}{N}_{\mathrm{N}}$ in the universal regime. For ${\Gamma }_{\mathrm{N}}\ll 1$, we observe an order-of-magnitude enhancement of the conductance towards $G\propto N_{\mathrm{N}}$ 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.

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Cited by in corpus (3)

• Controlling the Sign of Magnetoconductance in Andreev Quantum Dots
• Conductance and Thermopower of Ballistic Andreev Cavities
• Macroscopic Coherent Rectification in Andreev Interferometers