Figure 1

(a) Andreev reflection by a superconductor (S). An incoming electron (e) in a normal metal (N) near the Fermi energy $E_F$ is reflected as a hole (h) with opposite velocity. (b) Schematic of our system. A ballistic metallic cavity is connected to two normal ($L$ and $R$) metallic leads and two superconducting ($S_1$ and $S_2$) leads. The superconducting pair potentials have a phase difference of $\varphi$. Two periodic Andreev orbits contributing to macroscopic resonant tunneling at $\varphi =\pi$ are drawn.Reuse & Permissions

Figure 2

Conductance through a chaotic Josephson junction vs the phase difference $\varphi$ between the two superconductors. Circles are numerical results for ${\Gamma }_n=0.01$, $k_F{L}_c=8192$, $k_F{L}_c/N_n=20$, $k_F{L}_c/N_s=10$, and Lyapunov exponent $\lambda \simeq 1.3$. The upper curve is the analytical prediction obtained by summing the semiclassical resonant contributions of Eqs. (8) with the quantum universal contributions. The lower curve gives the universal prediction obtained from circuit theory. Left inset: Numerical data for the same classical parameters $k_F{L}_c/N_n=20$, $k_F{L}_c/N_s=10$, and $K=10$ as in the main plot, for $k_F{L}_c=128$, 512, 2048, and 8192 (from bottom to top). Note the change in peak-to-valley ratio.Reuse & Permissions