Magnetointerferometry of multiterminal Josephson junctions

We report a theoretical study of multiterminal Josephson junctions under the influence of a magnetic field B. We consider a ballistic rectangular two-dimensional metal N_0 connected by the edges to the left, right, top and bottom superconductors S_L, S_R, S_T and S_B, respectively. We numerically calculate in the large-gap approximation the critical current I_c versus B between the left and right S_L and S_R for various aspect ratios, with the top and bottom S_T and S_B playing the role of superconducting mirrors. We find the critical current I_c to be enhanced by orders of magnitude, especially at long distance, due to the phase rigidity provided by the mirrors. We obtain superconducting quantum interference device-like magnetic oscillations. With symmetric couplings, the self-consistent superconducting phase variables of the top and bottom mirrors take the values 0 or π, as for emerging Ising degrees of freedom. We propose a simple effective Josephson junction circuit model that is compatible with these microscopic numerical calculations. From the I_c(B) patterns we infer where the supercurrent flows in various device geometries. In particular in the elongated geometry, we show that the supercurrent flows between all pairs of contacts, which allows exploring the full phase space of the relevant phase differences.