Effect of Magnetic Field on Multi-terminal Josephson Junctions

Junctions with three or more superconducting terminals gained broad interest as they provide means to study physics and topology in higher dimensions and to braid Majorana fermions for fault-tolerant quantum computation. We study effect of perpendicular magnetic field on Andreev energy levels and critical currents in a 3-terminal Josephson junction with conventional s-wave superconducting leads and a normal 2DEG scattering region. In a 3-terminal junction, currents through two terminals determine the DC Josephson effect which occurs when the two currents are limited by the Critical Current Contour (CCC). We study the Fraunhofer diffraction patterns that manifest itself as oscillations in the diameter and area of the CCC. We show that the oscillations remain in 3-terminal devices but the additional terminal reduces the amplitude of the oscillations. We also show that magnetic field mixes with the superconducting phases in the leads and deforms the ground state energy landscape. We argue that a peculiar modulation of CCC with magnetic flux is the signature of coherent Josephson effect in multi-terminal Josephson junctions.