SQUID pattern disruption in transition metal dichalcogenide Josephson junctions due to non-parabolic dispersion of the edge states

We theoretically study Josephson junctions with a transition metal dichalcogenide zigzag ribbon as a weak link. We demonstrate that the spatial profile of the supercurrent carried by the edge modes determines the critical current dependence on the perpendicular magnetic field. We explore this finding and analyze the impact of Zeeman interaction and the orbital effects of the magnetic field on the Andreev bound states energies. We show that the unequal Fermi velocities of the spin-opposite edge modes lead to an anomalous shift of the Andreev bound states in the magnetic field. This is manifested in a pronounced modification of the SQUID critical current oscillations when two opposite edges of the ribbon are conducting and can be exploited in order to reveal the anomalous phase shift of the Andreev bound states in a single Josephson junction device.