Josephson penetration depth in coplanar junctions based on 2D materials

Josephson junctions and superconducting quantum interference devices with graphene or other 2D materials as the weak link between superconductors have become a hot topic of research in recent years, with respect to both fundamental physics and potential applications. We have previously reported ultrawide Josephson junctions (up to 80 μm wide) based on chemical-vapor-deposition graphene where the critical current was found to be uniformly distributed in the direction perpendicular to the current. In this paper, we demonstrate that the unusually large Josephson penetration depth $λJ$ that this corresponds to is enabled by the unique geometric structure of Josephson junctions based on 2D materials. We derive a new expression for the Josephson penetration depth of such junctions and verify our assumptions by numerical simulations.