Frustrated Frustration of Arrays with Four-Terminal Nb-Pt-Nb Josephson Junctions

We study the frustration pattern of a square lattice with in situ fabricated Nb-Pt-Nb four-terminal Josephson junctions. The four-terminal geometry gives rise to a checkerboard pattern of alternating fluxes f, f^{'} piercing the plaquettes, which stabilizes the Berezinskii-Kosterlitz-Thouless transition even at irrational flux quanta per plaquette, due to an unequal repartition of integer flux sum f+f^{'} into alternating plaquettes. This type of frustrated frustration manifests as a beating pattern of the dc resistance, with state configurations at the resistance dips gradually changing between the conventional zero- and half-flux states. Hence, the four-terminal Josephson junction array offers a promising platform to study previously unexplored flux and vortex configurations and provides an estimate on the spatial expansion of the four-terminal Josephson junction central weak link area.