Imaging vortex lattices in two-dimensional Josephson junction arrays

Two-dimensional (2D) Josephson junction arrays (JJA) provide a versatile platform to study the rich phases and dynamics of vortex matter. When the number of flux quanta f applied through each plaquette is rational, vortices are predicted to form periodic structures commensurate with the array lattice. Here, we directly probe the vortex configurations in Nb-Au-Nb JJAs by combining scanning superconducting quantum interference device (SQUID) microscopy and transport measurements. Distinct ground states at f = 1/4, 1/3, 2/5, and 1/2 in a square JJA manifest as critical current maxima and resistance dips in transport measurements, while scanning SQUID images reveal ordered vortex configurations at those fillings. Notably, imaging reveals additional ordered configurations at frustrations such as f = 1/8, 1/5, 3/10, 3/8, and 3/7 at which no signatures are detected in transport. Most of the observed configurations agree with predictions except at f = 1/4 and 3/10. In the range 1/3 ≤ f ≤ 1/2, the vortex lattices are found to have quasi-1D “staircase” structures along the diagonals of the array. Our work demonstrates direct imaging of vortex lattices in JJAs and paves the way to study and engineer exotic vortex matter and its dynamics in JJAs.