Exposing a Josephson junction array to a magnetic field (B) frustrates the system and results in a wealth of phenomena, which depend on the level of frustration [measured by the magnetic flux (f) per plaquette in units of the flux quantum], the lattice geometry, the underlying symmetries, and the nature of the excitations. A novel localization effect due to the interplay of B with a particular lattice structure, the dice lattice, has been theoretically predicted and observed in experiments exploring the phase boundary of wire networks. In this presentation, we report and discuss the results of sensitive magnetoinductance [L(f)] measurements performed on arrays of proximity-effect coupled junctions on a dice lattice. The inverse magnetoinductance L^-1(f) is found to exhibit prominent peaks at f=1/3 and f=1/6 (and weaker maxima also at f=1/9 and f=1/12) reflecting a high degree of superconducting phase coherence in the system. At f=1/2, on the contrary, L^-1(f) shows a deep minimum pointing to a strong suppression of phase coherence. Relying on a XY model description of the array, the ground-state vortex configurations for f=1/3 (Abrikosov state) and f=1/6 (rhombic state) are shown to correspond to remarkably compact phase structures, thereby explaining why these states are particularly robust against thermal fluctuations and, consequently, so prominent in L^-1(f). In striking contrast, the ground state at f=1/2 is predicted to exhibit a so-called accidental degeneracy allowing for the formation of zero-energy domain walls. Thus, ordering at f=1/2 should be quite vulnerable to thermal fluctuations, in agreement with our experimental observations. Using the star-triangle transformation, the inductance network associated with the frustrated dice lattice can be mapped on an anisotropic triangular lattice, thereby allowing L(f) to be calculated from the ground-state distribution of the gauge invariant phase differences and compared with the experimental data.

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