Vortex correlations in a fully frustrated two-dimensional superconducting network

– We have investigated the vortex state in a superconducting dice network using the Bitter decoration technique at several magnetic frustrations f = φ/φ0=1/2 and 1/3. In contrast to other regular network geometries where the existence of a commensurate state was previouly demonstrated, no ordered state was observed in the dice network at f = 1/2 and the observed vortex-vortex correlation length is close to one lattice cell. Introduction. – In the past decades, the vortex state of superconducting networks has been investigated by several groups using different imaging techniques (scanning Hall microscopy [1, 2], scanning SQUID microscopy [3] or Bitter decoration [4–6]). The vortex configuration was studied in square or triangular lattices as a function of the magnetic field. In superconducting arrays the relevant variable is the magnetic frustration, f , which represents the vortex filling factor. f is defined as f = φ/φ0 with φ0 = h/2e, the flux quantum, and φ, the magnetic flux per elementary plaquette. The vortex pattern reflects the spatial phase configuration of the superconducting order parameter resulting from the competition between the magnetic field and the underlying lattice [7]. For rational frustration f = p/q, with p and q integer numbers, a commensurate ground state is generally expected as for example the checkerboard state which was imaged in square lattices at f = 1/2 [1, 4]. The purpose of this Letter is to present the detailed results of a magnetic decoration experiment in a fully frustrated dice network. The unusual properties of the dice lattice were recently highlighted by the discovery of a peculiar destructive interference phenomenon occurring at f = 1/2 for the electronic wave function in the tight-binding model [8, 9]. This phenomenon was shown later to manifest itself as a broadening of the superconducting transition and a suppression of the critical current in the corresponding superconducting wire network [10,11]. This observation was indicative of the absence of commensurate vortex state in the dice network, in contrast to the square network which was shown to exhibit a sharp critical current peak at f = 1/2 [12]. We report here new careful decoration experiments on a series of high quality extended niobium dice networks under different magnetic fields. The analysis of the vortex correlation functions shows unambiguously that the vortex state is fully