Magnetic Field Induced Localization in a Two-Dimensional Superconducting Wire Network

Abstract

We report transport measurements on superconducting wire networks which provide the first experimental evidence of a new localization phenomenon induced by magnetic field on a 2D periodic structure. In the case of a superconducting wave function this phenomenon manifests itself as a depression of the network critical current and of the superconducting transition temperature at a half magnetic flux quantum per tile. In addition, the strong broadening of the resistive transition observed at this field is consistent with enhanced phase fluctuations due to this localization mechanism.PACS numbers: 72.15, 73.23, 74.25 In a recent paper [1] a novel case of extreme localization induced by a transverse magnetic field was predicted for non interacting electrons in a two-dimensional (2D) periodic structure. This new phenomenon, due to a subtle interplay between lattice geometry and the magnetic field, differs from Anderson localization on two essential points: it occurs in a pure system, without disorder, and the system eigenstates are not localized but nondispersive states. In a tight-binding (TB) approach, it can be simply understood in terms of Aharonov-Bohm effect which, at half a flux quantum per unit tile (halfflux), leads to fully destructive quantum interferences. For this flux, the set of sites visited by an initially localized wave-packet will be bounded in Aharonov-Bohm cages [1]. This effect is absent on other regular periodic lattices at half-flux, such as the square and the triangular lattices.Superconducting wire networks are suitable to address phase interference phenomena driven by a magnetic field [2]. These systems are extremely sensitive to phase coherence of the superconducting order parameter over the network sites which is exclusively determined by the competition between the external field and the network geometry [3]. Besides, the quantum regime is accessible even in low T c diffusive superconductors: since all Cooper pairs condense in a quantum state, the relevant wavelength is associated with the macroscopic superfluid velocity and can be much larger than the lattice elementary cell [4]. Also, the magnetic field corresponding to one superconducting flux quantum Φ o = hc/2e, is easily accessible: it is about 1 mT for a network cell of 1 µm 2 , in contrast to the unattainable 10 3 T for an atomic lattice. In addition, some features of the TB spectrum, namely the Hofstadter butterfly [5], are experimentally accessible in the model system of a superconducting wire network [3,6]. As shown by de Gennes and Alexander [7,8], the linearized Ginzburg-Landau (GL) equations for a superconducting wire network can be mapped onto the eigenvalues equation of a TB hamiltonian for the same geometry. This mapping is of particular relevance since one of the remarkable findings of Ref.[1] is the total absence of dispersion in the TB spectrum at half-flux. In the context of a superconducting network, the localization effect is expressed by the inability of the superconducting wave function to carry phase informati...

Localization effect in a two-dimensional superconducting network without disorder

“…The observed T c (H) transition line (Fig1.a) can be understood in its very details [8] from the ground state of the Landau level spectrum and will not be discussed here. The critical current curve measured at constant temperature, Note the behaviour at f = 1/2 strongly differs from the behaviour at other rational frustrations f = p/q.…”

“…The mapping between the superconducting properties with the tight-binding problem allows for a formal connection between the current carrying superconducting states and the Landau level spectrum. The observed magnetic field dependence of the critical current can be accounted for qualitatively [8] by expressing the supercurrent in terms of the curvature of the band edge ǫ(k). However, this mapping is only valid in the vicinity of the critical temperature.…”

Fluctuation-induced vortex pattern and its disordering in the fully frustratedXYmodel on a dice lattice

“…Since Hamiltonian (33) does not include linear terms, the result of the Gaussian averaging of P 4 (u j1 , u j2 , u j3 ) will have a form of a second order polynomial, P 2 (G j1j2 , G j2j3 , G j1j3 ), whose three arguments are the nearest neighbor correlation functions defined by Eq. (27). Instead of looking for the explicit form of P 2 , it is sufficient to notice that since the central vortex of a triad is always surrounded by the bonds with J jk equal to J 1 or J 3 , we will always have K j1j3 = K 1 and K j1j2 = K j2j3 = K 2 , and, as a consequence of Eq.…”

“…The set of states minimizing the free energy of such a network turns out to be in oneto-one correspondence with the set of the ground states of the fully frustrated XY model discussed on this article. In recent years magnetically frustrated wire networks and Josephson junction arrays with the dice lattice geometry have both been the subject of active experimental investigations [27,28,29].…”

“…Since it is known that the structure of the superconducting state in a wire network is determined (in the mean-field approximation) by the structure of the ground-state wave function of the single-electron problem with the same geometry [26], a suggestion has been put forward that at full frustrateion the superconducting state in a dice network may have a disordered (glassy-like) structure [25,27]. However, recently it has been shown [24] that the inclusion into analysis of the forth-order term of the Ginzburg-Landau functional strongly decreases the ambiguity in the determination of the structure of superconducting state in a fully frustrated wire network with the dice lattice geometry.…”