Superconducting phase boundary of aperiodic networks in a magnetic field

Abstract

We have used electron-beam lithography to fabricate superconducting "wire" arrays in a variety of patterns ranging from periodic to random and including the intermediate quasicrystalline and incommensurate configurations.Sweeping an applied magnetic field while observing the critical temperature reveals which fields are favorable or commensurate with the pattern. We find sharp dips in the T, (H) curve for periodic, incommensurate (quasiperiodic), and quasicrystalline arrays reflecting a lock-in of the flux lattice with the underlying network. We find no similar fine structure for random arrays. This allows us to generalize the concept of commensurability to nonperiodic structures.

Quasiperiodic tilings in a magnetic field

“…The study of quasiperiodic wire networks has been initially motivated by several experiments [24,25,26,27] in which the superconducting transition temperature as a function of the magnetic field was determined. Using a mapping between the linearized Ginzburg-Landau equations and the tight-binding model, the rich structure of this phase boundaries has been then computed by Nori and coworkers [28,29].…”

Uncorrelated behavior of fluxoids in superconducting double networks

“…In addition, the arrangements of fluxoids in the underlying network must fulfill the requirement of minimum energy. These two requirements give rise to correlated arrangements of fluxoids in periodic networks, the most famous one being the checkerboard arrangement of fluxoids in a regular square network 8,11,14,19 , manifested by secondary dips of the magneto-resistance at half integer values of…”

“…A variety of superconducting networks have been studied, both theoretically and experimentally, aiming at revealing correlated behavior of fluxoids in such networks [1][2][3][4][5][6][7][8][9][10][11][12][13][14] . The foundation of these studies traces back to the fluxoid quantization work of Little and Parks [15][16][17] who demonstrated in magnetoresistance measurements the theoretical prediction of F.…”

Interacting loop-current model of superconducting networks

“…The shortest length in our model is the basic loop size in contrast to the coherence length in Eq. (18). The supercurrent is assumed to flow in our network on a length scale n whereas in type-II superconductors it flows over a length A.…”

“…In the case of nonperiodic networks 25 such as the Fibonacci network studied experimentally by Behrooz et al 18 the numbers of nearest neighbors of the tiles are not constants, but statistical. Also, the lengths of the common bonds between adjacent neighbors are not all the same.…”