Microfluidic manipulation of magnetic flux domains in type-I superconductors: droplet formation, fusion and fission

Abstract

The magnetic flux domains in the intermediate state of type-I superconductors are known to resemble fluid droplets, and their dynamics in applied electric current is often cartooned as a "dripping faucet". Here we show, using the time-depended Ginzburg-Landau simulations, that microfluidic principles hold also for the determination of the size of the magnetic flux-droplet as a function of the applied current, as well as for the merger or splitting of those droplets in the presence of the nanoengineered obstacles for droplet motion. Differently from fluids, the flux-droplets in superconductors are quantized and dissipative objects, and their pinning/depinning, nucleation, and splitting occur in a discretized form, all traceable in the voltage measured across the sample. At larger applied currents, we demonstrate how obstacles can cause branching of laminar flux streams or their transformation into mobile droplets, as readily observed in experiments.Moving superconducting vortices are known to be the main source for energy dissipation in current-carrying type-II superconductors, limiting their large scale energy-related applications. For that reason, much attention has been given in the past to hampering vortex motion by introducing arrays of artificial pinning centers in superconductors, nanoengineered in size and geometry for optimal vortex pinning and enhancement of maximal sustainable magnetic field and electric current in the superconducting state [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] . Pinning is also of importance in type-I superconductors, for example in defining the structure of the intermediate state (IS) 18,19 , which is a very rich study object and has received a revival of interest in recent years [20][21][22][23][24][25][26][27][28][29][30][31][32] . Contrary to type-II superconductors, the competition between the interface energy (that favors the formation of large normal domains) and the magnetic energy (that tends to form small normal domains) results in the formation of different spatially modulated IS structures in type-I superconductors 23,30 . There, flux tubes and lamellae are the most encountered shapes [18][19][20] , formation of which strongly depends on the size and shape of the samples [22][23][24] , as well as on the magnetic history of the system 18,19 .Unlike Abrikosov vortices in type-II superconductors, each carrying a single flux quantum Φ 0 = hc/2e 33,34 , flux droplets in type-I superconductors may contain hundreds of flux quanta and are considered as building blocks for the IS flux patterns 35,36 . When driven by applied current, these flux structures can undergo different dynamic phases, where the motion of droplets can be periodic (with single or multiple periods) as well as chaotic 21 . Recent numerical simulations revealed that type-I flux droplets are always decomposed into singly-quantized fluxoids during dynamic interactions, reaffirming that one flux quantum is the smallest and fundamental building block of the IS in type-I superconductors 25 . Stat...