Suprafroth in type-I superconductors

Equilibrium intermediate-state patterns in a type-I superconducting slab in an arbitrarily oriented applied magnetic field

“…[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. For further background we refer the reader to several books and reviews.…”

“…55 To reflect these similarities tubular patterns in type-I superconductors have been called the "suprafroth". 18,48 The type-I superconductor represents an ideal system where uncontrolled coarsening in time is replaced by a controlled coarsening in a magnetic field and there is no "drainage" in the S/N walls. Theoretically, the problem of the intermediate state is difficult because of multiple contributions to the free energy, the interactions inside and outside the specimen, and various additional effects that altogether determine the geometric structure of the final pattern.…”

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

“…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 .…”

“…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 .…”

“…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 .…”