Equilibrium properties of superconducting niobium at high magnetic fields: A possible existence of a filamentary state in type-II superconductors

Abstract

The standard interpretation of the phase diagram of type-II superconductors was developed in 1960s and has since been considered a well-established part of classical superconductivity. However, upon closer examination a number of fundamental issues arise that leads one to question this standard picture. To address these issues we studied equilibrium properties of niobium samples near and above the upper critical field Hc2 in parallel and perpendicular magnetic fields. The samples investigated were very high quality films and single crystal discs with the Ginzburg-Landau parameters 0.8 and 1.3, respectively. A range of complementary measurements have been performed, which include dc magnetometry, electrical transport, µSR spectroscopy and scanning Hall-probe microscopy. Contrarily to the standard scenario, we observed that a superconducting phase is present in the sample bulk above Hc2 and the field Hc3 is the same in both parallel and perpendicular fields. Our findings suggest that above Hc2 the superconducting phase forms filaments parallel to the field regardless on the field orientation. Near Hc2 the filaments preserve the hexagonal structure of the preceding vortex lattice of the mixed state and the filament density continuously falls to zero at Hc3. Our work has important implications for the correct interpretation of properties of type-II superconductors and can also be essential for practical applications of these materials. PACS numbers:Interpretation of equilibrium properties of superconductors has a pivotal significance for the entire realm of quantum physics, extending from neutron stars to the standard model [1,2]. Therefore it is important to verify any concern related to description of these properties.Type-II superconductors subjected to a magnetic field H above the lower critical field H c1 can be found in three equilibrium states [3,4,6,7]: in the mixed state (MS), where average magnetic inductionB < H and currents form vortices organized in a hexagonal lattice; in a "surface superconductivity" state, where B = H everywhere except a sheath with thickness of the order of the Ginzburg-Landau (GL) coherence length near the surface parallel to H; and in the normal state (NS). The typical phase diagram of type-II superconductors of cylindrical geometry (such as, e.g., infinite circular cylinders and slabs with thickness greatly exceeding the penetration depth) in parallel magnetic field, or of massive samples with demagnetizing factor η = 1 [5] is shown in Fig. 1. Transitions between states, occurring at the critical fields H c2 and H c3 , are second order phase transitions. In ellipsoidal samples with η = 0 the sheath formes an equatorial band whose width decreases with increasing η. In samples with η = 1 (infinite slabs in perpendicular field) the band vanishes and surface superconductivity disappears. Since MS in such samples starts from H = (1−η)H c1 = 0, their phase diagram consists of a single curve H c2 . This interpretation of the properties of type-II superconductors is based on two well kno...

Intermediate State in Type-I Superconductors

“…In particular, the coherence length calculated from measured D using Eq. (16) agrees well with that obtained from the magnetic field profile measured in [36]. Here we confine our discussion by limiting cases.…”

“…H t in this graph corresponds to H cr in our notations. The tubular phase mentioned in the caption most probably corresponds to the filament state discussed in [36].…”

Onset of surface superconductivity beyond the Saint-James–de Gennes limit

“…(21) and trial wave function of the form Eq. (20). After multiplication by ∆(x) the integral on the left-hand-side of Eq.…”

“…It was revealed that the H c3 /H c2 ratio is not a universal number but rather a complicated function that exhibits pronounced dependence on both T and the mean-free time τ mediated by disorder scattering. Niobium became essentially a paradigmatic material to study various phenomena associated with surface superconductivity and multiple experiments continue to follow [14][15][16][17][18][19][20]. Naturally over time experimental efforts on surface superconductivity branched into different directions.…”

Meissner Effect: History of Development and Novel Aspects

“…(54) is derived assuming that superconductivity vanishes completely at H c2 , i.e. neglecting the filamentary state occurring at H c2 < H 0 < H c3[8,75] 55. In this work the type-II superconductivity was solidly established for the first time.…”