Scanning SQUID microscopy of vortex clusters in multiband superconductors

Abstract

In type-1.5 superconductors, vortices emerge in clusters, which grow in size with increasing magnetic field. These vortex clusters and their field dependence are directly visualized by scanning superconducting quantum interference device microscopy at very low vortex densities in MgB 2 single crystals. Our observations are elucidated by simulations based on a two-gap Ginzburg-Landau theory in the type-1.5 regime. DOI: 10.1103/PhysRevB.81.020506 PACS number͑s͒: 74.25.Uv, 74.70.Ad In magnesium diboride, 1 MgB 2 , the superconducting gaps open for both the two-dimensional ͑2D͒ band ͓gap size ⌬ = 7.1 meV ͑Refs. 2 and 3͔͒ and the three-dimensional band ͓⌬ = 2.2 meV ͑Refs. 3 and 4͔͒. The possibility of type-1.5 superconductivity 5 has been suggested for clean single crystals of MgB 2 , which lie in the type-1.5 regime: = 3.7Ͼ 1 / ͱ 2 ͑type-2͒ and = 0.66Ͻ 1 / ͱ 2 ͑type-1͒, where ␣ ͑␣ = , ͒ is the Ginzburg-Landau ͑GL͒ parameter for each band estimated from the band-structure calculations. 6In contrast to conventional type-2 superconductors, 7 in type-1.5 superconductors, vortex stripes and gossamerlike vortex patterns, i.e., vortex clusters emerge at relatively low applied fields, 5 which is due to a competition between attractive ͑type-1͒ and repulsive ͑type-2͒ vortex interactions governed by a two-gap GL theory. [8][9][10][11][12] Interestingly, a substantial difference in vortex structure between type-1.5 and type-2 superconductors, as a fingerprint of type-1.5 superconductivity, is expected at very low vortex densities because the intervortex distances in clusters are likely to be almost independent of the applied field in type-1.5 superconductors, whereas the intervortex distances in type-2 superconductors follow the conventional dependence ͑ 0 / B͒ 1/2 , where 0 ͑=2.07ϫ 10 −15 T m͒ is the flux quantum and B the magnetic field. This motivates strongly direct vortex visualization experiments aimed at investigating vortex structure at very low vortex densities in MgB 2 single crystals. Additionally, it is important to verify the existence of type-1.5 superconductivity in high quality MgB 2 crystals different from the ones used in Ref. 5.In order to study vortex structure in MgB 2 , we made scans with a scanning superconducting quantum interference device ͑SQUID͒ microscope on single crystals of MgB 2 which were grown by a pressure synthesis technique 13 ͑a crystal grown by this technique was used elsewhere 14 ͒. The superconducting transition temperatures T c of the crystals measured by a SQUID magnetometer are 38.5 K ͓the transition width ⌬T c = 0.8 K ͑10-90 % criterion͔͒. The surface of crystals was confirmed not to have any cracks or holes by using a field-emission scanning electron microscope in the secondary electron regime. High-resolution transmission electron microscope images and electron-diffraction patterns for the crystals show that the crystals have no grain boundaries. No impurity contamination was detected within 0.1% accuracy by an electron probe microanalyzer.Our scanning SQUID microscope is base...

Muon-spin rotation measurements of the vortex state inSr2RuO4: Type-1.5 superconductivity, vortex clustering, and a crossover from a triangular to a square vortex lattice

“…Multiple effective coherence lengths lead to a semi-Meissner state whereby a combination of long-range attractive and short-range repulsive intervortex interactions give rise to clusters of vortices nucleating within a Meissner-like state [21]. This behavior was termed type-1.5 superconductivity when reported in MgB 2 [22][23][24]. Nonpairwise interactions may also lead to tendencies to form chainlike or irregular clusters [20] not unlike those observed in some surface probe experiments [15,16].…”

Coherent Stern–Gerlach momentum splitting on an atom chip

“…However, practical atom chip schemes for interferometry with a wide dynamic range and versatile geometries are still very much sought after [23][24][25][26][27][28] . Such schemes may enable, for example, sensitive probing of classical or quantum properties of solid-state nanoscale devices and surface physics (for example, refs [29][30][31][32][33]. This is expected to enhance considerably the power of non-interferometric measurements with ultracold atoms on a chip, which have already contributed, for example, to the study of long-range order of current fluctuations in thin films 34 , the Casimir-Polder force [35][36][37][38] and Johnson noise from a surface 39 .…”

Simulation of the phase diagram of magnetic vortices in two-dimensional superconductors: evidence for vortex chain formation

“…6(d). These simulations might explain why the disordered chains or stripes were frequently observed [10,11,15], while the ordered line state was seldom found in experiments.…”

“…Although large amount of experimental and theoretical efforts in this field has been made [10][11][12][13][14][15][16][17][18], the nature of the vortex clustering in multiband superconductors is still an intensely controversial issue now [17,[19][20][21][22]. In principle, the vortex cluster formation means that there might exist some type of attraction between vortices in addition to repulsion.…”