Flux lattices

The classical tunneling experiment of Giaever (1960) provided unambiguous proof of the BCS theory of superconductivity. The STM as a local tunneling probe is certainly suitable to probe the local properties of superconductors, such as the local structure of the Abrikosov flux lattice. The work of Hess and co-workers (1989, 1990, 1990a, 1991) is a prominent example. 

Fig. 16.7. Abrikosov flux lattice observed by STM. Produced by a 1 T magnetic field in NbSe, at 1.8 K, the scan range is about 6000 A. The gray scale corresponds to dUdV ranging from approximately I X 10 mho (black) to 1.5 X 10 mho (white). (Reproduced from Hess et al., 1989, with permission.)...

Scanning tunneling microscope observation of the Abrikosov flux lattice and the density of states near and inside a fluxoid. Phys. Rev. Lett. 62, 214-216. 

Abrikosov flux lattice 333 observed by STM 333 tunneling conductance near a vortex 334 AFM... 

Instead of forcing the data to conform to the d-wave picture, we take the approach that the deviations from. v-wave behavior are due to quantifiable phenomena, most notably temperature-dependent fhixon de-pinning. Since the maximum temperature for the data acquired at each held is below the melting curve (see Fig. 4 of Ref. 11), the vortex lattice is subject to pinning, as occurs in very clean crystals where the flux lattice becomes locked-in by weak pinning at oxygen vacancies and/or other defects. 

The final evidence for the formation of an Abrikosov flux lattice of screw dislocations in liquid crystals was achieved by Zasadzinski et al. [39] via the visualization of the screw dislocations of (R)- and (S-)l-methylheptyl 4 -(4-n-tetradecyloxyphenylpropioloyloxy)-biphenyl-4-carboxylates using freeze-fracture transmission electron microscopy. Freeze-fracture transmission microscopy (TEM) is an essential tool for visualizing the TGBA phase at sufficient resolution in order to resolve the molecular organization. 

The nonnal threads are called vortices or fluxoids. The currents act so as to repel each other, so that the flux lines form an ordered structure called a fluxon lattice, flux lattice or vortex lattice. At the core of each flux vortex the material is effectively normal, but is surrounded by a region of superconductor. 

Owens, F.J. and Poole, C.P., Jr. (1996) The New Superconductors, Plenum Press, New York. A gentle introduction to ceramic superconductors includes a very readable account of the flux lattice. 

The crystal structure of UPts is hexagonal (see fig. 138, left) which gives rise to strong anisotropy of physical parameters (Shivaram et al. 1986, Zhao et al. 1991, Keller et al. 1994, Lussier et al. 1994, Fleddeijohann and Hirschfeld 1995). Direct detection of the vortex flux lattice by neutrons was reported by Kleiman et al. (1992). Magnetic neutron scattering and related work will be mentioned in context below. 

We will discuss the case where the motion of heavy atoms is confined to two dimensions, while the motion of light atoms can be either two- or three-dimensional. It will be shown that the Hamiltonian 10.76 with Ues in 10.44 supports the first-order quantum gas-crystal transition at T = 0 [68], This phase transition resembles the one for the flux lattice melting in superconductors, where the flux lines are mapped onto a system of bosons interacting via a two-dimensional Yukawa potential [73]. In this case Monte Carlo studies [74,75] identified the first-order liquid-crystal transition at zero and finite temperatures. Aside from the difference in the interaction potentials, a distinguished feature of our system is related to its stability. The molecules can undergo collisional relaxation into deeply bound states, or form weakly bound trimers. Another subtle question is how dilute the system should be to enable the use of the binary approximation for the molecule-molecule interaction, leading to Equations 10.76 and 10.44. 

The helical smectic A phase can form between the chiral smectic C phase and the isotropic phase [16a] or, alternatively, between the chiral nematic (cholesteric) phase and the isotropic phase [16bj. In the latter case, which was observed for a mixture of cholesteryl nonanoate (a homologue of (l.vii)) with p-nonyloxybenzoic acid, an interesting formal analogy exists between the smectic A phase and Abrikosov s flux lattice in type-II superconductors. 

Neutron scattering is an excellent probe (Cribier et al. 1964) of flux lattices in superconductors because the dipole moment of the neutron couples to the magnetic field inhomogeneities associated with such lattices. Of course, the length scales for the... 

Fig. 25. Diffraction pattern for flux lattice in superconducting UPtj at T = 50mK and a magnetic field H = 0.425T applied along a", perpendicular to the region of the (h,0,l) zone shown. The corners of the region are at ( 0.016A, 0, 0.016A" )- (a) Background-corrected data (b) calculated response of instrument to flux lattice with infinite-range order (c) the data of (a) symmetrized to reduce the statistical errors in the peak intensities. (Adapted from Kleiman et al. 1992.)...

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