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Register a new userEvidence for Cooper Pair Diffraction on the Vortex Lattice of Superconducting Niobium
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Added by
Alexander Maisuradze
Publication date
2013
fields
Physics
and research's language is
English
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We investigated the Abrikosov vortex lattice (VL) of a pure Niobium single crystal with the muon spin rotation (mu SR) technique. Analysis of the mu SR data in the framework of the BCS-Gorkov theory allowed us to determine microscopic parameters and the limitations of the theory. With decreasing temperature the field variation around the vortex cores deviates substantially from the predictions of the Ginzburg-Landau theory and adopts a pronounced conical shape. This is evidence of partial diffraction of Cooper pairs on the VL predicted by Delrieu for clean superconductors.
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Recent experiments [I.V. Grigorieva et al., Phys. Rev. Lett. 96, 077005 (2006)] on visualization of vortices using the Bitter decoration technique revealed vortex shells in mesoscopic superconducting Nb disks containing up to L=40 vortices. Some of the found configurations did not agree with those predicted theoretically. We show here that this discrepancy can be traced back to the larger disks with radii R ~ 1 to 2.5mu m, i.e., R ~ 50-100xi(0) used in the experiment, while in previous theoretical studies vortex states with vorticity L < 40 were analyzed for smaller disks with R ~ 5-20xi(0). The present analysis is done for thin disks (mesoscopic regime) and for thick (macroscopic) disks where the London screening is taken into account. We found that the radius of the superconducting disk has a pronounced influence on the vortex configuration in contrast to, e.g., the case of parabolic confined charged particles. The missing vortex configurations and the region of their stability are found, which are in agreement with those observed in the experiment.
Dissipative-free electric current flow is one of the most fascinating and practically important property of superconductors. Theoretical consideration of the charge carriers flow in infinitely long rectangular slab of superconductor in the absence of external magnetic field (so called, self-field) is based on an assumption that the charge carriers have rectilinear trajectories in the direction of the current flow whereas the current density and magnetic flux density are decaying towards superconducting slab with London penetration depth as characteristic length. Here, we calculate charge particle trajectories (as single electron/hole, as Cooper pair) at self-field conditions and find that charge carriers do not follow intuitive rectilinear trajectories along the slab surface, but instead ones have meander shape trajectories which cross the whole thickness of the slab. Moreover, if the particle velocity is below some value, the charge moves in opposite direction to nominal current flow. This disturbance of the canonical magnetic flux density distribution and backward movement of Cooper pairs can be entire mechanism for power dissipation in superconductors.
The vortex lattice (VL) symmetry and orientation in clean type-II superconductors depends sensitively on the host material anisotropy, vortex density and temperature, frequently leading to rich phase diagrams. Typically, a well-ordered VL is taken to imply a ground state configuration for the vortex-vortex interaction. Using neutron scattering we studied the VL in MgB2 for a number of field-temperature histories, discovering an unprecedented degree of metastability in connection with a known, second-order rotation transition. This allows, for the first time, structural studies of a well-ordered, non-equilibrium VL. While the mechanism responsible for the longevity of the metastable states is not resolved, we speculate it is due to a jamming of VL domains, preventing a rotation to the ground state orientation.
The field distribution in the vortex lattice of a pure niobium single crystal with an external field applied along a three-fold axis has been investigated by the transverse-field muon-spin-rotation (TF-$mu$SR) technique over a wide range of temperatures and fields. The experimental data have been analyzed with the Delrieus solution for the form factor supplemented by phenomenological formulas for the parameters. This has enabled us to experimentally establish the temperatures and fields for the Delrieus, Ginzburg-Landaus, and Kleins regions of the vortex lattice. Using the numerical solution of the quasiclassical Eilenbergers equation the experimental results have been reasonably understood. They should apply to all clean BCS superconductors. The analytical Delrieus model supplemented by phenomenological formulas for its parameters is found to be reliable for analyzing TF-$mu$SR experimental data for a substantial part of the mixed phase. The Abrikosovs limit is contained in it.
Bulk SC has recently been observed in the Al-Zn-Mg QC. To settle the several fundamental issues on the SC on the QC, we perform a systematic study on an attractive Hubbard model on the Penrose lattice. The first issue is the Cooper instability under an infinitesimal attractive interaction on the QC without a Fermi surface. We start from the two-electron problem outside the filled Fermi-sea, where we analytically prove that an infinitesimal Hubbard attraction can lead to the Cooper instability as long as the density of state is nonzero at the Fermi level, which provides the basis for the SC on the QC. Our numerical results yield that the Cooper pairing always takes place between a time-reversal partner, satisfying the Andersons theorem. On this basis, we perform a MF study on the system, at both the zero and finite temperatures. The MF study also shows that an arbitrarily weak attraction can lead to the pairing order, with the resulting pairing state well described by the BCS theory, and the thermal dynamic behaviors well consistent with experiment results. The second issue is about the superfluid density on the QC without translational symmetry. Its clarified that although the normal state of the system locates at the critical point of the metal-insulator transition, the pairing state exhibits real SC, carrying finite superfluid density that can be verified by the Meissner effect. Further more, our study reveals a fundamental difference between the SC on the periodic lattice and that on the QC: while the paramagnetic superfluid density in the former case vanishes at zero temperature, that in the latter case is nonzero due to the lack of translational symmetry, reflecting the consumption of superfluid density from the scattering by the non-periodic structure. These properties of the SC on the Penrose lattice revealed here are universal for all QCs.
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