K B Traito

Eilenberger and Ginzburg-Landau models of the vortex core in high κ-superconductors

Eilenberger approach to the cutoff parameter, ξh, of the field distribution in the mixed state of high κ-superconductors is developed. It is found that normalized value of ξh/ξc2 decreases both with temperature (due to Kramer-Pesch effect) and with impurity scattering rate Γ. Our theory explains μSR experiments in some low-field superconductors and different ξh values from the Ginzburg-Landau theory predictions in isotropic s-wave superconductors. A comparison with another characteristic length ξ1, describing the gradient of the order parameter in the vortex center, is done. They have very different Γ-dependences: monotonous suppression of ξh(B) values and crossing behavior of the ξ1(B) curves at various Γ. This is explained by the nonlocal effects in the Eilenberger theory.

Vortex core size in unconventional superconductors

Influence of the order parameter symmetries on the cutoff parameter ξh and vortex core size ξ2 (the distance from the vortex center at which the current density reaches the maximum value) in the mixed state are investigated in the framework of Eilenberger theory for unconventional superconductors. The cutoff parameter determines the field distribution in the generalized London equation obtained as a projection of the quasiclassical theory. It is used for the fitting of the μSR and small-angle neutron scattering experimental data. Anisotropic dx2−y2 and isotropic s±-wave superconducting pairings are studied. These pairing symmetries can be realized in iron pnictide superconductors. Conventional s++ pairing mediated electron-phonon interaction is also considered. Temperature, field, and impurity scattering dependences of ξh/ξc2 are obtained. It is found that normalized ξ2/ξc2(B/Bc2) dependence is increasing with pair breaking impurity scattering (interband scattering for s±-wave and intraband impurity scatt...

Quasiclassical Eilenberger approach to the vortex state in pnictide superconductors

Quasiclassical Eilenberger equations are solved for s±-wave superconductors in the mixed state. This symmetry has been proposed for multiband superconductors as pnictides. This mechanism can be realized because of Umklapp scattering between the electron and the hole Fermi surface pockets resulting in opposite sign of pairing gap in these pockets. The applicability of the phenomenological Hao-Clem theory is investigated. Magnetic, temperature and impurity scattering rate dependencies of vortex core size are calculated. It is found that the accuracy of the effective London model gets better with the presence of the impurity scattering and even near the second critical field it is below 6%. The model with the parameters of intraband and interband impurity scattering, describing well superfluid density in BaFe2As2, is also considered.

Coherence length of magnetic field in the mixed state of type-II superconductors

Influence of impurities on coherence length Ξh in the mixed state of s-wave superconductors is investigated in framework of quasiclassical Eilenberger theory. The increasing of impurity scattering rate results in decreasing of Ξh. The obtained field dependence of Ξh for clean superconductors has a minimum and it is similar to that in Hao-Clem and Miranovic-Ichioka-Machida theories for order parameter of coherence length. It is found that growing behavior of Ξh with magnetic field in dirty superconductors is different from order parameter coherence length determining by pairing potential near with vortex core. The magnetic field dependence of coherence length in normalized units, Ξh/Ξc2(B/Bc2), is nonuniversal and depends on impurity scattering potential.

Magnetic moment of single vortices in YBCO nano-superconducting particle: Eilenberger approach

Temperature dependence of single vortex magnetic moment in nanosize superconducting particles is investigated in the framework of quasiclassical Eilenberger approach. Such nanoparticles can be used for preparation of high-quality superconducting thin films with high critical current density. In contrast to bulk materials where the vortex magnetic moment is totally determined by flux quantum, in nano-sized specimens (with characteristic size, D, much less than effective penetration depth, λeff) the quantization rule is violated and magnetic moment is proportional to D2/λ2eff(T). Due to strong repulsion between vortices in nanoparticles only a single vortex can be trapped in them. Because of small size of particles the screening current of the vortex is located near the vortex core where the current is quite high and comparable to depairing currents. Therefore, the superconducting electron density, ns, depends on the current value and the distance from the vortex core. This effect is especially important for superconductors having gap nodes, such as YBCO. The current dependence of ns in nanoparticles is analogous to the Volovik effect in flux-line lattice in bulk samples. The magnitude of the effect can be obtained by comparing the temperature dependence of magnetic moment in the vortex and in the Meissner states. In the last case the value of screening current is small and superconducting response to the external field is determined by London penetration depth. Because of importance of nonlinear and nonlocal effects, the quantum mechanical Eilenberger approach is applied for description of the vortex in nanoparticles. The flattening of 1/λ2eff(T) dependence has been found. A comparison of the theoretical results with experimental magnetization data in Meissner and mixed states of YBCO nanopowders has been done. The presence of nonlinear and nonlocal effects in vortex current distribution is clearly visible. The obtained results are important for the description of pining in nanostructured high-Tc thin films.

Cutoff parameter versus Ginzburg-Landau coherence length in the mixed state of high-κ superconductors with impurities: quasiclassical approach

The influence of the impurities on the ratio of the cutoff parameter, ξh and the Ginzburg-Landau coherence length, ξc2, in the mixed state of high-κ s-wave superconductors is investigated in framework of the quasiclassical nonlocal Eilenberger theory. Quasiparticle scattering by impurities and lowering of the temperature reduce the value of ξh to values much less than ξc2. This is different from the prediction of the local Ginzburg-Landau theory where ξh is scaled by ξc2. Detailed comparison with the behavior of the order parameter coherence length ξ1 is done. It is found that impurities influence by different way on ξh and ξ1. The curve ξh/ξc2(B/Bc2) shifts downward with increasing of impurity scattering rate while ξ1/ξc2(B/Bc2) curve shifts upward in this case.

Effects of the order parameter symmetry on the vortex core structure in the iron pnictides

Effects of the order parameter symmetry on the cutoff parameter ξh (determining the magnetic field distribution) in the mixed state are investigated in framework of quasiclassical Eilenberger theory for isotropic s± and for s++ pairing symmetries of superconductors using computational methods. In s± pairing symmetry the gap function has opposite sign and equal absolute values of the electron and hole pockets of the Fermi surface and in s++ pairing symmetry the gap function has the same sign of the electron and hole pockets of the Fermi surfaces. The s± pairing symmetry results in different effects of intraband (Γ0) and interband (Γπ) impurity scattering on ξh. It is found that ξh/ξc2 decreases with the Γ0 leading to values much less than those predicted by the analytical Ginzburg-Landau (AGL) theory for high Γ0. At very high Γ0 the interband scattering suppresses ξh/ξc2 considerably less than the one in the whole field range making it flat. If Γ0 and Γπ are small and equal then the ξh/ξc2(B/Bc2) dependence behaves like that of the AGL model and shows a minimum with value much more than that obtained for s++ superconductors. With high Γπ the dependence of ξh/ξc2(B/Bc2) resides above the AGL curve. Such behavior is quite different from that in s++ pairing symmetry where intraband and interband scattering rates act in a similar way and ξh/ξc2 decreases monotonously with impurity scattering and resides below the AGL curve.