Vortex State Of type-II Superconductors Research Articles

Comparison of different methods for analyzingμSR line shapes in the vortex state of type-II superconductors

A detailed analysis of muon-spin rotation(μSR) spectra in the vortex state of type-II superconductors using different theoretical models ispresented. Analytical approximations of the London and Ginzburg–Landau (GL) models,as well as an exact solution of the GL model were used. The limits of the validity of thesemodels and the reliability for extracting parameters such as the magnetic penetration depthλ and the coherencelength ξ from theexperimental μSR spectra were investigated. The analysis of the simulatedμSR spectra showed that at high magnetic fields there is a strong correlation betweenλ and ξ obtained for any value of the Ginzburg–Landau parameterκ = λ/ξ. The smaller the applied magnetic field, the smaller the possibility of finding the correct value ofξ. A simultaneousdetermination of λ and ξ without any restrictions is very problematic, regardless of the model used to describe the vortex state.It was found that for extreme type-II superconductors and low magnetic fields, the fitted value ofλ is practicallyindependent of ξ. The second-moment method frequently used to analyzeμSR spectra by means of a multi-component Gaussian fit generally yields reliable values ofλ over the whole range of applied fields (Hc1 and Hc2 are the first and second critical fields, respectively). These results are also relevant for theinterpretation of small-angle neutron scattering experiments on the vortex state in type-IIsuperconductors.

Magnetic-field dependence of thermodynamic quantities in the vortex state of type-II superconductors

We develop an alternative method to solve the Eilenberger equations numerically for the vortex-lattice states of type-II superconductors. Using it, we clarify the magnetic-field and impurity-concentration dependences of the magnetization, the entropy, the Pauli paramagnetism, and the mixing of higher Landau levels in the pair potential for two-dimensional $s$- and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-wave superconductors with the cylindrical Fermi surface.

Influence of Fermi surface topology on the quasiparticle spectrum in the vortex state

We study the influence of Fermi surface topology on the quasiparticle density of states in the vortex state of type-II superconductors. We observe that the field dependence and the shape of the momentum and spatially averaged density of states is affected significantly by the topology of the Fermi surface. We show that this behavior can be understood in terms of characteristic Fermi surface functions and that an important role is played by the number of points on the Fermi surface at which the Fermi velocity is directed parallel to the magnetic field. A critical comparison is made with a broadened BCS-type density of states, which has been used frequently in analysis of tunneling data. We suggest a formula as a replacement for the broadened BCS model for the special case of a cylindrical Fermi surface. We apply our results to the two-gap superconductor ${\mathrm{MgB}}_{2}$ and show that in this particular case the field dependence of the partial densities of states of the two gaps behaves very differently due to the different topologies of the corresponding Fermi surfaces, in qualitative agreement with recent tunneling experiments.

Gap Anisotropy and de Haas-van Alphen Effect in Type-II Superconductors

We present a theoretical study on the de Haas-van Alphen (dHvA) oscillation in the vortex state of type-II superconductors, with a special focus on the connection between the gap anisotropy and the oscillation damping. Numerical calculations for three different gap structures clearly indicate that the average gap along extremal orbits is relevant for the magnitude of the extra damping, thereby providing a support for experimental efforts to probe gap anisotropy through the dHvA signal. We also derive an analytic formula for the extra damping which gives a good fit to the numerical results.

Dynamical Superfluid Density in Vortex State of Type-II Superconductors

The electromagnetic linear response both in the lattice state and liquid state of vortices in type-II superconductors are studied based on the dynamical superfluid density. The calculations are carried out paying special attention to the difference of the internal and the external vector potential. By use of the obtained dynamical superfluid density the static superfluid density, the electric conductivity and the magnetic permeability are studied. A significant difference in responses between the two states is found especially in the Lorentz force free configuration, namely when the supercurrent flows in the direction parallel to the applied magnetic field; the vortex lattice state is superconducting in this direction while the liquid state is not becaue of the vortex entanglement and cutting effects. The magnetic susceptibility, especially in lattice state, has been examined in detail.

Density of states in the vortex state of type-II superconductors.

The local, direction resolved density of states in the vortex state of clean type-II superconductors is calculated for arbitrary energies and inductions. It is obtained by solving numerically the quasi- classical equations of superconductivity, using parameters corresponding to Nb or V. The excitation spectrum is discussed for arbitrary inductions and, for the special case of large vortex distance, compared with previous theories. Tunneling states of quasiparticles are calculated explicitly for the first time and a shift of continuum states to energies higher than ${\ensuremath{\psi}}_{\mathrm{BCS}}$ is found. Some conclusions specific to the important materials Nb and V are drawn. The energy dependence of the local density of states near the vortex axis is found to be in qualitative agreement with recent scanning-tunneling-microscope measurements.

Theory of Electron-Spin Resonance in Gapless Superconductors

The transverse dynamic spin susceptibility for conduction electrons in dirty gapless superconductors, in particular, in the vortex state of type-II superconductors, is calculated. It is shown that in the gapless region the dynamic susceptibility consists of two terms, the regular term and the anomalous term. In the low-frequency region of experimental interest, the regular term reduces to the static spin susceptibility, which is determined, for example, by the Knight-shift measurement in superconductors, while the anomalous term has a pole, which is associated with a resonance of the spin of conduction electrons. The resonance linewidth ${T}_{2}^{\ensuremath{-}1}$ is determined from the imaginary part of the resonance frequency. It is shown that ${T}_{2}^{\ensuremath{-}1}$ behaves quite differently in the superconducting state depending on whether ${T}_{2}^{\ensuremath{-}1}$ in the normal state is primarily due to the spin-orbit scattering or due to the exchange scattering from the magnetic impurities.

Temperature and Frequency Dependence of the Surface Resistance in the Vortex State of Type-II Superconductors

Temperature and Frequency Dependence of the Surface Resistance in the Vortex State of Type-II Superconductors