title:
Critical State Flux Penetration and Linear Microwave Vortex Response in
  YBa_2Cu_3O_{7-x} Films

abstract:
  The vortex contribution to the dc field (H) dependent microwave surface
impedance Z_s = R_s+iX_s of YBa_2Cu_3O_{7-x} thin films was measured using
suspended patterned resonators. Z_s(H) is shown to be a direct measure of the
flux density B(H) enabling a very precise test of models of flux penetration.
Three regimes of field-dependent behavior were observed: (1) Initial flux
penetration occurs on very low field scales H_i(4.2K) 100Oe, (2) At moderate
fields the flux penetration into the virgin state is in excellent agreement
with calculations based upon the field-induced Bean critical state for thin
film geometry, parametrized by a field scale H_s(4.2K) J_c*d 0.5T, (3) for very
high fields H >>H_s, the flux density is uniform and the measurements enable
direct determination of vortex parameters such as pinning force constants
\alpha_p and vortex viscosity \eta. However hysteresis loops are in
disagreement with the thin film Bean model, and instead are governed by the low
field scale H_i, rather than by H_s. Geometric barriers are insufficient to
account for the observed results.


title:
Density of States and NMR Relaxation Rate in Anisotropic
  Superconductivity with Intersecting Line Nodes

abstract:
  We show that the density of states in an anisotropic superconductor with
intersecting line nodes in the gap function is proportional to $E log (\alpha
\Delta_0 /E)$ for $|E| << \Delta_0$, where $\Delta_0$ is the maximum value of
the gap function and $\alpha$ is constant, while it is proportional to $E$ if
the line nodes do not intersect. As a result, a logarithmic correction appears
in the temperature dependence of the NMR relaxation rate and the specific heat,
which can be observed experimentally. By comparing with those for the heavy
fermion superconductors, we can obtain information about the symmetry of the
gap function.


title:
Ginzburg Landau theory for d-wave pairing and fourfold symmetric vortex
  core structure

abstract:
  The Ginzburg Landau theory for d_{x^2-y^2}-wave superconductors is
constructed, by starting from the Gor'kov equation with including correction
terms up to the next order of ln(T_c/T). Some of the non-local correction terms
are found to break the cylindrical symmetry and lead to the fourfold symmetric
core structure, reflecting the internal degree of freedom in the pair
potential. Using this extended Ginzburg Landau theory, we investigate the
fourfold symmetric structure of the pair potential, current and magnetic field
around an isolated single vortex, and clarify concretely how the vortex core
structure deviates from the cylindrical symmetry in the d_{x^2-y^2}-wave
superconductors.