In the simple view, a vortex core is a cylinder of normal material whose radius is the Ginzburg-Landau coherence length . Over this length scale the order parameter and the supercurrent density J(r) fall monotonically to zero at the core centre. Although the Ginzburg-Landau formalism is only truly valid near the transition temperature Tc, the core radius is also commonly defined as the temperature dependent coherence length at low temperatures, where it becomes approximately a BCS coherence length . Employing this assumption Caroli, de Gennes and Matricon  investigated the quasiparticle excitations of energy localised near an isolated vortex line in a clean ( ) type II superconductor, where is the bulk value of the BCS energy gap. They determined these quasiparticles to have at least an energy , and above this a density of states like that of a cylindrical normal region of radius . This traditional vortex core picture implies that at low temperatures the core radius, being roughly a BCS coherence length , is essentially temperature independent.
The Kramer-Pesch effect, predicted for isolated flux lines in clean s-wave
superconductors , refers to the
rapid contraction of the vortex core radius
to around a Fermi
wavelength 1/kF upon cooling at low temperatures. This flux line
narrowing stems from the thermal depopulation of the quasiparticle bound
states. The bound state energy levels
the BCS energy gap
as their corresponding
become infinite, and the low energy radial
wavefunctions are greatest at a distance
from the core
centre . The reduction in core radius terminates at
in the quantum
. Here only the
lowest energy bound state remains occupied .
down to near the quantum limit temperature T0,
the core radius
shrinks linearly as
Experimental observations reveal the shrinking of the vortex cores upon cooling to be more limited than expected from the predicted Kramer-Pesch effect. Indirect evidence supporting the proposed Kramer-Pesch effect comes from the logarithmic singularity in the current-voltage characteristic for Nd1.85Ce0.15CuOx films . Muon spin rotation (SR) measurements of the core radius as a function of temperature show a surprisingly weak Kramer-Pesch effect in NbSe2  ( ), YBaCu3O6.95  ( ) and YBaCu3O6.60 ( ). The core radius in NbSe2 saturates at , many times larger than the anticipated low temperature radius of around . The temperature dependence of the vortex size is weaker in YBaCu3O6.95, and even more so in YBaCu3O6.60. The apparent absence of significant core shrinking in YBaCu3O6.60and YBaCu3O6.95 possibly reflects the attainment of the quantum limit . The quantum limit temperature T0 should be much higher in these materials than in NbSe2, since they have a considerably smaller BCS coherence length . The substantially larger-than-predicted core radii found at very low temperatures in NbSe2 are attributed to interactions between the vortices, and to their possible zero point motion. To date, all theoretical works concerning the Kramer-Pesch effect suppose isolated vortices, an assumption which likely fails for the transverse field SR experiments mentioned here. Also, in quasi two-dimensional (2D) superconductors such as NbSe2 and YBaCu3O , longitudinal disorder of vortices potentially inflates the value of the core radius determined with SR, since a flux line in such materials consists of a column of 2D pancake vortices which could wobble . Flux lines should be stiffer in three-dimensional (3D) superconductors, leading to a simpler dependence of the core radius on temperature. This makes the clean 3D type II s-wave superconductor LuNi2B2C an ideal candidate for observation of the predicted Kramer-Pesch effect with SR. The next chapter describes the characteristics of this material.