Superconductivity refers to the unusual electrical and magnetic behaviour
exhibited by certain materials below their critical temperature Tc,
usually near absolute zero. These phenomena include negligible resistance to
electric current and the expulsion of external magnetic fields, and
find application in Magnetic Resonance Imaging (MRI) and high capacity power
transmission cables. Based on their response to the applied
magnetic field H, superconductors fall into two major classes, type I and
type II, as illustrated in Figure 1.1.
This thesis focusses on the behaviour of the vortex core radius as a function of temperature T in LuNi2B2C, as studied with muon spin rotation (SR) spectroscopy. (For a discussion of the field dependence, see .) Whereas the core radius is often assumed to remain constant at low temperatures , theoretical works  propose that the core radius should contract linearly with falling temperature , and stop shrinking at a quantum limit temperature T0, where the radius is on the order of a Fermi wavelength. Experimental confirmation of such a temperature dependence, known as the Kramer-Pesch effect, would necessitate a reconsideration of the common assumption that the radius remains constant at low temperatures. To date, SR observations  of the core radius have revealed only a fairly weak Kramer-Pesch effect. These experiments dealt with quasi two-dimensional materials, introducing the possibility of systematic overestimation of the core radius as a result of longitudinal disorder of vortices . This complication has much less impact in the case of LuNi2B2C, a member of a new family of materials that exhibit unusual superconducting behaviour, because LuNi2B2C is nearly isotropic. This superconductor is thus a prime candidate with which to see the predicted Kramer-Pesch effect.
This thesis proceeds as follows. The next chapter outlines basic relevant superconductivity concepts, and goes into detail about the expected Kramer-Pesch effect and previous experimental results concerning it. A general overview of the properties of LuNi2B2C appears in Chapter 3, along with a quantitative estimate of the Kramer-Pesch effect anticipated for this superconductor. Chapter 4 describes the transverse field SR technique and the experimental setup. Chapter 5 explains how the time dependent muon polarisation signal P(t) is fitted to a nonlocal London model developed for borocarbides, and how the core radius is calculated from the fitted internal magnetic field profile B(r). It also examines the quality of the fits as a function of the penetration depth , the nonlocality parameter C and the core radius . Chapter 6 presents the resulting temperature dependence of the fitted penetration depth and nonlocality parameter C, and the extracted core radius , for LuNi2B2C under a constant applied field of . It compares the low temperature behaviour of the core radius measured in LuNi2B2C with the predicted Kramer-Pesch effect, as well as the core radius temperature dependences observed previously in NbSe2 and YBaCu3O under an applied field . This chapter also contrasts the internal magnetic field distributions n(B) of the nonlocal and local London models. Finally, Chapter 7 summarises these results and their implications.