Local Hall probe measurements and differential magneto-optical imaging with high spatial resolution have been used to investigate the magnetic state of high temperature superconducting Bi2Sr2CaCu2O8+� (BSCCO) micro-disks and platelet single crystals. The results obtained by magneto-optical imaging demonstrate that the field at which flux quantised vortices enter the disks decays exponentially with increasing temperature and the measured data agree well with analytic models for the thermal excitation of individual pancake vortices over Bean-Livingston surface barriers. Scanning Hall probe microscopy images are used to directly map the magnetic induction profiles of individual micro-disks at different applied fields and the results can be quite successfully fitted to analytic models which assume a continuous distribution of flux in the sample. At low fields, however, the characteristic mesoscopic compression of vortex clusters in increasing magnetic fields has been observed. Even at higher fields, where single vortex resolution is lost, it is still possible to track configurational changes in the vortex patterns, since competing vortex orders impose unmistakable signatures on local magnetisation curves as a function of the applied field. These observations are in excellent agreement with molecular dynamics numerical simulations which lead to a natural definition of the lengthscale for the crossover between discrete and continuum behaviours in this system. In closely related experiments, Hall magnetometry is used to probe the out-of-plane local magnetisation of platelet BSCCO single crystals. The magnetisation is found to depend on the strength and direction of an in-plane magnetic field in the crossing vortex lattices regime. The remanent magnetisation in zero out-of-plane field is found to exhibit a pronounced anisotropy, being largest with the in-plane field parallel to the crystalline a-axis, and smallest when it is parallel to the orthogonal b-axis. This behaviour is attributed to the presence of underlying linear disorder. Finally, spectral analysis of the local magnetisation data is used to estimate a lower cutoff for the characteristic frequency of thermal fluctuations of vortex positions.

This thesis studies the intrinsic disorder effects and the transport and magnetic properties of ring-shaped epitaxial thin films and superconducting tunnel junctions (STJs) of the high temperature superconductor YBa$_2$Cu$_3$O$_{7-delta}$. We used an unconventional contactless technique that allows us to directly measure the persistent current of superconducting rings. In order to study the disorder effects on the persistent current, we slowly increased oxygen vacancies in YBa$_2$Cu$_3$O$_{7-delta}$ by changing $delta$ from 0.03 to 0.55 in steps of $sim$0.021. Monitoring the corresponding changes in the temperature dependence of the persistent current revealed an anomaly in its flow within a certain range of disorder. We found that this anomaly is directly related to the occurrence of a spinodal decomposition of oxygen vacancies in YBCO, which we explain as a competition between two coexisting phases, oxygen rich and oxygen deficient. The analysis of the time dependence of the persistent current revealed that increasing oxygen vacancies transforms the vortex structure from quasi-lattice into a glass and subsequently into a pinned liquid phase. Our results also exhibited the first evidence of self-organization of the vortex structure with increasing disorder. We also performed the first direct measurement of the temperature dependence of the $c$-axis persistent current ($J_c$) that is purely due to tunnelling Cooper-pairs through intrinsic Josephson junctions (IJJs) of YBCO. This is made possible by incorporating IJJs of YBCO into ring-shaped films. Then, we studied the temperature dependence of the persistent current of YBCO nanowires embedded in SrTiO$_3$-barrier integrated between two semi-ring-shaped YBCO thin films and systematically varied the nanowires length. Our observations revealed that $J_c$ has two different temperature dependences: a GL-dependence ($J_c propto (T_c - T)^{3/2}$) at low temperatures which we found the same in all studied samples, and another power law dependence ($J_c propto (T_c - T)^{alpha > 3/2}$) at high temperatures which turned out to depend on the length of the nanowires. We attribute the cross-over between these two temperature dependences to the depinning and the dissipative motion of vortices. These experimental approaches and findings not only provide new information, but more importantly open new avenues of investigating the transport and magnetic properties of superconducting films, junctions, and nanowires.

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