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A finite-size scaling of the nanoscale magnetization m on size averaging R of a single vortex in d -wave bulk superconductor is developed using quasiclassical Eilenberger equations. Nanoscaling is anchoring around the linear London approximation for bulk superconductors. Comparing the results with those obtained in local nonlinear approach demonstrated the importance of the nonlocal contribution. Temperature dependences of two-point correlation function χ ( T , R 1 , R 2 ) = m ( T , R 2 ) / m ( 0 , R 2 ) − m ( T , R 1 ) / m ( 0 , R 1 ) with R 2 > R 1 and one-point function χ ( T, R 1 → ∞, R 2) are calculated. It is found that χ ( T, R 1, R 2), R 2 > R 1, is a nonmonotonous function of temperature and changes sign at high temperatures. This nonmonotonous temperature dependence can be understood as a result of competition between various effects i) Volovik effect and nonlocal corrections to superconducting electron density dominating in low temperature range, and ii) current-induced suppression of the order parameter dominating at high temperatures. The introduced nonmagnetic disorder greatly suppresses the low temperature nonlocal and nonlinear effects, leaving the order parameter effects to prevail in the whole temperature range. Nonlocal pairing and tunneling effects are investigated at the superconductor - normal metal border by considering a d -wave superconducting dot ( d -dot) inside a normal diffusive metal. These effects result in a suppression of the supercurrent in the vortex core and are essential in nanodots with relatively small sizes. At sizes larger than a temperature dependent characteristic length the nanoscale physics transforms into bulk solution.

Hall effect and flux pinning in YBa 2 Cu 3 O 6 + x (YBCO) thin films doped with BaZrO 3 (BZO) nanoparticles is investigated. The results show that sign reversal of the Hall coefficient from positive hole-like to negative electron-like occurs in vortex-liquid regime of undoped and BZO-doped YBCO films. With increasing BZO concentration the amplitude of the negative Hall effect is suppressed while the temperature position of the anomalous Hall effect does not depend significantly on doping level. In addition, it is shown that Hall conductivity increases non-monotonically with increasing BZO doping. These results support a model where BZO at low doping concentration induces point pinning centres turning to strong columnar pinning defects in films doped with 4% BZO.