With the high-temperature superconductors a qualitatively new regime in the phenomenology of type-II superconductivity can be accessed. The key elements governing the statistical mechanics and the dynamics of the vortex system are (dynamic) thermal and quantum fluctuations and (static) quenched disorder. The importance of these three sources of disorder can be quantified by the Ginzburg number $Gi=\frac{{\left(\frac{T_c}{H_c^2}\varepsilon {\xi }^3\right)}^2}{2}$, the quantum resistance $Qu=\left(\frac{e^2}{\hslash }\right)\left(\frac{{\rho }_n}{\varepsilon \xi }\right)$, and the critical current-density ratio $\frac{j_c}{j_o}$, with $j_c$ and $j_o$ denoting the depinning and depairing current densities, respectively (${\rho }_n$ is the normal-state resistivity and ${\varepsilon }^2=\frac{m}{M}<1\mathrm{}$ denotes the anisotropy parameter). The material parameters of the oxides conspire to produce a large Ginzburg number $\mathrm{Gi}\sim {10}^{-2\mathrm{}}$ and a large quantum resistance $\mathrm{Qu}\sim {10}^{-1\mathrm{}}$, values which are by orders of magnitude larger than in conventional superconductors, leading to interesting effects such as the melting of the vortex lattice, the creation of new vortex-liquid phases, and the appearance of macroscopic quantum phenomena. Introducing quenched disorder into the system turns the Abrikosov lattice into a vortex glass, whereas the vortex liquid remains a liquid. The terms "glass" and "liquid" are defined in a dynamic sense, with a sublinear response $\rho ={\frac{\partial E}{\partial j}|}_{j\to 0}$ characterizing the truly superconducting vortex glass and a finite resistivity $\rho (j\to 0)>0$ being the signature of the liquid phase. The smallness of $\frac{j_c}{j_o}$ allows one to discuss the influence of quenched disorder in terms of the weak collective pinning theory. Supplementing the traditional theory of weak collective pinning to take into account thermal and quantum fluctuations, as well as the new scaling concepts for elastic media subject to a random potential, this modern version of the weak collective pinning theory consistently accounts for a large number of novel phenomena, such as the broad resistive transition, thermally assisted flux flow, giant and quantum creep, and the glassiness of the solid state. The strong layering of the oxides introduces additional new features into the thermodynamic phase diagram, such as a layer decoupling transition, and modifies the mechanism of pinning and creep in various ways. The presence of strong (correlated) disorder in the form of twin boundaries or columnar defects not only is technologically relevant but also provides the framework for the physical realization of novel thermodynamic phases such as the Bose glass. On a macroscopic scale the vortex system exhibits self-organized criticality, with both the spatial and the temporal scale accessible to experimental investigations.

DOI:https://doi.org/10.1103/RevModPhys.66.1125