Brief introduction to flux pinning and vortex dynamics in high temperature superconductors

Abstract

Superconductivity is achieved through macroscopic phase coherence; the charge carriers are Cooper pairs. In absence of an external magnetic field and applied current, the behavior of these Cooper pairs can be described by a single wave function <inline-formula><tex-math id="M3">\begin{document}$ \psi = {\psi _{\rm{0}}}{e^{i\varphi }}$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201881_M3.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201881_M3.png"/></alternatives></inline-formula>, and the phase is uniform over the space. When applying an external field but still below a certain threshold, a screening current will be established at the surface, which prohibits the entering of magnetic field, that is so-called Meissner effect. When the external field is larger than this threshold, the magnetic flux will penetrate into the sample, forming the interface of superconducting and normal state regions. According to the sign of this interface energy, we can categorize superconductors into type-I (positive interface energy) and type-II (negative interface energy). Most superconductors found so far are type-II in nature. Due to the negative interface energy in type-II superconductors, the penetrated magnetic flux will separate into the smallest bundle, namely the quantum flux line, with a quantized flux <inline-formula><tex-math id="M4">\begin{document}${\varPhi _0} = h/2e$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201881_M4.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="1-20201881_M4.png"/></alternatives></inline-formula> (<i>h</i> is the Planck constant and <i>e</i> is the charge of an electron). There are weak repulsive interactions among these vortices, thus usually they will form a lattice, called mixed state. When applying a current, a Lorentz force will exert on the flux lines (vortices) and will make them to move, this will induce energy dissipation and the appreciable feature of zero resistance of a superconductor will be lost. By introducing some defects, impurities or dislocations into the system, it is possible to pin down these vortices and restore the state of zero resistance. The study concerning vortex pinning and dynamics is very important, which helps not only the understanding of fundamental physics, but also to the high power application of type-II superconductors. This paper gives a brief introduction to the vortex dynamics of type-II superconductors.