Abrikosov vortex lattice

Description

Consider a type-II superconductor described by Ginzburg–Landau theory, with Ginzburg–Landau parameter $\kappa > 1/\sqrt{2}$. Let the applied magnetic field $H$ lie between the lower critical field $H_{c1}$ and the upper critical field $H_{c2}$. In this range the field enters the sample as a set of parallel flux lines, called Abrikosov vortices. Around each vortex the complex order parameter $\psi$ vanishes at the core, and its phase winds once by $2\pi$. Each vortex then carries exactly one flux quantum $\Phi_0 = h/(2e)$, where $h$ is Planck's constant and $e$ is the elementary charge. The vortices repel each other and settle into a periodic two-dimensional lattice, the Abrikosov vortex lattice. Check of the density: let $B$ be the mean magnetic induction. Each lattice cell carries flux $\Phi_0$, so the cell area is $\Phi_0 / B$ and the vortex density is $B / \Phi_0$.