Resumen de Lowest Landau level approach in superconductivity for the Abrikosov lattice close to Hc2
Amandine Aftalion, Sylvia Serfaty
We study the Ginzburg–Landau energy for a superconductor submitted to a magnetic field hex just below the “second critical field” Hc2 . When the Ginzburg–Landau parameter ε is small, we show that the mean energy per unit volume can be approximated by a reduced energy on a torus. Moreover, we expand this reduced energy in terms of Hc2 −hex: when this quantity gets small, the problem amounts to a minimization problem on a finite-dimensional space, equivalent to the “lowest Landau level” in other approaches. The functions in this finite-dimensional space can themselves be expressed via the Jacobi Theta function of a lattice. This connects the Ginzburg–Landau energy to the “Abrikosov problem” of locating vortices optimally on a lattice.
