Lowest Landau level approach in superconductivity for the Abrikosov lattice close to Hc2

• Amandine Aftalion ^[1] ; Sylvia Serfaty ^[2]
  1. [1] Pierre and Marie Curie University

     Pierre and Marie Curie University

     París, Francia

     
  2. [2] Courant Institute of Mathematical Sciences
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 13, Nº. 2, 2007, págs. 183-202
• Idioma: inglés
• DOI: 10.1007/s00029-007-0043-7
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• Resumen

  • 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.