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

Amandine Aftalion, Sylvia Serfaty

Research output: Contribution to journalArticle

Abstract

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.

Original languageEnglish (US)
Pages (from-to)183-202
Number of pages20
JournalSelecta Mathematica, New Series
Volume13
Issue number2
DOIs
StatePublished - Sep 1 2007

Keywords

  • Abrikosov lattices
  • Lowest Landau level
  • Second critical field
  • Superconductivity
  • Theta functions
  • Vortices

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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