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 2007

Fingerprint

Landau Levels
Superconductivity
Lowest
superconductivity
Ginzburg-Landau
Energy
energy
Theta Functions
Superconductor
Jacobi
Minimization Problem
Expand
Vortex
Torus
Magnetic Field
vortices
optimization
Unit
magnetic fields

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Lowest Landau level approach in superconductivity for the Abrikosov lattice close to Hc2 . / Aftalion, Amandine; Serfaty, Sylvia.

In: Selecta Mathematica, New Series, Vol. 13, No. 2, 09.2007, p. 183-202.

Research output: Contribution to journalArticle

Aftalion, Amandine ; Serfaty, Sylvia. / Lowest Landau level approach in superconductivity for the Abrikosov lattice close to Hc2 . In: Selecta Mathematica, New Series. 2007 ; Vol. 13, No. 2. pp. 183-202.
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