Periodic Magnetic Schrödinger Operator in Superconductivity
Since the discovery of type II superconductivity by Abrikosov, the
distribution of superconductivity near the second critical field is
a challenging mathematical problem. In this talk, I will discuss the
asymptotic behavior of the Abrikosov energy in a large domain, and
the connection between the Abrikosov and Ginzburg-Landau energies.
In this discussion, a key role is played by the spectrum of the
Schrödinger operator with a constant magnetic field in a lattice.
As a matter of application, I will write a new formula for the
distribution of superconductivity near the second critical field. I
will conclude the talk with a hierarchy of energies: the Abrikosov
energy, the bulk energy of superconductivity, and the reference
energy for a superconducting surface. Part of these results are
obtained jointly with S. Fournais and with B. Helffer.