Past exam of the condensed matter physics major option course of the University of Oxford / 2016 / 8 / c

The competition between magnetic screening over the London penetration depth $\lambda$ and condensate recovery over the superconducting coherence length $\xi$ is measured by the Ginzburg-Landau parameter $\kappa =\lambda /\xi$. In the single-component local theory the boundary is $\kappa =1/\sqrt{2}$. For $\kappa <1/\sqrt{2}$, a normal–superconducting interface has positive energy: a type-I superconductor favours macroscopic regions and a thermodynamic critical field $H_c$. Demagnetizing fields may create an intermediate state of normal and superconducting domains.

For $\kappa >1/\sqrt{2}$ the interface energy is negative. A type-II superconductor admits flux vortices between the lower and upper critical fields, with normal-like cores of size $\xi$ and circulating screening currents over $\lambda$. Each singly quantized vortex carries ${\Phi }_0=h/(2e)$; a vortex lattice and pinning-controlled irreversible response can occur. Pairing strength, carrier density, Fermi velocity and impurity scattering affect these lengths; $T_c$ alone does not determine the type. The stated boundary is the standard Ginzburg–Landau result near $T_c$.