= Solution
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 $\kappa=1/\sqrt2$. For $\kappa<1/\sqrt2$, 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 $\kappa>1/\sqrt2$ 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 $T_c$.
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