The Superconducting Phase Boundary
Every superconductor has a critical temperature Tc and a critical magnetic field Hc that together define a phase boundary in the T-H plane. Below and to the left of this parabolic curve, the material is superconducting; above it, normal. The empirical law Hc(T) = Hc₀(1 - (T/Tc)²) was discovered in the 1930s and later derived from Ginzburg-Landau theory.
Type-I vs Type-II
The Ginzburg-Landau parameter κ = λ/ξ cleanly divides superconductors into two classes. Type-I materials (most elemental metals like Pb, Sn, Al) have κ < 1/√2 and undergo a first-order transition at Hc — the entire sample switches abruptly between superconducting and normal. Type-II materials (alloys, compounds, all high-Tc cuprates) have κ > 1/√2 and exhibit the mixed state between Hc1 and Hc2.
The Mixed State
In type-II superconductors between Hc1 and Hc2, magnetic flux penetrates as quantized vortices, each carrying exactly one flux quantum Φ₀ = h/2e = 2.07 × 10⁻¹⁵ Wb. The vortices arrange in a triangular lattice — the Abrikosov lattice. This mixed state is what makes practical superconducting magnets possible: NbTi wire in MRI magnets operates entirely in this regime.
Engineering the Phase Diagram
Materials scientists engineer superconductors to maximize Hc2 and the irreversibility field. Alloying increases κ and thus Hc2. Artificial pinning centers — nano-precipitates, grain boundaries, irradiation defects — prevent vortex motion and maintain zero resistance under high current. The resulting J-B-T critical surface defines the operating envelope of every superconducting device.