Superconductor classification

​, where $\lambda$λ is the London penetration depth and $\xi$ξ is the coherence length, leading to incomplete magnetic flux expulsion in intermediate magnetic fields. Unlike type I superconductors, they exhibit two distinct critical magnetic fields: the lower critical field $H_{c1}$Hc1​, above which magnetic flux begins to penetrate the material in the form of quantized vortices, and the upper critical field $H_{c2}$Hc2​, beyond which superconductivity is fully destroyed. The thermodynamic critical field $H_c$Hc​ relates to these as $H_c = \sqrt{H_{c1} H_{c2}}$Hc​=Hc1​Hc2​

​, providing a measure of the energy scale for the superconducting transition. This behavior enables type II superconductors to operate in much higher magnetic fields, making them essential for practical applications. In the mixed state, between $H_{c1}$Hc1​ and $H_{c2}$Hc2​, magnetic flux penetrates as an Abrikosov vortex lattice, a regular array of quantized flux lines predicted theoretically in 1957. Each vortex carries a single flux quantum $\Phi_0 = h/(2e) \approx 2.07 \times 10^{-15}$Φ0​=h/(2e)≈2.07×10−15 Wb, where $h$h is Planck's constant and $e$e is the elementary charge, and features a normal-conducting core with a radius on the order of the coherence length $\xi$ξ. The lattice structure arises from the balance between repulsive interactions among vortices and the applied field, allowing partial superconductivity to persist despite flux penetration. This mixed phase was first theoretically described for materials with $\kappa > 1/\sqrt{2}$κ>1/2

​, resolving earlier experimental observations of intermediate magnetic behavior in alloys. Flux pinning enhances the utility of type II superconductors by trapping vortices at defects such as grain boundaries, dislocations, or impurities, preventing their motion under current and thereby supporting high critical current densities $J_c > 10^5$Jc​>105 A/cm². This pinning stabilizes the vortex lattice against Lorentz forces, minimizing energy dissipation and enabling persistent currents in magnets. The critical state model, developed by C. P. Bean in 1962, describes the resulting hysteresis in magnetization, where the current density reaches a maximum pinning-limited value throughout penetrated regions, leading to calculable AC losses in time-varying fields. Engineered pinning landscapes, often via irradiation or nanostructuring, further optimize $J_c$Jc​ for high-field performance. Prominent examples include niobium-based alloys, which dominate practical applications due to their robust properties. Niobium-titanium (NbTi) has a critical temperature $T_c \approx 9.7$Tc​≈9.7 K and upper critical field $H_{c2} \approx 12$Hc2​≈12 T at 4.2 K, powering the superconducting magnets in the Large Hadron Collider (LHC) for beam steering in particle accelerators. Niobium-tin (Nb$_3$3​Sn) offers higher performance with $T_c \approx 18$Tc​≈18 K and $H_{c2} \approx 25$Hc2​≈25 T, used in advanced MRI systems for generating fields up to 7 T with superior resolution. Pure niobium, with $T_c = 9.2$Tc​=9.2 K and $H_{c2} \approx 0.2$Hc2​≈0.2 T, exhibits type II behavior at low temperatures and serves as a baseline material in radiofrequency cavities. These materials were first identified as type II in alloy form during the 1930s, with systematic studies of lead-bismuth and other binaries revealing the mixed state, culminating in Abrikosov's theoretical framework that explained the vortex lattice.

Classification by Superconducting Mechanism

Conventional Superconductors