🧊 Superconductor Meissner Effect

The London penetration depth λ is the characteristic distance over which an external magnetic field decays exponentially as it enters a superconductor's surface, following B(x) = B₀·exp(−x/λ). It is not a hard wall — the field is not zero at the very surface, it just falls off fast, typically over tens to a few hundred nanometres depending on the material. λ grows as temperature approaches Tc, formally diverging as λ(T) = λ₀ / √(1 − (T/Tc)⁴) in the London/BCS picture, meaning the superconductor "leaks" more field just below its transition.

In 1957, John Bardeen, Leon Cooper and Robert Schrieffer (BCS theory) showed that below Tc, electrons that would normally repel each other can form weakly bound pairs — Cooper pairs — mediated by lattice vibrations (phonons): one electron slightly distorts the ion lattice, and that distortion attracts a second electron. These pairs behave as bosons and condense into a single coherent quantum state that moves through the lattice without scattering, which is the microscopic origin of both zero resistance and the Meissner effect.

Type-I superconductors (mostly pure elemental metals like mercury, lead and tin) show complete Meissner expulsion up to a single critical field Hc, above which superconductivity collapses abruptly and completely. Type-II superconductors (alloys and ceramics like niobium-titanium and YBCO) expel flux completely only below a lower critical field Hc1; between Hc1 and a much higher Hc2 they enter a "mixed state" where magnetic field penetrates in quantized flux vortices while the rest of the material stays superconducting. This mixed state, and the flux pinning it enables, is what makes practical high-field magnets and stable levitation possible.

Mercury, the first superconductor discovered (Heike Kamerlingh Onnes, 1911), has Tc ≈ 4.2 K, requiring liquid helium cooling. Niobium-titanium, used in MRI and particle-accelerator magnets, has Tc ≈ 9–10 K. The high-Tc ceramic superconductor YBa₂Cu₃O₇ (YBCO), discovered in 1987, has Tc ≈ 93 K — above the 77 K boiling point of liquid nitrogen, which made superconductivity vastly cheaper to demonstrate and use.

Not quite. Two ordinary magnets pushed apart by like poles are inherently unstable sideways — they slip and flip. A superconductor levitating a magnet via the Meissner effect, especially a Type-II superconductor with pinned flux vortices, is locked into place in all directions: push it sideways and the pinned vortices pull it back, tilt it and it self-corrects. This "flux pinning" stability, not just repulsion, is what lets demonstrations levitate a magnet on a curved track or hold it suspended at an angle.

The search for room-temperature superconductivity is one of condensed-matter physics' biggest open problems. Hydrogen-rich compounds such as lanthanum hydride (LaH₁₀) have shown superconductivity above 250 K, but only under enormous pressures (over a million atmospheres), which limits practical use. Researchers are also exploring iron-based superconductors, twisted bilayer graphene (which becomes superconducting at a "magic angle"), and topological superconductors that could host exotic quasiparticles useful for fault-tolerant quantum computing.