Phenomenon Standard physics Substrate model
Meissner effect Superconductor expels magnetic flux below Tc. Surface screening currents cancel B in bulk. Cooper pair vortices collectively refuse external co-rotating flow that would disrupt their shared seams. Surface currents create counter-flow to cancel the field. Cheaper than breaking all pair vortices.
core mechanism
London penetration depth Characteristic depth over which B field decays exponentially inside surface. Depends on superfluid density. Depth of cooperative screening flow. More pair vortices = denser counter-flow = shorter penetration. Grows as T approaches Tc because pairs break.
core mechanism
BCS energy gap Minimum energy to break a Cooper pair. Creates gap in excitation spectrum. Vanishes at Tc. Energy stored in the shared counter-rotating vortex seam. To break the pair, must tear this vortex apart. Strongest at T = 0, vanishes at Tc when thermal energy overwhelms vortex binding.
core mechanism
Flux quantization Trapped flux in a ring = integer multiples of Φ₀ = h/(2e). Factor of 2 from pair charge. Pair pilot wave must complete integer cycles around the ring — boundary-matching quantization, same math as hydrogen orbitals and modon eigenvalues. Factor of 2e because the circulating object is a pair.
core mechanism prediction: same math as Sec. 7
Isotope effect Tc proportional to M⁻¹ᐟ². Heavier isotopes suppress Tc. Proves phonon-mediated pairing. Heavier nuclear core = harder to displace = weaker channel compression = weaker pairing vortex = lower Tc. Connects nuclear mass directly to pair vortex binding strength.
prediction confirmed
Type I vs type II Determined by κ = λ/ξ. Type I: complete flux expulsion or full breakdown. Type II: allows partial flux penetration via vortex tubes. Ratio of screening depth to pair vortex extent. Type I: vortices too wide to coexist with flux — all or nothing. Type II: compact vortices survive between flux tubes, creating a mixed state.
observable
Abrikosov vortex lattice Flux penetrates type II as quantized vortex lines that self-organize into triangular lattice. Flux tubes are channels where external co-rotating flow threads through. Screening eddies around each tube repel, self-organizing into minimum-energy triangular packing — a visible, macroscopic echo of substrate boundary physics.
observable visual analog from Sec. 10
Josephson effect Cooper pairs tunnel through thin insulating barrier. DC: supercurrent at zero voltage. AC: oscillating current at frequency 2eV/h. Pair vortex (100 nm) bridges a 1-2 nm barrier — vortex eddies thread through gap maintaining coherence on both sides. Voltage shifts phase across the bridge, oscillating pairs back and forth.
core mechanism
Critical current Maximum supercurrent before superconductivity breaks down. Related to gap and geometry. High drift velocity shears the shared pair vortex — upstream electron leads, downstream trails. At Jc the shear exceeds vortex binding energy and pairs tear apart, cascading into normal state.
prediction
Critical field (Hc, Hc1, Hc2) Magnetic field thresholds for destroying superconductivity. Type I: single Hc. Type II: Hc1 (first flux entry) to Hc2 (full breakdown). External co-rotating flow overwhelms pair vortex binding. Hc1: first flux channel punctures pair lattice. Hc2: channels so dense that normal cores merge and no pairs survive.
observable
Coherence length Spatial extent of Cooper pair. Sets vortex core size. ξ = ℏv_F / (πΔ). Extent of the shared counter-rotating vortex. Fast channel flow stretches it; strong binding tightens it. Sets Abrikosov vortex core diameter and determines type I vs II.
core mechanism
Macroscopic coherence All pairs share one wavefunction. Phase θ is macroscopically observable. Enables SQUIDs and quantum computing. All pair vortices phase-lock — a Bose-Einstein condensate of synchronized counter-rotating seams. Phase θ = collective vortex oscillation. Phase gradients drive supercurrents. Nothing abstract — it is synchronized fluid dynamics.
core mechanism prediction: phase is physical