Superconductor Phase Transition Simulator

Superconductor Lattice

Temperature 300 K

Applied field 0.00 T

State

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Resistance

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Levitation

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How it works

Above the critical temperature T_c, conduction electrons scatter off vibrating lattice ions (phonons) at random, so their drift is chaotic and dissipates energy as resistance. Cool the crystal below T_c and electron-phonon coupling instead glues electrons into opposite-momentum, opposite-spin Cooper pairs that condense into one macroscopic quantum state — the whole condensate moves in lock-step through the lattice without scattering, so resistance drops to exactly zero.

R(T) = R_n           for T > T_c
R(T) = 0              for T ≤ T_c  and  B ≤ B_c(T)
B_c(T) ≈ B_c(0)·[1 − (T/T_c)²]   (Meissner expulsion)

Temperature — this lattice's T_c is 92 K (YBCO-style cuprate). Cross below it and the electron stream snaps from a jittery random walk into a smooth persistent current loop.
Applied field — a magnetic field the superconductor must expel (Meissner effect) to stay superconducting. Push it past the critical field B_c while cold and the condensate quenches back to a normal, resistive state.
Cooper pairs — toggles the bonds drawn between paired electrons so you can see the pairing mechanism itself, without changing whether the lattice is superconducting.
Test magnet — a small permanent magnet above the sample. Below T_c and B_c it hovers, levitated by the expelled field (Meissner effect); above either threshold it settles onto the surface.

Real-world relevance: this is the same physics behind MRI magnets, maglev trains and REBCO fusion-reactor coils — all rely on a persistent, resistance-free current once the material is pushed below both its critical temperature and its critical field.

Lattice ion Electron Cooper-pair bond Test magnet

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