Condensed Matter Ep 6: Superconductivity

On the eighth of April, nineteen eleven, Kamerlingh Onnes pumped a mercury thread down to about three kelvin and the resistance vanished — and he read it as confirming his own prediction that a pure metal slides smoothly to zero. He was wrong, and it took him half a year to find out. The cliff arrived on the twenty-sixth of October: within a hundredth of a degree, at four point two kelvin, from unmeasurable to a tenth of an ohm. Nothing slides like that. He suspected a short circuit first, and looked for one. And then twenty-two years passed before anybody discovered the property that actually defines the state. Zero resistance is not it. A perfect conductor would trap whatever field was threading it when it cooled — its final state would depend on its history, which means it has no thermodynamic state at all and no free energy to write down. What Meissner and Ochsenfeld found in nineteen thirty-three is that a superconductor *expels* the field either way. History-independence is what buys you a phase, a boundary, and everything Landau's machinery can do — seven years before anyone knew what the electrons were doing. The central puzzle is why pairing happens at all. The attraction between two electrons in a metal is absurd: an electron dragging a wake of displaced positive ions, an effect a ten-thousandth the size of the repulsion it is fighting. In free space an attraction that weak binds nothing — there is a threshold, and it is a *counting* fact, because the number of available states vanishes at zero energy. Cooper's move is to notice that the Fermi sea blocks everything below its surface, so the counting starts where the density of states is a large constant instead of zero. Constant density with an energy in the denominator gives a logarithm, and a logarithm has no ceiling: it can always be made to match one over any coupling, however small. Which means the normal state was never stable. The calculation destroys its own starting assumption. Then the number that settles the argument. Thread a superconducting ring, insist the wavefunction be single-valued, and the trapped flux must come in whole units of Planck's constant over the carrier's charge. Deaver and Fairbank in Stanford and Doll and Näbauer in Munich measured the period independently in nineteen sixty-one, back to back in the same volume. It comes out at *twice* the electron charge. One number, read off the spacing of an oscillation, and the thing doing the condensing is a pair. Also: the gap and what tunnelling sees; Ginzburg–Landau as Landau theory with a charged order parameter, and Gor'kov deriving it from BCS nine years later; type one versus type two, Abrikosov's vortex lattice — which he sat on for four years and then got the wrong shape for; what actually holds the magnet up over the cooled ceramic (not expulsion, which cannot suspend anything below a plate, but thousands of millions of pinned flux threads); the Josephson effect and the volt; and Anderson showing in nineteen sixty-three that the photon acquires a mass inside a superconductor — the mechanism particle physics borrowed the following year. The limit is stated plainly: BCS does not explain the copper oxides. Four specific failures, not a slogan. ——— Series: Physics - Tutorial · Grad level. Every equation spoken in full, no chalkboard required. Built by Fermi AI.