11. Superconductivity and the Anderson-Higgs connection
Pairs, current and magnetic response #
In conventional BCS theory, electrons form Cooper pairs and a coherent condensate. Zero resistance and magnetic screening are distinct observable properties. The exponential field profile assumes a planar surface and the local London limit. The quoted gap relation applies to weak-coupling conventional superconductors; it is not a universal formula for every material.
11.1 What superconductivity is not #
Zero DC resistance in a superconductor is not explained by “ordinary resistance disappearing at low temperature plus photons becoming massive so radiation stops.” A conventional BCS superconductor forms a coherent condensate of Cooper pairs and develops an energy gap. Electromagnetic response is reorganized, producing persistent current and the Meissner effect. Theory of Superconductivity (1957)
For weak-coupling BCS theory,
This is a model result for conventional weak-coupling superconductors, not a universal equality for every superconductor.
11.2 London penetration depth #
The magnetic field inside a simple superconductor decays approximately as
where is the London penetration depth. A Proca-like equation for the electromagnetic response can be written heuristically as
This mathematical resemblance to a massive gauge field motivated Anderson’s insight that a gauge field interacting with a condensate can acquire an effective gap without destroying gauge consistency. Plasmons, Gauge Invariance, and Mass (1963)
11.3 Why the analogy to the Higgs mechanism is profound but limited #
The condensed-matter Anderson mechanism and relativistic Brout-Englert-Higgs mechanism share the central idea that gauge-field excitations can become gapped through coupling to an ordered medium/field. But a laboratory superconductor is a material with a preferred rest frame, finite density, lattice, and electromagnetic environment; the Standard Model vacuum is not literally a superconductor made of Cooper pairs. Analogies are valuable when their limits are stated.