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Superconductivity and Cooper pairing

A superconductor carries electrical current with zero DC resistance below a critical temperature and expels magnetic flux from its bulk through the Meissner effect. Zero resistance alone would describe a perfect conductor; flux expulsion shows that superconductivity is a distinct thermodynamic phase.

In conventional superconductors, electrons near the Fermi surface can experience an effective attraction mediated by lattice vibrations. Although the bare Coulomb interaction is repulsive, this retarded interaction allows electrons with opposite momenta and spin to form correlated Cooper pairs.

A Cooper pair is not a tightly bound molecule in ordinary space. Many pairs overlap and condense into a coherent many-body quantum state. Exciting ordinary quasiparticles requires breaking the paired state across an energy gap $\Delta$, so low-energy scattering channels are strongly suppressed.

Magnetic fields penetrate only over a finite length scale and superconducting current can flow only up to critical fields and currents. Type-II superconductors admit quantized magnetic-flux vortices above a lower critical field while retaining superconductivity between vortices.

The magnetic flux quantum associated with paired charge $2e$ is $$\Phi_0=\frac{h}{2e}.$$ Its appearance in flux quantization is direct evidence of macroscopic quantum coherence.

Superconductivity illustrates how collective behavior can create properties absent from isolated particles. The relevant physics combines Fermi statistics, lattice excitations, phase coherence and spontaneous symmetry breaking rather than merely 'electrons moving without collisions'.