Electrons repel — yet cool a metal enough and they pair up. One electron tugs the lattice of ions, the ripple attracts a second electron, and the two bind into a single object that behaves like a BOSON. Below a critical temperature all the pairs lock into one quantum state and flow with ZERO resistance: a superconductor. Slide the temperature down and watch the pairs form.
Cooper’s result (1956): against a filled Fermi sea, an arbitrarily WEAK attraction binds two electrons into a pair — the phonon-mediated attraction (one electron distorts the ion lattice, a second is drawn to the distortion) overcomes their Coulomb repulsion near the Fermi surface. Below the critical temperature Tc a gap Δ(T) opens (the pair binding), all pairs condense into ONE macroscopic wavefunction, and current flows without scattering — superconductivity (BCS, 1957). A fail-loud self-check throws unless the binding is positive below Tc and exactly zero above. ◆ real condensed-matter physics, node-verified.
A schematic gap Δ(T) rising below Tc (the BCS temperature dependence in spirit, not the exact self-consistent integral); the two-electrons-bind-into-a-boson-below-Tc and the zero-above are the exact, defining facts.