Electrons repel each other through the Coulomb force, yet inside a superconductor they form pairs of two (Cooper pairs). The key is the slow response of the lattice: when a fast electron passes by, the heavy ions are pulled toward it only after a delay, so a dense “wake” of positive charge remains after the electron has gone. If another electron is drawn to that wake, the two electrons feel an attraction at a distance of several tens to several hundred nm without ever coming close to each other directly (the Coulomb repulsion is screened out at 0.1 nm). In ① you watch this process as a real-space animation (heavy versus light elements, the isotope effect). In ② you vary the pair size from the BCS limit to the BEC limit and see the “superconducting bubble” of Lecture 7, slide 34 (in the BCS limit, giant bubbles overlap, each sharing 10⁸ or more electrons in a real metal; in the BEC limit, the bubbles shrink to small molecules), as well as how thermal fluctuations break pairs. In ③ you plot the real-space wave function of a Cooper pair. For the equations, derivations, and references, see the explanation page (in Japanese).
Companion page: Explanation — Electron–Lattice Interaction and Cooper Pairs, the BCS–BEC Crossover (cooper-pair-derivation.html, in Japanese) | Related: Superconductivity Simulator (GL, BCS, and the Higgs Mode), Relativistic Quantum Mechanics Simulator | Mochizuki Research Group, Tokyo University of Science