When Repulsion Gives Birth to Pairs: A New Perspective on the Riddle of Superconductivity ✛ ✎ ✦

For nearly forty years, high-temperature superconductivity in cuprates has remained one of the deepest riddles of condensed matter physics. In ordinary metals, electrons pair into Cooper pairs thanks to lattice vibrations, but here the isotope effect is extremely weak. This points to the dominant role of electronic interactions. But how can one overcome the crushing Coulomb repulsion? Back in 1965, just a few years after the triumph of BCS theory, John Bardeen voiced a visionary thought: in a many-body environment, repulsion can be dynamically screened, turning into effective attraction. Curiously, Bardeen later shared a second Nobel Prize precisely for BCS, yet his insight about screening went far beyond it. The idea waited decades for a mathematical embodiment.

Imagine a crowded hall: two strangers, feeling mutual dislike, instinctively move apart. But the crowd, pressing in from all sides, compresses them, and they end up side by side — against their own will. In cuprates, the role of such a “crowd” is played by extra holes in the CuO₂ planes. Their virtual hops between copper d-orbitals and oxygen p-orbitals, generated by quantum fluctuations, create a complex screening cloud. The Pauli principle and Coulomb prohibitions turn into a paradox: two holes, repelling the environment, unwittingly attract each other.

The key step is to realize that in a coherent superposition of states allowed by quantum entanglement, virtual processes become the decisive force. The formalism of quantum field perturbation theory shows how the system’s energy restructures, making the phase with a hole pair energetically favorable. Mathematically, this is expressed by the condition of negative pairing energy: U = E₂ + E₀ − E₁ − E₁' < 0. Generalizing the triad model to the whole lattice via quantum-statistical averaging yields a phase diagram remarkably close to experiment. At εp = 0.4 eV and Upd = 1.55 eV, a superconducting dome emerges, and alongside it — pseudogap and strange metal, like shadows following the doping.

This work changes the very strategy of searching for new superconductors. Instead of hoping for a lucky phonon accident, one can purposefully design materials with strong superexchange and a finely tuned energy gap εp. Ahead lie verification of predictions in nickelates and iron pnictides, precision ARPES experiments, and numerical modeling. If the mechanism is confirmed, the road to room-temperature superconductivity will cease to be a utopia, and energy and transport will gain a new, almost magical reality — on a solid quantum foundation.