How Electrons, Repelling Each Other, Tie Knots in an Atomic Chain ⚡ экспресс
The effect of electron-electron interaction on polarization density in a one-dimensional SSH topological insulator has been studied. Using Thirring theory (of low-energy fermions), it was analytically shown that the topological invariant gains an additional factor due to the scaling dimensions of the fields. This was interpreted as a change in the effective charge: a contribution from the 'smearing' of quasiparticles in the Fermi liquid and the topological charge of solitons from the bosonized model (sine-Gordon). Even in the simplest chain, collective effects give birth to new particles with unusual charges — like a wave in a crowd changes the 'weight' of each.
A chain of carbon atoms resembles a rope with weights. Where the tension is slack, waves get stuck—this is how materials where current flows only at the edges are built. But when electrons start repelling each other, knots spontaneously form in this rope. These knots are not just a disturbance. They alter the collective charge of the whole chain. Repulsion adds two corrections to the charge of each particle: the first is the familiar 'coat' of neighboring electrons, the second is a knot that can't be untied. This knot travels along the chain without changing shape, like a sailor's knot on a wet rope—only it tightens itself.
Such effects already appear in thin conducting tracks on crystals. Understanding how repulsion generates fractional charge will bring us closer to creating electronics immune to noise—where signals run along unbreakable knots.
🎯 In everyday life, the electron charge is an indivisible constant. But inside matter, where electrons are crowded, their effective charge can change, like a coin passed from hand to hand losing or gaining a 'commission'. And in the described knots, this commission goes so far that the charge splits in half.