How Electrons, Repelling Each Other, Tie Knots in an Atomic Chain ⚡ экспресс
The interacting SSH model is an ideal system for studying the connection between topological insulator phases and electron-electron interactions. Polarization density as a topological invariant in the low-energy sector of the one-dimensional SSH model has been studied. The topological invariant is formulated through Green's functions, and its behavior has been derived from Thirring field theory. It has been shown that in the continuous theory, polarization density describes standard topological phases but contains an additional factor related to the scaling dimensions of the fields. This was interpreted as a measure of the modified charge of new excitations. Two contributions have been identified: Renormalization of the electron charge e in the Fermi liquid due to the smearing of quasiparticles, and the topological charge of the soliton arising in the bosonized version of the Thirring model — the sine-Gordon model.
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.