At low temperatures, many materials become superconductors — current flows without resistance. But how exactly does this happen if electrons were initially trapped in an insulator? Half a century ago, Philip Anderson suggested that the answer lies in a special quantum dance of particles. Now, his idea has been tested on a triangular lattice — a flat grid of atoms arranged like a honeycomb but with triangular cells.
In such a lattice, at half-filling, two different parent states emerge. With weak interactions, it's an integer quantum Hall insulator — electrons move strictly along the edges, and current is impossible inside. With stronger interactions, it's a chiral spin liquid, where the magnetic moments of electrons (spins) constantly fluctuate but do not freeze into order. The transition between them resembles a change in aggregate states: ice melts into water, but here it's not matter that melts, but topological order.
When a few extra electrons were added to such a system (a process called doping), superconductivity emerged. Moreover, on both sides of the transition, from the insulator and from the spin liquid, electrons formed pairs with the same pattern (d+id type). But here's the surprise: the very ability of current to flow without loss, or superfluid stiffness, sharply increased near the critical point where one state gives way to the other. The order parameter, a measure of how strong the pairs are, barely changed.
Thus, for the first time, using neural network methods, it was shown that topological superconductivity can arise from a continuous quantum phase transition. The work opens the way to searching for materials where superconductivity can be controlled by slightly changing conditions (pressure, composition, or magnetic field) and entering the vicinity of the critical point.
The triangular lattice used in the model is found in real materials, for example, in some layered cobaltates, where cobalt atoms form a triangular grid, and electrons can behave in a similar way.
In Peter Watts' novel Blindsight, alien creatures use quantum states for information processing — perhaps such transitions between topological phases underlie their computational abilities.