hubbard model

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.

The dance floor is packed: everyone moves on their own, no one holds hands. Suddenly the music gets louder and more rhythmic — neighbors start grabbing each other, forming pairs that spin in sync. That's roughly what the experiment looked like in the lab, where a cloud of lithium atoms, cooled to near absolute zero, was made to suddenly strengthen its mutual attraction.

An orchestra where every musician plays their own part, and the conductor tries to catch the overall melody. That's roughly how physicists view electrons in cuprates — ceramic materials that conduct electricity without resistance at temperatures above liquid nitrogen.

A piece of magnetite, an ordinary iron stone, behaves strangely. At room temperature, it conducts electricity, but cool it below minus 150 degrees, and its resistance jumps sharply. This jump, discovered back in 1939, physicists could not explain for nearly a century. A new study offers a solution.

Picture a packed bus where every passenger is an electron. In a superconductor, passengers pair up and move in sync, losing no energy. But in high-temperature superconductors like cuprates, this idyll only works when extra passengers are added. If you drop some off, the pairs start acting strangely.

Superconductivity is when electric current flows without losses, like water through a perfectly smooth pipe. It usually occurs at very low temperatures, but there are materials where it appears at higher ones.

A hawk soars over a field, its wings tracing an intricate dance. Each flap, each tilt is not random but a combination of simple motions that can be broken down into components. Collective behavior in the air may seem intuitive, but behind it lies strict mechanics. Scientists recorded the hawks' movements using cameras that track the position of every point on the wing and tail.

In twisted bilayer graphene, electrons behave like people on a crowded bus: each takes up space and gets in the way of neighbors. The strength of this "reluctance to share space" is called the Hubbard parameter U. It determines whether the material will be a conductor or an insulator, but measuring U directly is very difficult.

The classic BCS theory of superconductivity, developed by John Bardeen, Leon Cooper, and Robert Schrieffer, describes the mechanism by which electrons pair up into Cooper pairs and move without resistance.

Snap the bottom of a soda can: it will dent inward and stay that way. Press again: it pops outward. That's bistability: a system with two stable states, like a light switch. An elastic arch is the simplest example. It can curve upward or downward, and to flip it, you need to apply force.

Electrons in a conductor usually behave like a gas: they dart around chaotically, collide, and don't hold formation. But if you spread them far apart and cool them down, their mutual repulsion can force them into place, like attendees in an overcrowded hall who settle into every other seat.

Ordinary wires: electrons jostle, lose energy, and heat up: that's resistance. In superconductors, some electrons pair up in sync, like dancers swirling without collisions. But these pairs hide: you can't see them directly, only infer their presence from flawless coordination.