edge states

The triptycene molecule resembles a three-pointed star with rigid arms. When such stars are scattered on a lead surface, they spontaneously assemble into a pattern like a woven basket: triangles and hexagons alternate, and at each node sits not one star but a pair.

In a narrow corridor, people walk in rows rather than as a crowd. The number of rows depends on the width of the passage. In graphene, this corridor is a quantum point contact — a constriction where electrons move ballistically without scattering.

A vortex in a magnetic material is like a whirlpool, but instead of water, the directions of magnetization twist. An electron flying through such a vortex feels not just a magnetic field, but a curvature of space: its path bends as if it were rolling down a funnel with a narrow neck.

Take two thin sheets of a semiconductor. One is saturated with free electrons, like a packed café where every table is taken. The other, by contrast, is full of empty spots—'holes' eager to be filled. When these sheets are brought close together, a spark of attraction jumps between them: electrons and holes begin to feel each other across the thin gap.

In a pot of boiling water, steam bubbles appear and disappear — a similar struggle takes place in two-dimensional materials. Here, electrons both create magnetism and try to extinguish it.

A thin silver thread nearly as long as a hair's width, and inside it, pristine quantum laws hold sway. Physicists built a conductor where electrons can only move forward or backward, like on a perfectly straight single-lane road with no shoulders. On such a road, any pothole or pebble would normally destroy the fragile quantum state.

A thin sandwich made of two different materials. You run an electric current through it, and the top slice magnetizes in one direction, the bottom in the opposite. This isn't a magic trick; it's the layer Edelstein effect, just described by physicists.

In the world of two-dimensional materials, states sometimes emerge that are as extraordinary as they are fragile. One of them — the fractional anomalous Hall crystal (FAHC)—is like a quantum centaur: half ordered lattice, half topological liquid.

In a world locked in a crystal lattice and cooled nearly to absolute zero, matter knows how to hide its deepest secrets. A quantum spin liquid is a state where electron spins never freeze, even at zero temperature, remaining in an eternally flickering superposition.

A superconductor is like an ideal highway with no traffic lights: electrons race along without hindrance. But apply a voltage, and the picture changes. In a new experiment, physicists found that an electric field penetrates the superconductor and creates a mixed regime inside.

Two dice lie in different rooms. If they are 'entangled,' a roll of one instantly determines the outcome of the other — even at a distance. In the quantum world, such a link is called steering: one party, by performing measurements on their side, seems to dictate the state of the partner.

A long, narrow pan, and a thin pancake sets in uneven stripes. For decades, scientists saw a similar picture when modeling the behavior of electrons in superconductors — materials that conduct electricity without loss. They used elongated "cylinders," and the result was always the same: rigid magnetic "stripes" that were thought to hinder superconductivity.

A balloon doesn't deflate all at once: first, dents appear on its surface, which run, merge, and finally the balloon shrivels into a point. Domain walls behave in much the same way — thin partitions that divided space in the first moments after the Big Bang.

River water often swirls into funnels. But in semiconductors, the foundation of microchips, electrons at low temperatures and high purity also turn into a fluid. If you create a circular cavity, vortices appear, just like in a river backwater.

A fabric that stretches lengthwise but not crosswise. That's roughly how a semi-Dirac material works: electrons can move freely in one direction but barely budge in the other. Because of this unusual anisotropy, special tracks, one-dimensional channels, emerge at the edges of the two-dimensional crystal. Electrons race along them only along the perimeter, like water in a trough.

A crystal that looks like a stack of pancakes was placed on a smooth substrate of magnesium oxide. The result was a film only a few hundred atoms thick. When they ran a current through it and switched on a magnet, the resistance jumped by nearly a quarter—22.5% in a 9-tesla field. Inside the film, electricity is carried by two streams of particles.

Imagine a triangular grid with tiny magnetic arrows at each node. Electrons, the charge carriers, run across this grid. Usually, the arrows align simply: all pointing the same way (ferromagnet) or alternating in the plane.

A mosaic floor made of many small tiles, each turned in a different direction. It seems that any pattern trying to cross such a floor would get scrambled and vanish. That's how people usually think about disorder in crystals: if atoms aren't arranged in a perfect lattice, delicate quantum effects should fall apart.

A superconductor is like a city where electric current flows without traffic lights or jams. But the crystal UTe2 has a quirk: its surface follows different rules than its interior. On the tellurium atoms sitting at the surface, electrons found a 'loophole'—states with energies that are forbidden inside the crystal.

Water in a stream doesn't flow in a uniform sheet; it carves winding paths where the current runs faster. Electrons in a Hall thruster, a device that pushes a spacecraft with a jet of plasma, behave much the same way. Inside the thruster, a magnetic field confines electrons, which ionize the gas and produce thrust.

Two layers of a magnetic material, rotated relative to each other by fractions of a degree, like two slightly offset screens on a window. In their normal state, they don't produce anything special, but at a certain twist angle, an unexpected effect emerges.

The quantum Hall effect has long been suspected of superfluidity — the ability to flow without friction. Imagine a cook following a recipe: for each unit of magnetic flux, he must add exactly a certain number of electrons.

A cooled layered crystal resembles a stack of thin sheets, with electrons wandering between them. At around 17 K, tiny regions appear where electrons line up into a wave, like ripples on water frozen in place. These regions are called charge puddles, and they were previously thought to be static.

In layers of molybdenum telluride twisted at a specific angle, electrons behave unusually: they can split into parts. This is akin to a whole pie suddenly being cut into perfectly equal slices, even though there's only one knife. In ordinary materials, the electron's charge is indivisible, but in these layers, under strong cooling, states emerge where the charge splits into three parts.

A superconducting qubit is a tiny electrical circuit that behaves like an artificial atom. In its normal state, current flows through it without resistance, and the energy levels are evenly spaced, like steps on a staircase. But if a single electron gets stuck in the circuit, everything changes.

If you force water through a narrow neck, the flow speeds up right at the edge, and a whirlpool forms behind the obstacle. Electrons in ultra-clean two-dimensional materials, such as a thin layer of graphene, behave in much the same way.

Graphene is a carbon sheet just one atom thick, a fantastic conductor. But its surface is crinkly, like a wrinkled tablecloth that hasn't been ironed. Scientists built a 'sandwich': two of these sheets pressed together with a non-conductive spacer in between. They iron out each other's folds, like two halves of a sandwich making the surface perfectly even.

Quantum particles in a strongly disordered environment behave like dancers executing steps in sync: each knows its own move and never collides with others. This kind of coordinated, frictionless flow, superfluidity, unexpectedly emerged in an experiment on a superconducting quantum chip.

Picture a globe divided into cells: near the poles they shrink into narrow wedges, while at the equator they stretch into wide bands. If you connect random points on such a globe with lines, the compass arrows will lie: connections will point to where there are more cells, not where the flows actually go.

A stone falls into water, and ripples spread outward. In the quantum world, a magnetic impurity (that pebble) in a metal perturbs the surrounding electrons, and they form a special cloud around it. This is called the Kondo cloud. Like ripples on water in the dark, it long remained elusive.