edge state

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.

An ultrathin film of tellurium, tantalum, and iridium atoms behaves as an insulator in its interior but conducts current along its edges. This property, the quantum spin Hall effect, promises lossless electronics. However, calculations of the electronic structure did not predict such a phase for the 1T-TaIrTe₄ monolayer.

Graphene, a sheet of carbon just one atom thick, can change its magnetic properties the way water changes shape: sometimes flowing, sometimes freezing into ice. In a new study, physicists peered inside this process for the first time using a sensor the size of a needle tip.

A highway where opposing flows are separated not just onto different sides, but onto two independent roads: each with its own entrance and exit. Something similar happens to electrons in a new type of topological insulator described by the authors of the study.

A house with cork walls suddenly gets covered in copper sheets, but only when frost sets in. That's roughly how FeSb₂ behaves when made into a film just a few atomic layers thick. Under normal conditions, it's a narrow-gap insulator: electrons sit tightly in place like spectators in an overcrowded hall.

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.

Cut a spin chain, and particles without an energy gap appear at the edges. They are called zero modes, and they live only at the boundary. Previously, they were counted using complex topological invariants, but now there is a simpler way.

Bending a sheet of paper is easy. But compressing it by pushing from the edge is a different story: the paper will crumple but barely transmit the force further. That's how ordinary elasticity works — deformation depends on where and how you press. The new three-dimensional lattice pushes this contrast to the limit.

The book is open to the middle. Current runs along the spine, while the pages remain cool. That's roughly how a two-dimensional topological insulator works — a material where electricity flows only along the edges, while the interior stays still.

In the new model, each active particle has an internal rhythm: it spins either left or right. Chirality is key: some twirl clockwise, others counterclockwise. But when such a particle bumps into an obstacle or a neighbor, it flips its spin, like a figure skater who, after touching the board, explodes into a reverse pirouette.

A sheet of rubber is squeezed from two sides. At first glance, it's just deformation. But inside, deep within the material, a hidden order awakens. This is not just wrinkles on the surface. It's the birth of special zones where vibrations become trapped, as if in a cage. Previously, it was thought that such effects require intricate lattices and periodic structures.

In a long corridor, a crowd of people tries to keep as far apart as possible. In a spacious hall, they would simply spread out, but here the walls squeeze them so tightly that they have to move single file, coordinating every step. Electrons in graphene layers twisted by a tiny angle behave in a similar way.

Strike a tuning fork: it rings and gradually fades. Roughly the same happens to the edges of special quantum chains when they are suddenly "shaken": oscillations decay, and memory of the initial state disappears. But physicists have discovered that in some cases this ringing lasts surprisingly long.

In the Atlantic, a giant invisible conveyor operates: warm surface waters flow north, cool, sink, and return south. This circulation, AMOC, carries heat, making Europe noticeably milder than Canada at the same latitudes. But the conveyor isn't eternal: if diluted by fresh water from melting Greenland ice, the engine stalls.

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.

Two thin layers of a semiconductor were twisted relative to each other by 2.29 degrees, like two sheets of transparent paper with printed grids. Where the lines nearly align, a large pattern of dark and bright spots emerges. Electrons in this pattern behave very differently from those in a regular crystal.

Since time immemorial, physicists have dreamed of tunnels piercing the cosmos — wormholes, capable of connecting far-flung corners of the Universe in an instant.

Imagine a line of people holding hands but facing in opposite directions: some look north, others south. That's how a p-wave magnet is arranged. Electrons in it align their magnetic moments (spins) not randomly but in a strict wave-like pattern.

Light, discovered by Maxwell, behaves differently in different media. In a new study, researchers simulated a two-dimensional crystal that absorbs light and has magnetic properties. In it, light waves behave like passengers on a one-way escalator: they relentlessly move toward edges and corners, where they accumulate.

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.

Ordinary magnetic measurements only see the surface of a superconductor, where barriers and viscous flows of magnetic field get in the way. Inside, in the so-called intermediate state, superconducting and normal domains coexist, separated by thin walls. These walls can oscillate, but hearing them directly has been difficult.

A single-atom-thick sheet of tungsten telluride is like thin foil: electrons can't pass through because there's a band gap between their possible states, like a moat you can't jump across. Add two more layers, and the moat disappears; the material becomes a metal, and current flows. Add more layers, and the properties change again, as if someone is flipping modes with a single button.

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.

A struck tuning fork fades: its vibrations leak into the air. But there are systems where the oscillation does not decay, even though there are plenty of free waves around, ready to carry energy away. Physicists call such 'captured' states bound states in the continuum (BIC).

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.

A laser beam twisted into a spiral looks like a drain vortex in a sink: light moves not only forward but also in circles. Such vortex beams already help move tiny particles and transmit more data. But once they pass through an inhomogeneous medium, the vortex falls apart, like water from a leaky bucket.

Atoms settled along a chain of traps, like a line of coastal forts. Nearby, a quantum sea: a Bose-Einstein condensate (a substance with zero resistance, where particles move as a single wave).

A uranium crystal the size of a grain of rice was cooled to one-fiftieth of a degree above absolute zero. At such temperatures, heat is not transported chaotically but strictly according to the rules of the quantum world.

Certain materials, when placed in a strong magnetic field at low temperatures, exhibit a surprising property: their interior stops conducting, becoming an insulator, while along the very edge of the sample electricity runs like a river along a channel, always in one direction.

Two-dimensional bismuth on a silicon substrate is a promising material for future electronics. Its edges conduct current without loss, like a highway with no traffic lights. But bismuth itself is delicate: air and moisture quickly degrade its properties.

A chain of red phosphorus atoms is like a train where the cars are atoms and the couplers are chemical bonds. Sometimes the couplers are stronger, sometimes weaker, and that affects how electrons run through the train.

A stack of identical pancakes on a plate is just a stack. But if you arrange them with a certain order, something new suddenly appears: for example, a pattern that was not visible in each pancake individually. Physicists have performed a similar trick with thin layers of materials.

A sheet of carbon just one atom thick is placed in a strong magnetic field and cooled to thousandths of a degree above absolute zero. A microwave microscope slides along the sheet's edge, measuring how well that edge conducts electricity.

The crystal CeRh₂As₂ behaves like a switch: cool it down and it becomes a superconductor, then bring a magnet close and it abruptly jumps to another superconducting state. Such behavior is rare: most superconductors have only one state, but here there are two, separated by a sharp boundary.

The popping lid of a jam jar is the hero of this story. Press it, and with a loud click it flips from a convex to a concave shape. Exactly the same happens with a hinged beam inside each cell of a new mechanical lattice. Scientists assembled these snapping beams into a hexagonal grid, like honeycomb, but made of elastic plates. When one beam is sharply compressed, it snaps and pushes its neighbor.

Light from many tiny emitters — atoms or artificial "quantum dots"—usually scatters in all directions, like a crowd where everyone shouts on their own. But if you make them "sing in chorus," the flash becomes many times brighter.

Sound in a thin plate behaves like ripples on water: it travels, reflects off edges, and changes shape. But sound has a peculiar trait: it can pass through places where waves are forbidden to exist. It's as if ripples on a pond suddenly vanished before a stone barrier and reappeared on the other side, without going around it.

A quantum chip is like a musical instrument that goes out of tune at the slightest touch. In devices made from strained germanium, a material where atoms are slightly stretched for better conductivity, the main source of off-key notes is defects at the interface between the semiconductor and the insulating layer.

An ordinary insulator conducts no current, neither in its interior nor along its edges. A topological insulator is a different story: it remains insulating inside but conducts electricity without loss along its edges.

Electronic charge is a tumbleweed that moves camp depending on energy. In tungsten selenide (WSe₂) crystals, this is seen with utmost clarity: at a bias of −1.4 V, near the K point of the Brillouin zone, the maxima of tunneling current sit in the centers of hexagons, where there are no atoms.