crystal lattice

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.

A deck of cards in which each card is slightly rotated cannot lie flat: the backs and faces will never align. But if the cards are flexible, they will start to adjust, shifting by fractions of a millimeter to find the perfect match. Something similar happens inside crystals when two thick layers of MoS2 or MoS2 with WS2 are stacked with a twist of 1–2 degrees.

In a thin layer of liquid crystal, molecules usually lie like matches in a box — aligned in one direction but randomly oriented: some point up, others down. To make all the matches point the same way, you need a special molecular architecture. Scientists have found a chemical trick that does this almost automatically.

The laser beam in an optical tweezer is not just a spot of light but a force bag. A particle caught in it usually rolls toward the brightest point, like a ball into a dimple.

Inside a piece of aluminum, atoms are arranged in neat rows, like bricks in a wall. But sometimes a row ends before reaching the edge, and a "step" appears in the crystal, which physicists call a dislocation. These defects determine how strong, ductile, and how a metal behaves under load.

In a crystal of rutile niobate, nickel atoms sit in oxygen cages — octahedra. Sometimes one atom loses an electron, and the charge hops to a neighboring atom like a baton in a relay race. But this hop is not random: it is triggered by vibrations of the entire lattice.

The crystal is like a city with different streets: on some, cars drive fast and far, on others, they crawl and get stuck. In the layered material CrPS₄, magnetic waves that carry spin (a particle's intrinsic angular momentum) behave the same way.

A piece of metal smaller than a millimeter, when cooled to minus 256 degrees Celsius, behaves like a kaleidoscope: in one corner, magnetic arrows align in neat rows, while in a neighboring corner, they twist into a screw. This was observed by directing a narrow X-ray beam at the sample and slowly sweeping it across the surface, like a flashlight along a dark wall.

In a pot of water, microscopic spheres, colloidal particles, are floating. Each sphere is coated with long polymer chains that look like a brush and carries an electric charge. If you get the temperature and solution composition right, the spheres start arranging themselves into ordered patterns — crystals.

Every battery or supercapacitor has an unassuming player — the polymer glue. It binds the active material particles together and helps them stick to the current collector. Previously, it was considered just inert mass: it's there, as long as it doesn't get in the way. But in this work, the glue takes center stage.

In a crystal, heat travels on waves. Atoms vibrate, and these vibrations, called phonons, carry energy from the hot edge to the cold one. For a long time, it was believed that if phonons hit resonance (their frequencies exactly match) and can exchange energy, heat would flow like an avalanche. It turns out that's not the case.

The crystal Mn₂Mo₃O₈ resembles a tiny city where manganese atoms are arranged in strict order: their magnetic moments (tiny internal arrows) point alternately up and down. This state is called collinear altermagnetism.

A guitar string plucked exactly at its middle produces only odd overtones. The same prohibition holds in symmetric crystals: when light knocks out electrons, their re-emitted radiation contains only odd harmonics. But physicists have found a way to bypass this rule — without shifting a single atom. The secret is electric current.

Moiré patterns are familiar to everyone. Two combs with different spacing, placed on top of each other, show dark fringes. Something similar has emerged in time. Physicists took a cloud of Rydberg atoms, particles with unusually large electron orbits, and illuminated it with two lasers.

A quantum chain is like a string of lights, where the bulbs are the spins of particles. Ideally, all bulbs glow in sync, following a common rhythm: that's symmetry. But if you cut off a piece of the string, the rhythm can get out of step: within that segment, symmetry is broken. Physicists study a chain of strongly interacting particles (the XYZ model).

A solid under a microscope is not a monolith at all. In glass, polymer, or solidified resin, atoms are arranged randomly, and as a result, the material's properties vary from point to point. On large scales, we are used to describing them with smooth fields, like temperature or pressure in a room. But when you zoom down to a few atomic layers, that smoothness disappears.

In extreme cold — minus 268 degrees — a crystalline perovskite film starts transmitting light differently depending on its polarization. The beam seems to split in two: one part travels slightly faster, the other slightly slower.

A row of soldiers turns in unison at the command. In magnetic materials, the soldiers are the spins of atoms — tiny magnetic arrows. In an ordinary magnet, they all point the same way, but in a triangular lattice, things are trickier: neighbors interfere with each other, leading to an intricate dance.

Hit a table, and the sound quickly fades. Elastic waves in solids usually behave like ripples on water: they spread from the source and die out. But there is a way to make them freeze in place — by creating a 'flat band' in the frequency spectrum. This is a range where waves lose their speed and pile up, like cars in a traffic jam.

In an ultrathin sheet of four-layer graphene, electrons can behave like a frozen liquid. When cooled strongly and subjected to an electric field, they stop darting around and line up into a regular pattern — a Wigner crystal. It's similar to how water droplets on a frosty morning turn into ice honeycombs.

A tuning fork struck once rings pure and long. But if you shake the fork itself while it sounds, the tone wavers and dies out quickly. Something similar happens to electrons in any piece of matter. Atoms in a lattice never stay put: thermal vibrations keep them jittering.

Every atom in a magnet is like a tiny compass needle. These needles can point in different directions, and their collective dance determines the material's properties. But calculating this dance directly, atom by atom, is a task too heavy even for supercomputers. The new model, named STEP, takes on the role of a conductor.

A mosaic of squares and triangles covers the floor without gaps, yet it never settles into a simple repeating pattern. Such a pattern is a quasicrystal — a solid where atoms are arranged not periodically but according to a pattern of several waves of different lengths. These waves are incommensurate with each other, and together they create long-range order.

Crystals glued to the outside and inside of a metal wall act as an invisible channel. One, receiving current, starts to tremble, and these vibrations, like ripples on water, spread out in all directions through the metal. The inner crystal catches this tremor and generates electricity again.

A light wave is like a rope that has been shaken: it oscillates in a specific plane. This property, polarization, reveals the shape and composition of objects. But capturing it is not easy, especially when you need to cover a wide range of colors. Usually, this requires bulky systems of lenses and filters.

An orchestra of billions of cesium atoms struck a single note, and it sounded for 17 hours without fading. That’s no exaggeration: Chinese physicists created a continuous time crystal with a record-breaking lifespan. A time crystal is a system that breaks time symmetry, spontaneously pulsating in an unchanging rhythm.

An ionic conductor resembles a crowded bus where passengers (ions) try to squeeze toward the exit. Previously, it was thought that fast exit could be achieved either by a gently swaying bus (soft lattice) or by passengers standing in chaotic order (geometric disorder). The new work shows these are not two different tricks but the same one.

A pendulum that swings on its own, without any winding — in the quantum world, such 'pendulums' are called time crystals. In them, rhythmic motion arises spontaneously and does not decay. But until now, controlling this rhythm was nearly impossible: any intervention threatened to destroy the fragile order.

A tuning fork produces a pure tone, but if you strike it too hard, it starts to rattle, and a musician might mistake that rattle for complexity in the sound.

Electrons in a crystal are like cars on city streets: some race down avenues, others get stuck in traffic jams. In certain lattices, motion freezes entirely — velocity stops depending on energy, and electrons become "flat." This isn't a traffic jam but a special rhythm of the network where waves cancel each other out.

A sugar cube squeezed between your fingers will almost certainly crumble rather than compress evenly. A similar challenge faces quantum computer builders. They need to slightly stretch or compress miniature silicon plates — qubits are later placed on them.

A tellurium crystal resembles a tiny spiral staircase: its atoms are twisted into a helix. When heat runs through such a crystal, it is carried not by electrons but by sound waves — vibrations of the lattice itself. These waves don't just push back and forth; they also rotate around their axis like a spinning top.

Time crystals are quantum phases of matter that spontaneously oscillate, like a tuning fork with an infinitely decaying echo. If an ordinary spatial crystal repeats an atomic pattern in space, breaking translational symmetry, a time crystal exhibits periodicity in time, breaking time translation symmetry.

A time crystal resembles an eternal clock: its atoms spontaneously perform rhythmic movements. In ordinary clocks, a pendulum is driven by a spring or battery, but here the motion arises without an energy supply — the system simply returns to its initial state at regular intervals. This idea was proposed by Frank Wilczek in 2012.

Imagine a packed dance floor where dancers glide without any friction — passing through each other without a touch. That's a superfluid. In a neutron star's crust, neutrons could behave this way, but a rigid lattice of ions gets in the way, like suddenly sticking the dance floor full of pillars.

Light can be more than just a beam: it can be a precision ruler. If you take very short pulses, shorter than a fly's wingbeat, and fire them one after another, you get an optical comb: a set of colors spaced at exactly equal intervals, like the teeth of a comb. This rainbow lets you measure distances, time, and the composition of materials with unimaginable accuracy.

The pendulum of an old clock swings because a spring mechanism gives it a regular nudge. Now imagine a pendulum that decides on its own when to swing, and does so with a steady rhythm, just because the room is warm and there's a slight draft. That's exactly how time crystals behave, born in clumps of light and matter inside a semiconductor chip.

An ordinary pendulum swings at the same frequency as the push it receives. But in the quantum world, you can create a system that responds to a push two, three, or more times slower, as if it has its own rhythm. Such systems are called discrete time crystals.

An infinite chain of atoms spaced at equal intervals. Shift the entire chain by one step, and the picture doesn't change. That's translational symmetry: the world looks the same wherever you look. You'd think such a simple rule would give rise to simple states, like a crystal lattice assembled from identical building blocks. But the authors counted those blocks anew.

A hot spoon in a cup of tea — heat runs along the metal from the hot end to the cold one. Textbooks describe this process as atoms jiggling and passing on their jolts to each other. But atoms don't just jiggle: they also spin, like tiny tops. Until now, physicists had no common language to describe both motions at once. The authors of the work built such a language.