monolayer

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.

Three voices merging into a single chord. In the physics of quantum materials, this image takes on a literal meaning: three layers of graphene, separated by thin spacers, force electrons and holes from different layers to move as a single fluid.

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.

Light passing by a tiny structure changes direction. If the structure is smaller than the wavelength of the light, it acts like a lens and focuses the light into a spot smaller than the wave itself.

Graphene, a two-dimensional carbon crystal, has long tantalized physicists with the hope of high-temperature superconductivity. Its electrons obey the relativistic equation of Paul Dirac, racing at tremendous speed, barely noticing each other.

Two passengers step into an empty car on a ring subway line and take their seats. After one full loop, they are surprised to find themselves in each other’s seats — even though nobody moved. That’s pretty much how monodromy plays out in vineyards — families of persistence diagrams, a method rooted in the work of Henri Poincaré.

Imagine a multilayered shell where metal and insulator layers alternate like pages in a book. Such a structure can make an object hidden inside invisible to an observer. Light bends around it as water smoothly flows around a smooth stone: no ripple, no splash — no reflection, no shadow.

Finding the right molecule among billions of options is like finding a single grain in a sack of rice. To avoid sifting through everything by hand, chemists increasingly turn to neural networks. But large models require powerful computers, while small ones often lack the big picture. GLACIER tackles this problem like a bright student learning from several mentors at once.

Crocheting, but instead of yarn you have individual molecules, and instead of a hook, a gold surface. Until now, attempts to knit such molecules into a smooth fabric ended in a tangle: the threads hooked where they shouldn't, and the pattern went awry. A team of scientists has found a way to fix this.

A crystal is like a row of soldiers on a parade ground: every atom is in its place, and electrons march through it in neat waves. An amorphous material is like a crowd at a train station, where there is no order, just a jostling throng. In such a crowd, an electron usually gets stuck quickly, like a person trying to push through a dense mass of people.

Tile a floor with identical triangles, and you get a boring repeating pattern. But what if you want the pattern to never repeat, yet use just one tile? For a long time, mathematicians were sure it couldn't be done: you'd need at least two different shapes. The famous Penrose mosaic is a case in point: rhombi with acute and obtuse angles arrange into an infinitely varied but strictly ordered pattern.

A sheet of paper weighs almost nothing, but stack a hundred sheets and you get a noticeable pile. That's roughly what scientists did with a material that excels at converting one color of light into another, but only when it's just one atom thick. A single layer is like a single sheet: it works beautifully, but it's too thin to produce much light.

A thin film of soap on your hand conforms to the shape of your palm, but clench your fingers and the tension changes unevenly. A monolayer of molybdenum disulfide on a graphite substrate behaves in a similar way.

A sheet of graphene is a mesh of carbon atoms one atom thick. Even the slightest contamination shows up on it, like dust specks on eyeglass lenses. Ten years ago, researchers learned to hide graphene between layers of boron nitride, like placing a fragile sheet between two pieces of plastic wrap.

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.

If you dump a handful of coins on a table, the surface becomes bumpy. But add more coins, and they spread out into a flat layer on their own. Something similar happens when you deposit ultra-thin films of individual molecules onto a substrate. At first, islands appear on the surface — molecules cluster together like people in a queue. The film gets rougher and rougher.

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.