interlayer coupling

A stack of pages that has been flipped through many times remembers it: some sheets lie flat, others stick up, and creases remain here and there. Layered materials behave much the same way when ions enter them.

A door lock with two different keys: one turns easily, the other demands noticeable effort. That is how two layers of hexagonal boron nitride behave when twisted relative to each other. This material consists of boron and nitrogen atoms arranged in a hexagonal lattice, and its layers can sit in different registries, like two identical grids shifted by different angles.

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.

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.

A sheet of paper with magnetic properties: that's roughly what the new material 1T-CrS₂ is like. Its layers are held together by weak forces, like the pages of a notebook, but each layer is a true magnet.

Two ropes glued along their length naturally twist into a double helix. That's how DNA works — except the glue is hydrogen bonds between bases, and the stiffness comes from the chains themselves.

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.

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.

A thin film of molybdenum disulfide, less than a micron thick, acts as a miniature photon-pair factory built right into a fiber-optic connector. Ordinary optical fiber is not just a glass thread for the internet.

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 layered cake of atomic planes of nickel and oxygen: that's how bilayer nickelates are built. Two such planes are separated by a spacer layer. If an oxygen atom sits in that spacer, it acts as a bridge: it links the layers and triggers a state in which electrons move without resistance.

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.

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.

Turbulent flow near a wall resembles a crowd where everyone pushes in their own direction. Vortices form and break apart, creating chaotic jolts. If you embed a defective acoustic lining into the wall, like a tuning fork that rings only on one note, it starts responding only to a narrow range of frequencies.

Rubbing a comb against wool creates a spark. A similar principle works in triboelectric nanogenerators — devices that convert mechanical touches into electricity. The problem is that ordinary materials produce a weak charge.

Two sheets of graphene — carbon film one atom thick — without a twist resemble a harbor clogged with shoals: lithium ions either run aground or rush past without stopping. But a 9.43° twist lays out a perfect fairway. The ion ships dock securely to carbon 'piers' and immediately cast off without losing speed.

A sheet of graphene one atom thick is like a flexible metal mesh through which electrons zip almost unimpeded. Stack two such sheets with a slight twist, and the material's properties change dramatically: it can become an insulator that blocks current.

Superconducting circuits often rely on Josephson junctions — places where current flows without resistance through a thin barrier. Typically, this barrier is an oxide layer, but its properties are hard to control at the nanoscale. In this new work, the barrier is a thin layer of niobium or titanium nitride sandwiched between niobium layers.

Certain materials, near absolute zero, superconduct: electricity flows without loss. The critical temperature starts this. John Bardeen and colleagues explained that atomic vibrations glue electrons into Cooper pairs.

The layer of cells lining internal organs is like a crowd in a packed subway: everyone stands shoulder to shoulder, but sometimes the crowd starts to flow, and people slip past each other. Biologists call this behavior a transition from a jammed, solid state to a fluid one.

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.

Light hits a thin film, and an electric current instantly appears in it. This is how a pair of two materials works: molybdenum disulfide and cobalt. The first is a semiconductor, the second is a magnet. Between them, as it turns out, an invisible intermediary layer is born.

The layered material (SnS)1.15(TaS2) resembles a stack of paper, where the sheets conduct electricity and the interlayers prevent them from sticking together. At ambient pressure, this material conducts current without resistance, making it a superconductor.

An ordinary piece of semiconductor weakly changes the color of light passing through it. For decades, physicists worked around this limitation by placing the crystal in clever surroundings, but the material itself remained the same. Now researchers have assembled a "sandwich" of alternating thin layers of gallium arsenide and aluminum gallium arsenide.

A magnet that stacks up like a pile of pancakes: that's how the material CrSBr is structured. At low temperatures, each layer is magnetized, but neighboring layers point in opposite directions, and their magnetic fields cancel each other out. This order is called antiferromagnetic, and it's fragile: just a slight warming demagnetizes the layers.

The NbSe2 crystal is like a stack of paper: layers lie tightly packed, and their properties blend together. Chemists found a way to pry this stack apart by nearly double — inserting long organic molecules between the layers like spacers. Now each layer behaves as if it were all alone, just one atom thick.

Inside a high-power transistor, heat escapes through junctions between different crystals, like water through narrow locks. For aluminum and gallium nitrides, key materials in power electronics, that lock is often a thin layer of their alloy. It is added deliberately or forms on its own during crystal growth.

Vanadium oxide is a material that can act as an insulator, not conducting electricity, or as a conductor, like a metal. The switch takes trillionths of a second, and that's what makes it a candidate for ultrafast electronic devices. But exactly how it happens has long been a mystery.

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.