twisted bilayer graphene

A Stradivarius violin can only be made from wood that grew under special conditions. For a long time, it was believed that graphene for delicate quantum effects had to be exfoliated from graphite with tape, and that a crystal grown in a test tube was incapable of such feats. This work shows that graphene grown from a gas mixture can sound like a Stradivarius.

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 Stradivarius violin can only be made from wood that grew under special conditions. For a long time, it was believed that graphene for delicate quantum effects had to be exfoliated from graphite with tape, and that a crystal grown in a test tube was incapable of such feats. This work shows that graphene grown from a gas mixture can sound like a Stradivarius.

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.

The mirror races along at nearly forty thousand kilometers per second. Light that strikes it bounces back, but changed, like a ball volleyed by a racket in mid-swing. That's exactly the kind of mirror scientists have built inside an ultra-thin glass thread filled with hydrogen. First, a powerful laser pulse is sent down the fiber.

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 water pipe: the wider it is, the more water flows through. In superconducting contacts — Josephson junctions (bridges through which current flows without resistance)—it's usually the same: the better the material conducts in its normal state, the larger the superconducting current that flows through it.

Hidden within thin layers of tantalum selenide (TaSe₂) is a property that defies conventional physics. When guest atoms were added between the layers of this material, the structure lost its center of symmetry, and inside, superconductivity with armor emerged.

Usually, light does not turn an insulator into a conductor: that requires powerful laser pulses that break the material's structure. But in twisted bilayer graphene at the magic angle, things are different.

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.

Two sheets of tungsten diselenide (not carbon, but a compound of tungsten and selenium) are rotated relative to each other by a tiny angle, about 5 degrees. This creates a moiré pattern: an enlarged periodic lattice where electrons behave very differently than in a regular crystal.

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.

A switch that knows which way to let current flow. That's how a Josephson diode works — a superconducting bridge where current goes willingly in one direction but meets resistance in the other. In the new study, such a bridge was made from graphene — a sheet of carbon just one atom thick.

A tightly twisted phone cord snaps and scatters sparks. Magnetic fields on the Sun behave the same way: they twist, break, and reconnect, powering flares. For the first time, astronomers have witnessed this process directly. One loop was twisted by 540 degrees — one full turn and then half again. That’s three times more than previously thought possible.

Two ultra-thin sheets, each just one atom thick, are placed on top of each other and slightly rotated. Like two sheets of colored tracing paper: while they lie flat, the picture is one thing, but give them a twist and a moiré pattern appears. Here, though, the pattern isn't visible to the eye, but it completely changes how the material handles light.

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.

Two paper-thin sheets of a semiconductor are stacked and slightly rotated — by about three to four degrees. The atomic lattices don't match, creating a large-scale pattern — a moiré, like the ripples from two washboards shifted by a small angle. In this pattern, electrons move quite differently than in a regular crystal.

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.

Layers of a thin material rotated relative to each other resemble stacked grids. Where the lines intersect, a new pattern emerges — a moiré. In this pattern, electrons move differently than in a regular crystal and can form unexpected states. In the new study, researchers took two layers of molybdenum telluride and twisted them by 4.8 degrees.

A graphene sheet is a one-atom-thick grid of carbon atoms. Stacking several such sheets with a specific twist yields a material with unusual properties: it can be a magnet or a superconductor depending on how you poke it. The trouble is that in natural graphite, such 'properly twisted' layers are rare, and growing them artificially is tricky.

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.

Graphene is a carbon film exactly one atom thick. Two such sheets placed on top of each other with a slight twist behave very differently from a single sheet. At an angle of about 1.1 degrees, electrons slow down so much that the material can become a superconductor or an insulator — depending on the conditions.

Superconductivity is like a dance of electrons: they move in pairs without losing energy. In conventional superconductors, this dance is set by the electron velocity.

Think of a stack of paper: when the sheets lie perfectly aligned, light passes through them uniformly. But turn one sheet by a few degrees, and the picture changes. Something similar happens with layers in certain materials: rotate them relative to each other, and their properties change — sometimes dramatically. Spectroscopy isn't the key here, or rather, it's not the method used.

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 sheet of graphene, a carbon lattice just one atom thick, under a powerful laser beam behaves like a road where a toll barrier suddenly appears. Electrons that were freely racing through the material suddenly hit a forbidden zone: an energy gap they cannot leap across. This was predicted theoretically before, but no one had ever seen it directly.

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 woven basket made of willow twigs holds its shape thanks to the interweaving. A similar pattern, triangles linked into a flat network, has been found in a new crystal with the formula Cs₃V₉Te₁₃. Here, vanadium atoms form two sets of triangles that pierce each other like threads in fabric. This pattern is not just pretty: it forces electrons to move along special "flat" energy pathways.

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.

A sheet of graphene one atom thick is twisted at a small angle, and it starts behaving like a layered pie with layers slightly rotated relative to each other. At a certain twist angle, this material becomes a superconductor: electrons begin to move in pairs, like dancers in a waltz, without losing energy. But what exactly happens inside has remained a mystery.

The crystal bismuth selenide (Bi₂Se₃) is symmetric by itself, like a neatly stacked sandwich: flip it over, and nothing changes. But twist one layer slightly relative to the other, and the symmetry breaks. The material begins to 'feel' which side the light comes from and responds with an electric 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.

A sheet of graphene one atom thick is like a perfectly smooth tablecloth on which electron marbles roll. Place an electric barrier in their path, and usually they'll bounce back. But in graphene, it's different: under certain conditions, electrons pass through the barrier without even noticing it, as if the wall were made of mist.

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.

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 laser flash hits a one-atom-thick layer of silver sitting on bilayer graphene, and within quadrillionths of a second, a gap opens in graphene's electronic structure where none existed before. It's as if an ordinary wire momentarily became a semiconductor: electrons stop flowing freely, and a band gap appears.

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 superconductor is a material where electric current flows without loss, like water through a perfectly smooth pipe. But if vortices appear, the current starts to 'stumble' over these tiny whirlpools. In graphene twisted at a special angle, such vortices can be created and studied one by one.

A bell doesn't ring with a single note — after being struck, it sounds with several harmonics at once. An atomic nucleus vibrates in much the same way: after a collision, it can oscillate, and these oscillations show up in the emitted gamma rays.