Takashi Taniguchi

A material just one atom thick and of record purity — only one foreign atom per million — becomes the setting for a remarkable phenomenon. When cooled to near absolute zero, the electrons inside, like musicians in an orchestra, freeze into a strict order, forming a crystal. This state, predicted by Eugene Wigner nearly a century ago, has now been observed in detail.

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.

In a superconductor, electrons move in pairs, like dance partners. Usually, through a junction between two superconductors, one pair passes at a time. But add a third contact, and the dance gets more complex: two pairs can move together, forming a foursome. It's this four-part resonance that has been seen for the first time in a graphene junction with three terminals.

A single light source in a thin layer of boron nitride flashes on and off in a couple of nanoseconds. You can create many such sources in the material, but each one used to work on its own. In the new work, they were made to glow together, like musicians playing in unison.

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.

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.

Twisted layers of atoms in a material form a pattern of tiny regions, domains, each of which can be electrified in one of two directions, like a compass needle pointing north or south. Previously, such materials were studied only as a whole, measuring thousands of domains at once, and their collective behavior was like a choir where individual voices are not heard.

A thin crystal of hexagonal boron nitride is a relative of graphite, but transparent and insulating. Occasionally, single defects appear in its lattice: a boron or nitrogen atom is missing, leaving a trap for electrons. Such a trap can absorb light and re-emit it, like a tiny flashlight.

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.

Inside a boron nitride crystal, defects sometimes occur — places where atoms are knocked out or sit where they shouldn't. One such defect, the B-center, can emit light: it absorbs energy and releases it as a single photon. It's like a tiny light bulb that only lights up when asked, without any stray glow.

An ordinary superconductor loses resistance when cooled, and current flows through it without loss. But in ultrathin films, things are different: the material fluctuates between normal and superconducting states, and in this transition zone, strange resistance waves emerge. Resistance rises and falls as if someone were turning a volume knob.

A quantum dot is a box so small that an electron inside cannot have just any energy, but only strictly defined values, like the steps of a staircase. Each step can accommodate several electrons, but exactly how many is the question. If a step is double, two electrons can stand on it; if single, only one.

An ordinary superconductor expels magnetic fields, but this ring does the opposite: it creates a magnetic field inside itself. The ring is made of Fe(Te,Se) — a compound of iron, tellurium, and selenium that loses its electrical resistance at very low temperatures.

A thin sheet of graphene, just a few micrometers thick, was placed in a weak magnetic field, and it began to push the field out of itself, like a sponge squeezing out water. This effect, known as the Meissner effect, is the hallmark of a superconductor: a material that conducts electricity without loss.

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.

Light from thin semiconductor layers can be polarized: its waves oscillate in a single plane. Previously, it was thought that the direction of oscillation was set by how the sample was illuminated.

The glow of an ultrathin sandwich made of two semiconductor layers, molybdenum selenide and tungsten selenide, resembles a tangled musical score: many narrow colored lines that merge into a general background. Figuring out which line comes from where is nearly impossible. The authors did not try to disentangle the lines one by one.

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 crystal is like a city: if the streets are crooked, traffic jams. In a crystal, the streets are atomic rows, and the traffic is the flow of electrons. Any tiny imperfection, impurity, or atomic displacement makes electrons scatter. Scientists from several labs have learned to grow crystals so that the "streets" are almost perfectly straight. The method is called horizontal vapor transport.

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.

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.

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 well-coordinated orchestra of electrons in a superconductor is easily thrown off rhythm. Thermal jolts destroy the fragile order, and resistance returns. For decades, scientists have sought ways to strengthen this ensemble — mostly by changing the material's composition or compressing it to unimaginable pressures.

A tiny defect in a boron nitride crystal behaves like a microscopic indicator bulb. Shine light on it, and it glows, with the shade shifting with temperature: the warmer it gets, the redder the glow.

A sheet of paper with square grid, one with diamond grid, and one with honeycomb — three different universes for an ant. Change the sheet, and the rules of movement change. That's roughly how electrons experience the crystal lattice: geometry dictates whether they become little magnets, superconductors, or something else. In ordinary materials, the lattice is as rigid as if engraved.

In a pool, water usually spreads in circles from a thrown stone. But if you direct the flow strictly along the rim, it will run only along the edge. Something similar has been noticed in pieces of the superconducting crystal FeTe0.55Se0.45.

Superconductors usually don't get along with magnets: a strong field destroys the state in which current flows without resistance. But in thin layers of carbon, things are different.

Imagine a quantum phase transition as an intricate dance. Electrons whirl in strict order, each step representing their spatial arrangement, and the rhythm their dynamics. For decades, physicists could only see a blur of motion, unable to tell if the figures were changing or the music speeding up.

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.

In a pot of water carefully heated above its boiling point, the liquid remains calm. But the slightest disturbance, and it violently turns to steam. Physicists call this a metastable state: it seems stable, but in reality it's ready to break apart at the slightest nudge.

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.

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 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.

On the table lies a layered cake of hexagonal boron nitride flakes, a material similar to graphite but made of boron and nitrogen atoms. One flake is carefully transferred onto another, and at the spot where they overlap, after heating in oxygen, bright single light sources are born.

A compass needle trembles when an invisible current passes nearby. Physicists built a tiny compass from a single defect in diamond and brought it close to the edge of a superconductor to listen to the electric currents running there. These currents are unlike ordinary ones: they flow only along the boundary, like water along a riverbank, and do not scatter off obstacles.