Here is a thing that was not supposed to work. In March 2025, Guangyu Zhang and colleagues at the Chinese Academy of Sciences published a paper in Nature describing the creation of stable, freestanding sheets of metal exactly one atom thick. Not metal oxides. Not metal-containing compounds. Pure elemental metals: bismuth, tin, lead, indium, gallium. Monolayers. The method they used was, by the standards of modern materials science, almost offensively simple. They melted the metal, pressed it flat between two atomically smooth crystal surfaces, and let it cool. The crystals acted as anvils. The confinement did the rest.
The technique has a name—van der Waals squeezing—which is accurate but undersells the conceptual move. Van der Waals forces are the weakest of intermolecular interactions: the faint electrostatic attraction between transiently polarized electron clouds. They are what makes geckos stick to walls and what holds graphite layers loosely together. Zhang’s group exploited them in reverse. Instead of relying on van der Waals forces to maintain a layered structure (as in graphite, where the layers already want to separate), they used the van der Waals attraction between the crystal anvils and the molten metal to force the metal into a geometry it would never adopt on its own. The gap between the anvils—atomically flat surfaces of mica or hexagonal boron nitride—was narrow enough that only a single atomic layer could fit. The metal had no choice but to be flat.
Physics World named it the 2025 Breakthrough of the Year. To understand why, you need to understand what was supposed to be impossible about it.
Carbon forms graphene because carbon is not isotropic in its bonding. A carbon atom in a graphite crystal forms three strong covalent bonds in-plane—the sp2 hybridization that gives graphene its hexagonal lattice—and interacts with the layers above and below only through weak van der Waals forces. The bonding is directional. It has a preferred plane. When Geim and Novoselov peeled off a single layer with Scotch tape in 2004, they were separating along a natural cleavage—breaking weak bonds while leaving strong ones intact. The structure was already two-dimensional in its bonding; they just isolated it.
Metals do not work this way. Metallic bonding is, to a first approximation, nondirectional. The valence electrons delocalize into a shared sea that permeates the entire crystal. Every atom bonds to every neighbor with roughly equal strength in all three dimensions. There is no preferred plane. No natural cleavage. No layer that wants to separate from the one above it. A gold crystal is not a stack of gold sheets held together by weak forces; it is a single three-dimensional object all the way through. Asking a metal to form a stable monolayer is like asking water to form a stable monolayer—there is no energetic reason for it to stop at one atom of thickness rather than collapsing into a droplet or a bulk crystal.
This is not a hand-waving objection. The Mermin-Wagner theorem, proved in 1966, establishes that continuous symmetries cannot be spontaneously broken in two dimensions at finite temperature when interactions are sufficiently short-ranged. For practical purposes, this means that a two-dimensional crystal of a simple metal should be thermodynamically unstable: thermal fluctuations at any nonzero temperature should destroy long-range order. The atoms should buckle, cluster, island, do anything but remain in a flat sheet. The theoretical prohibition was not absolute—it depends on assumptions about interaction range and dimensionality that real materials can violate in various ways—but it was strong enough that most materials scientists treated two-dimensional metals as a closed question. Not worth trying. Known to be impossible.
The history of two-dimensional materials is a history of impossibility claims being quietly retired. Graphene was the first. Before 2004, the prevailing view—supported by Mermin-Wagner and by Landau and Peierls’s earlier arguments from the 1930s—was that strictly two-dimensional crystals could not exist as stable, freestanding structures. Thermal fluctuations would destroy them. Then Geim and Novoselov isolated graphene, and it turned out that the fluctuations were there (graphene sheets ripple) but they did not destroy the crystal. The sheet survived. The Nobel Prize followed in 2010.
After graphene, the search expanded. Transition metal dichalcogenides—compounds like molybdenum disulfide (MoS2) and tungsten diselenide (WSe2)—turned out to exfoliate into stable monolayers with electronic properties radically different from their bulk forms. MoS2 transitions from an indirect to a direct bandgap semiconductor when thinned to a single layer, which is not a small change; it is the difference between a material that barely emits light and one that can be used in optoelectronics. Hexagonal boron nitride followed. Then phosphorene (monolayer black phosphorus), with its anisotropic electronic properties and tunable bandgap. Each new class of material brought a version of the same surprise: the monolayer was not just a thinner version of the bulk. It was a different material with different physics.
But through all of this, metals remained the holdout. Every successfully exfoliated or synthesized 2D material shared a structural feature: layered bonding in the bulk. They were all van der Waals solids, or at least had strongly anisotropic bonding that created natural two-dimensional planes. Metals lacked this. The consensus was clear: you could flatten anything that already had layers. You could not flatten something that did not.
Zhang’s approach bypassed the bonding problem entirely. Instead of trying to find or engineer a cleavage plane within a metal crystal—which does not exist—the group imposed two-dimensionality from outside. The procedure, stripped to its essentials: take two atomically flat crystals (mica, hBN, or similar van der Waals surfaces). Place a small amount of metal between them. Heat until the metal melts. Let the van der Waals attraction between the two crystal surfaces pull them together, squeezing the molten metal into the narrowest gap the geometry allows. Cool. Peel apart. The metal, now solidified, remains as a monolayer adhered to one of the crystal surfaces.
The confinement itself provides the stabilization that the metal’s own bonding does not. Sandwiched between two van der Waals surfaces, the metal atoms experience an asymmetric potential—attracted to the crystal surfaces above and below, confined in the vertical direction, free to organize only in-plane. The result is a two-dimensional crystal that is metastable: it would not form spontaneously, and if you heated it enough it would presumably bead up into three-dimensional islands, but at room temperature and below, it persists. The van der Waals interaction with the substrate surface provides enough energetic penalty for vertical growth that the monolayer geometry is a local minimum. Not the ground state. But stable enough.
What strikes me about this is not the cleverness of the technique but its directness. Melt it. Press it flat. Let it cool. The sophistication is in choosing the right anvil materials and controlling the gap thickness, but the core idea is one that a blacksmith would recognize. The 2D materials community spent two decades developing increasingly elaborate methods—chemical vapor deposition, molecular beam epitaxy, electrochemical exfoliation—for synthesizing monolayers of materials that wanted to be monolayers. Zhang’s group took materials that explicitly did not want to be monolayers and just forced them. The confinement geometry did the theoretical work that the material’s own chemistry refused to do.
The point of making two-dimensional metals is not the achievement itself. It is what happens to the physics. When you confine a metal to a single atomic layer, you do not get a thinner version of the same metal. You get something else.
Monolayer bismuth, in Zhang’s measurements, showed enhanced electrical conductivity compared to bulk bismuth—which is notable because bulk bismuth is actually a semimetal with poor conductivity, an oddity among metals. The monolayer also exhibited a nonlinear Hall effect: a Hall voltage that depends on the square of the applied current rather than linearly, which is a signature of Berry curvature effects in the electronic band structure. This does not happen in bulk bismuth. It is a property that emerges only in two dimensions, where the reduced symmetry and quantum confinement reshape the electronic bands into something the bulk material never accesses.
New phonon modes appeared as well—vibrational frequencies of the atomic lattice that have no counterpart in the three-dimensional crystal. This matters because phonons govern thermal conductivity, superconducting behavior, and the coupling between electrons and the lattice. Different phonons mean different thermal transport, different electron-phonon interactions, and potentially different phase transitions. The monolayer is not a thin film. It is a distinct phase of matter.
The theoretical implications are dense. Two-dimensional metals could exhibit exotic quantum states—topological surface states, unconventional superconductivity, charge density waves—that are either absent or buried in the bulk. Lead and tin, both conventional superconductors in three dimensions, might show modified or enhanced superconducting behavior in the monolayer limit. Indium and gallium, with their unusual low-melting-point chemistry, could behave as two-dimensional liquid metals at accessible temperatures. None of this has been fully explored yet. The materials are too new. But the design space has been opened, and it is large.
What interests me most is the pattern this fits into. Not the specific physics of monolayer bismuth, but the repeated structure of the discovery process across two decades of 2D materials research.
It goes like this. A class of materials is identified as being unable to exist in two dimensions. The reasons are principled—rooted in symmetry arguments, thermodynamic calculations, the known physics of bonding. Then someone finds a way to make it work, usually by violating an assumption that was treated as fundamental but was actually contingent. The 2D material turns out to have properties that the bulk does not, and a new subfield opens. Then the next class of materials is identified as the true limit, the one that really cannot be flattened. And the cycle repeats.
Graphene broke the first barrier: freestanding 2D crystals exist at all. Transition metal dichalcogenides broke the second: compounds with complex unit cells can be monolayers. Phosphorene broke the third: even elements that oxidize rapidly in air can form stable (if air-sensitive) 2D allotropes. And now metals have broken the fourth: nondirectional bonding does not prohibit two-dimensional stability if you impose the geometry externally.
Each time, the impossibility claim was not wrong exactly. It was correct within its assumptions. Two-dimensional crystals are unstable according to Mermin-Wagner, if you assume short-range isotropic interactions and strict two-dimensionality. Metals cannot form monolayers, if you require the monolayer to be the thermodynamic ground state of the unsupported material. The theorems hold. The assumptions do not. The gap between a proven theorem and an impossibility in nature is the gap between a mathematical statement and a physical one, and that gap has turned out to be large enough to drive an entire field through.
There is a deeper point here, and it is the one I keep returning to. We talk about dimensionality as though it is a property of matter—as though a material is three-dimensional the way it is crystalline or metallic. But what Zhang’s work demonstrates, along with the entire history of 2D materials, is that dimensionality is better understood as a constraint. Matter does not have a fixed number of dimensions. It has a number of dimensions that are accessible under given conditions. Change the conditions—confine it between surfaces, exfoliate it with tape, grow it on a substrate that templates a particular geometry—and the accessible dimensionality changes. The properties change with it.
This is not just a semantic point. It reframes the question of what is possible. If dimensionality is intrinsic, then asking whether a material can exist in 2D is a question about the material’s nature, and the answer might be no. If dimensionality is a constraint, then the question becomes: under what conditions can this material be confined to two dimensions, and what stabilizes it there? The answer to the second question is never “it is impossible.” It is “we have not found the right confinement yet”—or, more honestly, “we have not looked.”
The van der Waals squeezing technique is a proof of concept for this way of thinking. It does not rely on anything special about bismuth or tin or lead. It relies on geometry and confinement. In principle, any metal that can be melted and wetted onto a van der Waals surface is a candidate. The periodic table of 2D materials, which was already startlingly large, has just expanded to include most of the metallic elements. The technique is simple enough to be scaled. The materials are common. The barriers, it turns out, were not in the physics. They were in the framing.
I think about this in contexts well beyond materials science. The structure is general: a principled argument establishes that something cannot be done, the argument is correct within its assumptions, and then someone does the thing by violating an assumption that was not recognized as an assumption. The impossibility was real but narrow—a statement about a specific path, mistaken for a statement about the destination. The metals could not form monolayers on their own. Nobody asked whether they could form monolayers with help.
There is a temptation to extract a motivational lesson from this—something about persistence, or creativity, or the value of trying the impossible. I do not think that is the right takeaway. Most impossibility claims in physics are correct and will remain correct. You cannot build a perpetual motion machine. You cannot send information faster than light. The Mermin-Wagner theorem is not going away. What Zhang’s work illustrates is something more specific and more useful: that the boundary between a theorem and its application to real materials is a space where assumptions live, and assumptions are worth examining individually, especially the ones that feel too obvious to state. “A monolayer must be the ground state of the unsupported material” is an assumption. “Thermodynamic stability requires global energy minimization rather than local metastability” is an assumption. “If the bonding is isotropic, the geometry must be three-dimensional” is an assumption. All three turned out to be wrong, or at least optional.
What I find myself sitting with is a question about how many other domains have load-bearing assumptions of this kind—premises so deeply embedded in the framing of a problem that they do not register as premises at all. Not wrong, exactly. Just quietly limiting the space of what anyone thinks to try.