THE tenets of physics can seem carved in stone. The speed of light is a constant. There are four fundamental forces. Theoretically, rules like these are open to revision. But new contenders had better come with a chisel and a very big hammer.
You would be forgiven for thinking this confidence also applies to something as fundamental as the different states of matter. As we learned in school, there are three of them: solid, liquid, gas. Right?
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Actually, these are only the start. We now know of all sorts of exotic states, from superconductors to Bose-Einstein condensates, quantum spin liquids to topological insulators. The sheer number is as bewildering as their names. Strangely, no one can give you a definitive list: there could be as few as four of them or perhaps thousands.
Sorting this mess out isn’t just a matter of satisfying our curiosity. If we can pin down exactly what constitutes a state of matter, we should be better able to predict and discover new ones. That would not only have great technological benefits, but it could also give us fresh ways to probe the nature of reality.
Such predictive power is central to how physics typically works: we predicted the Higgs boson existed and built a particle collider to find it. But where states of matter are concerned, precision and prediction have eluded us – until now, thanks to the recent discovery of a whole new class of matter.
The rules we are taught at school to define states of matter, based on nothing more complex than shape, seem simple enough. A solid has a fixed shape. A liquid flows to take the shape of the bottom of the container it is in. A gas expands its shape to fill its confines.
Throwing shapes
At first glance, the behaviour of these different states tallies with what the atoms or molecules of the substance are doing. In a solid, the atoms are bound together in a rigid three-dimensional lattice. In a liquid, they are free to move around each other, so that their combined mass flows. In a gas, they have so much energy that they fly around all over the place, scarcely touching. All you do to switch between states of matter is to add or take away energy in the form of heat.
But we have known things are actually more complicated than this for a long time, with high pressures, low temperatures and odd geometries among the things leading to exotic behaviours difficult to explain in terms of conventional states of matter. Even something as familiar as glass confuses things. Glass retains its shape like a solid even though its atoms are arranged messily, as in a liquid. Then there is a state of matter that many of us hold in our hands each day: a liquid crystal. These materials have optical properties that make them go-to ingredients in smartphone displays. They can also flow like a liquid, despite having their atoms arranged like a typical solid. Handy for technology – not so handy if the goal is to neatly categorise the states of matter.
Liquid-crystal elastomers muddy the waters even further. First made in 1975, they consist of molecules that always align in parallel with each other. This results in some odd properties. Try to pull the material apart and it will resist; on most of its faces it feels springy. But rub it on one particular face, and it will begin to flow. “It deeply challenges our conception of what is a solid and what is a liquid,” says at the University of Cambridge.
“Such materials challenge our conception of what is a solid and what is a liquid”
Warner suggests that using a more precise definition of shape could make things clearer. But that doesn’t get us far. It wouldn’t help, for instance, when it comes to plasmas, the state of matter from which the sun is largely made. Plasmas are like a gas in which the atoms have split apart into charged particles, and so they conduct electricity. Its behaviour is unusual, but shape-wise, a plasma is identical to a gas. Or how about the various forms of magnetism? These are routinely spoken of as states of matter. Their special properties come from a quantum property called spin, which can be thought of like an arrow attached to each of a material’s electrons. It is the arrangement of these spins – not the material’s shape – that gives magnets their attractive qualities.
It would be easy to see this as worrying over unimportant semantics. Isn’t a plasma just an electrically charged gas? Isn’t a magnet just a solid that happens to be magnetic? For a physicist, it isn’t that simple. There is no objective way to mark solidity as more fundamental than magnetism, or gaseousness as more fundamental than charge.
This is why physicists turned to a different concept called symmetry to categorise states of matter. Imagine you have two circles of paper, one covered with dots in a grid, the other covered in random dots. Now rotate the pieces of paper a bit. It will be obvious that the grid pattern has been turned, but less obvious that the random dots have changed. The random dot pattern has high symmetry, whereas the ordered grid doesn’t.
The grid and the random dots are akin to the arrangement of atoms in solids and liquids, so symmetry can be used to differentiate the two. The concept also applies far more widely, including to the organisation of spin in magnets and charge in plasmas. “Symmetry is a powerful concept,” says at Rice University in Houston, Texas.
Surprise discoveries
Too powerful, perhaps. Defined according to symmetry, something as simple as water ice can come in at least 17 different states of matter, depending on how its atoms are arranged. “You might argue that many different states are variations on the same theme,” says Frank Wilczek at the Massachusetts Institute of Technology. “If you classify things sufficiently coarsely, then there might be a finite number of fundamentally different states of matter, or maybe only one.” Symmetry is useful, but it doesn’t solve the problem with classifying states of matter.
All this means an authoritative list of the states of matter doesn’t exist. At the root of the problem is our inability to predict new states. Historically, most novel states have been surprise discoveries. The few that were predicted belong to a select group governed by simple mathematical rules that come into play only under extremely unusual conditions. One example is the Bose-Einstein condensate, a type of superfluid that has proved useful for modelling the edges of black holes (see “Strange stuff: Super powers“).
The scale of the lack-of-predictability problem was emphasised in 2000 by US theorists Robert Laughlin at Stanford University in California and the late David Pines. They that when more than 10 or so electrons become involved in real materials, strong neighbour-to-neighbour interactions can make it impossible to computationally simulate their effect on material behaviour; the maths just becomes unthinkably complicated. “It’s like doing a seating plan at a wedding,” says Natelson. “If no one cares who they’re next to, it’s easy. But if, oh gosh, we can’t put Alan next to Barbara, and Barbara can’t be next to Charlie, it becomes very challenging.”
This unpredictability means we can’t know whether the states of matter we are aware of are all there is. Materials science, argued Laughlin and Pines, is different from other areas of physics with their predictions and experiments. Like plant hunters heading into the field, people studying matter must be content to find things by chance. Explanation and classification can only be done in retrospect.
At least, that used to be the case. Over the past 15 years or so, we have discovered a new group of states of matter, the members of which are, apparently, predictable after all. The groundwork for this revolution was laid in 1980, when Klaus von Klitzing discovered the quantum Hall state of matter. It occurs in semiconductors, like those in computer chips, when they are very flat and sandwiched between other materials. Switch on a magnetic field, and suddenly the semiconductor changes state so that it conducts flawlessly around its edge, while insulating everywhere else.
Nothing so bizarre had been seen before. Symmetry wasn’t enough to explain it; an additional classification was needed. The answer is topology, a branch of maths that describes features of shapes, such as holes and twists, in terms that ignore changes that can be made by deformations of those shapes. The way the quantum Hall state funnels electrons into specific trajectories turns out to be fundamentally topological by nature.
This got theorists thinking. By 2005, researchers at the University of Pennsylvania and another group at Stanford University the possibility of a state of matter . We now call it the quantum spin Hall state. The idea was that materials adopting this state would marshal electrons in different ways according to their spin. Spin-down electrons would go one way around the material’s edge, spin-up electrons the other. Within two years, the state of matter was observed in a real compound. “That was a first in physics,” says Andre Bernevig, one of the Stanford authors.
“This vast landscape of states has great technological promise”
Topology complements symmetry rather than replaces it. But at last it allowed predictions to be made. A couple of years after the experimental discovery of the spin Hall state, theorists found that they could map out topology in combination with three different fundamental symmetries to produce a whole “periodic table” of topological states. Bernevig and others have now expanded this to include all the symmetries that underpin the structures of crystals. In all, they have . This is very impressive, says Natelson. “As calculational methods continue to improve, the realm of predictability will continue to become larger.”
In a gold mine
Early indications suggest that this vast landscape of topological states has great technological promise, especially in quantum computing (see “Strange stuff: Deeply twisted“). The challenge now is to identify which materials might adopt these states. Recent estimates by Bernevig and others suggest that more than four-fifths of all known simple compounds – those whose behaviour can be approximated without running into the electron-electron interactions that bothered Laughlin and Pines – could be topological states of matter. “We’re in a gold mine,” says Bernevig.
What about non-topological states of matter, might we ever have a complete list of those too? Wilczek is certainly confident that there are more to be discovered – and coming from the person who predicted a strange state of matter called the time crystal, that isn’t to be taken lightly (see “Strange stuff: The misfits“).
Still, the electron problem that concerned Laughlin and Pines hasn’t gone away. Ross McKenzie at the University of Queensland, Australia, says one of the last successful predictions of a complex state of matter was made by British physicist Duncan Haldane in 1983 for a type of “spin liquid”, in which electron spins remain resolutely unordered even at the lowest temperatures. “The fact that there have been no more for 40 years suggests to me that any optimism is misplaced,” says McKenzie. “I would love to be wrong.”
Bernevig thinks he might be. He says modern computing is taming even the vexed mathematics of multiple electron interactions. Maybe, one day, we will end up with a list that is, to most physicists’ satisfaction, final. “If you had asked me 10 years ago whether all these things were predictable, I would have said no,” he says. “Now, I’m not so sure.”
Strange stuff – UNDER PRESSURE
Ratcheting up the pressure is just one of the ways physicists have discovered beguiling and extreme new states of matter
DEGENERATE MATTER
At pressures a thousand billion times higher than at the centre of Jupiter, matter gets so squeezed that it butts up against a fundamental physical law. The Pauli exclusion principle says that identical particles can’t occupy the same quantum state. In places like white dwarf stars, this is thought to produce matter that is technically a gas, but has odd properties, like being virtually incompressible.
QUARK MATTER
Go to higher pressures still and even the most basic components of matter, quarks, hit the Pauli rule, and theoretically form quark matter. It could be lurking in “quark stars” hiding at the centre of neutron stars. If so, it is the universe’s most dense state of matter, except for that trapped inside a black hole.
Strange stuff – SUPER POWERS
Cool ordinary stuff down enough and it adopts quantum properties you can see with the naked eye
SUPERCONDUCTORS
Superconductors don’t behave as if made from zillions of individual particles, but like they are a single super-particle. These materials conduct electricity with zero resistance and so allow us to transport electricity without wasting a jot. They were first discovered in 1911, but they only worked at extremely low temperatures of about -273°C. These days, we have superconductors that work at higher temperatures, but are still looking for one that works at room temperature and pressure.
SUPERFLUIDS
Cool helium to just above absolute zero and it will become a superfluid, a material with zero viscosity. It can flow uphill and, if stirred, will never stop spinning. Superfluid behaviour also arises in Bose-Einstein condensates, a rare example of a state of matter that was predicted before it was discovered (see main story). Albert Einstein and the Indian physicist Satyendra Bose predicted it in the 1920s. It was observed 70 years later, when physicists could supercool a cloud of atoms with lasers. The atoms spontaneously begin to behave as an ethereal fluid that can swirl and explode. Thanks to its quantum properties, this state is useful for modelling the quantum goings-on near the edge of a black hole.
SUPERSOLIDS
A 1969 theory suggested that holes in a solid lattice of atoms can, at very low temperatures, form a kind of ghostly matter that can pass through other solids. In 2004, Moses Chan and Eunseong Kim, both then at Pennsylvania State University, reported evidence for such a supersolid, when part of an oscillator made of cooled, solid helium appeared to stop moving, while the remainder passed to and fro through it, unhindered. Chan later backtracked and said what was observed was a normal change in elasticity due to the cooling. Despite claims of supersolid behaviour in certain Bose-Einstein condensates, it remains to be seen whether a convincing supersolid can be made.
Strange stuff – DEEPLY TWISTED
States of matter with properties governed by a type of geometry called topology could be the basis of amazing computers
TOPOLOGICAL INSULATORS
The simplest types of topological matter consist of materials that normally insulate, but that exhibit strange types of conduction when layered together. A two-dimensional topological insulator funnels “spin up” electrons one way, and “spin down” electrons the other. This effect could be exploited to make super-fast “spintronic” computers that process information based not just on charge like existing machines, but electron spin too.
TOPOLOGICAL SUPERCONDUCTORS
This state seems to harbour a highly unusual particle called the Majorana fermion. These particles have never been observed in isolation, but electrons inside topological superconductors can team up and behave in a way that is indistinguishable from them. Because they can withstand interference much better than electrons, Majorana fermions could be used for the quantum bits in next-generation quantum computers.
TOPOLOGICAL SEMI-METALS
Like topological superconductors, semi-metals can behave as though they are hosting an unusual particle. In this case, its the Weyl fermion, which is like an electron with no mass. Incredible electrical conduction is one property that results. Potentially more important, however, is that no matter how many impurities it has, a topological semi-metal will always conduct electricity superbly. This could be useful for making robust computers, or detectors with extreme sensitivity.
Strange stuff – THE MISFITS
A few states of matter are so odd that they defy any classification
TIME CRYSTALS
In 2010, physicist Frank Wilczek wondered what would happen if the atoms in ordered ranks inside solid crystals were regularly arranged not in space, but in time. He soon came up with the idea of a time crystal, a bizarre state of matter that oscillates by itself – and never stops. By 2017, Christopher Monroe at the University of Maryland and his colleagues had created a time crystal, in a string of trapped ytterbium ions. Once the team temporarily flipped the magnetic spin of one of the ions with a laser, the rest of the ions flipped back and forth in turn, like a never-ending atomic Mexican wave.
RYDBERG POLARONS
Atoms usually consist of a tight knot of protons and neutrons orbited by electrons. But in 2018, a team at Rice University in Texas used a blast from a laser to propel an atom’s electron into an unusually large orbit – so large that more than 100 of the neighbouring atoms became caught inside. These atoms-within-an-atom, known collectively as a Rydberg polaron, turn our normal notions of matter upside down.
