IN A lab in Dresden, Germany, physicist Frank Steglich is watching a small crystal flout the traditional precepts of physics. This crystal, a cocktail of ytterbium, rhodium and silicon, is conducting electricity, but no one knows how. Common wisdom says that when electricity flows through a material, it’s the electrons that do the job. But as Steglich and his colleagues at the Max Planck Institute for the Physics of Complex Systems cool their crystal down toward absolute zero under a strong magnetic field, the electrons come to a halt, unable to move. The experiments suggest that the electrons may even be splitting apart. And yet the current keeps flowing. How?
The crystal is not the first to show such inexplicable behaviour. Twenty-five years ago, researchers stumbled over substances in which the electrons seemed too heavy. Then came the infamous “high-temperature” superconductors – complex materials of copper, oxygen and other elements that show no resistance to the flow of electrical current at temperatures as high as 138 kelvin. These days, physicists are finding new recipes for materials with similarly exotic properties every few weeks. And now, at last, they think they might know where they come from.
New research is suggesting that the uncertainty principle of quantum mechanics supports the existence of a shadowy world in which the electrons in solid materials undergo a bizarre identity crisis. The result is a “quantum critical” material with hitherto inexplicable characteristics.
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Although physicists still have only an inkling of the strange laws of this world, quantum criticality has become one of the hottest ideas in physics. Many researchers now think that, thanks to this discovery, the long-awaited explanation of high-temperature superconductivity is close at hand. And there might be even bigger pay-offs. These strange materials raise the possibility that in probing the deepest secrets of fundamental physics, gargantuan particle accelerators might one day be upstaged by tiny crystals sitting on laboratory benches.
The roots of this revolution can be found in something as mundane as electrical resistance. In all the exotic materials, resistance just doesn’t work as traditional theories say it should. Inside a material that conducts electricity, a cloud of electrons moves about within a lattice of atoms and ions. The electrons interact with one another, and so the movement of one will tend to stir up a complicated local storm in the motions of others. Potentially, this could make the task of understanding material properties exceedingly complicated. But physicists in the 1950s and 1960s, inspired by earlier work of Russian physicist Lev Landau, showed that an electron plus its local storm can be viewed collectively as a kind of particle – a “quasi-particle” – and that the electronic properties of conducting materials can be understood by thinking of the motions of such particles.
It follows that the electrical resistance of a material should depend on the kinds of obstacles that impede quasi-particle motion, and how those obstacles are affected by temperature. At low temperatures, quasi-particles should move relatively freely, the only impediment being occasional collisions with other quasi-particles. According to standard physics, in this scenario the resistance increases as the square of the temperature. At higher temperatures, the vibrations of the atomic lattice should also come into play, disturbing quasi-particle motion and further increasing resistance, though in more complicated ways that depend on the material in question. These predictions have been shown to hold true for thousands of materials, from metals to semiconductors, and by the 1980s the quasi-particle view had earned virtually unassailable status.
Crystal misfits
However, a vast range of other materials discovered in the past 20 years simply refuse to fit the picture. For example, the crystal Steglich and colleagues were looking at, YbRh2Si2, in the right magnetic field, has a resistance that increases in direct proportion to temperature all the way from 10 millikelvin up to 10 kelvin. This flies in the face of the quasi-particle picture. “From the traditional perspective,” says Jan Zaanen, a physicist at Leiden University in the Netherlands, “this behaviour is utterly unreasonable.”
Understanding why tradition fails, and replacing it with something better, is far from easy. In materials that follow the rules, electrons tend to be either tied strongly to specific atoms – and therefore unable to move – or completely “delocalised” and moving as quantum waves. “In either case,” says physicist Subir Sachdev of Harvard University, “the physics is simple.” You get a material that conducts electricity poorly in one case, and well in the other.
But some materials fall between these two extremes, and this is where things get a lot more complicated. In the late 1970s, for example, researchers discovered so-called “heavy fermion” materials in which the electrons come in two types – some localised and others spread out. These electrons interact in complex coordinated ways that can make them act as if they are 1000 times heavier than normal.
Similar complexity lives within high-temperature superconductors, in which some electrons act as magnets, fixed to atoms, while others flit through the material without hindrance. Out of the coordinated activity emerges superconductivity – in a way that has defied explanation for nearly 20 years.
The phenomenon of quantum criticality may help to explain these mysteries. It deals with the peculiar quantum manifestation of phase transitions, the abrupt change in a material from one regime of atomic order to another, as when heated water turns to vapour or a material becomes magnetic that was not before. Physicists have studied such transformations for well over a century, and they know that things get particularly interesting at the “critical point” between two phases, at which the material lies on a knife-edge between different kinds of organisation. In this critical regime, materials don’t settle into one phase or another, but fluctuate violently between them.
It is usually changes in temperature that trigger phase transitions, as this alters the balance between the forces that create more or less order within a substance. But 30 years ago, physicist John Hertz, then at the University of Chicago, suggested that under certain conditions the irreducible jostling of quantum noise might do the same.
Quantum noise arises from the uncertainty principle of quantum theory, which states that the characteristics of a physical system can never have precisely defined values. Because of quantum uncertainty, even the vacuum of “empty” space seethes with short-lived particles, and an atom cooled to absolute zero still vibrates.
On the basis of quantum theory, Hertz explored what would happen if the temperature of an “ordinary” phase transition could be tuned to happen at absolute zero, by changing the pressure, say, or applying magnetic fields. His equations showed that if you take the “noise” of temperature away, quantum indeterminacy becomes important. This should lead, he predicted, to quantum versions of phase transitions.
Quantum reach
This may seem like a rather esoteric theoretical observation; after all, temperature is never exactly zero in the real world and so quantum phase transitions seem to be mathematical oddities rather than real, physical phenomena. But physicists since Hertz have discovered that the mere possibility that a quantum critical point can exist has surprising consequences for a material’s properties under ordinary “real world” conditions. In other words, even though the point is never reached, tuning the material so that the point would occur at absolute zero changes the material’s properties at higher temperatures.
Take the crystal YbRh2Si2, for example. Ordinarily, it becomes magnetic only when its temperature falls below about 70 millikelvin. In experiments two years ago, Steglich and colleagues showed that by applying a magnetic field to the crystal, this transition temperature can be reduced. If the magnetic field is strong enough, it will even reach zero, thereby creating a quantum critical point (see Graphic). The existence of this point strongly influences the material’s properties. While the crystal is in the magnetic field, the way it conducts electricity follows the quantum critical pattern, with extremely heavy electrons. The electrons appear to be so heavy that they do not move, yet the crystal still carries a current.
Why quantum critical points “bleed out” to be so influential away from the zero temperature ideal remains unexplained. But it is precisely this surprising reach that has researchers so excited, as it seems to reveal something about the fundamental nature of what goes on in these materials. Measurements of specific heat and resistivity tell us that electrons have come to a halt in these materials. That means quasi-particles no longer offer a convenient shorthand. So something else must carry the electrical current. But what? “The big question,” says Andrew Huxley of the French Atomic Energy Commission in Grenoble, “is how do we describe the soup that is left when we can no longer talk about particles?”
Some physicists suggest that quantum fluctuations themselves may be key – that is, that some transitory charge carriers, rather than anything with a permanent existence, may be carrying the current. Earlier this year, Senthil Todadri of the Indian Institute of Science in Bangalore, working with Sachdev and others, came up with another idea. These researchers suggested that the particles that exist in the quantum critical state may be different from those existing under other conditions, and the electron itself may split apart into particles that separately carry its charge and spin.
“Physicists are finding new recipes for materials with exotic properties every few weeks”
No one is suggesting that electrons aren’t fundamental particles. Rather, the idea is that the electrons in the quantum critical soup live within complex “composites” that don’t behave like individual electrons. “Even though the particles are ‘made up’ of electrons,” says Sachdev, “they can carry fractions of electron properties.” He and his colleagues hope to build more detailed and effective theories by thinking in terms of these “natural” particles, rather than electrons.
It is this kind of work that might finally explain high-temperature superconductors. These materials tend to be magnetic at low temperatures, but when “doped” with impurities, the temperature at which the magnetism appears becomes lower. If they are doped to the right level to make magnetism appear at zero, these materials simultaneously become “strange” conductors at high temperatures: their electrons don’t act as well-behaved quasi-particles. When made colder, they become superconductors. Somehow, there is a link between superconductivity and quantum criticality.
The link, though still vague, seems all the more enticing as researchers continue to find surprising new kinds of superconducting materials that have quantum critical points. A team of researchers led by Huxley noticed in experiments, for instance, that URhGe, a compound of uranium, rhodium and germanium, has a quantum critical point for a strong magnetic field, rather than a particular doping level. They wondered whether, near that point, it might show unusual behaviour – and they weren’t disappointed.
Disappearing trick
At very low temperatures, URhGe is superconducting. As Huxley and his colleagues applied a magnetic field, the superconductivity first went away, as would be expected because magnetic fields ordinarily suppress superconductivity. But as the team increased the field further, the superconductivity reappeared – something never seen before (Science, vol 309, p 1343).
So what is going on? Andy Schofield of the University of Birmingham, UK, suggests that quantum critical points might arise from “hidden” order of some kind: not a regular lattice of atoms, or a magnetic structure, but something entirely unknown. The behaviour of high-temperature superconductors and all other exotic materials may represent different manifestations of such hidden order, and physicists hope that a grand theory of the quantum critical point may help bring its character into focus.
That theory could have repercussions far beyond the physics of solid materials. Quantum criticality may reveal itself in such materials, but it originates in the fundamental nature of quantum indeterminacy and so is likely to arise in many other settings. A group of researchers including physicist George Chapline of Los Alamos National Laboratory in New Mexico and Nobel prizewinner Robert Laughlin of Stanford University in California recently suggested that quantum criticality may even demand a fundamental rethinking of the physics of black holes.
At the event horizon of a black hole, the flow of time – as viewed by someone far away – should cease. This follows from the principles of general relativity, but doesn’t sit well with the basics of quantum theory, which always assumes a flow of time. To make relativity fit with quantum theory, Chapline and colleagues argue that the physics at the surface of a black hole should be that of a quantum critical point. This, they say, might have implications for many of the “mysteries” of cosmology, such as the dark energy that many astrophysicists believe is driving the accelerating expansion of the cosmos. “This idea,” says Chapline, “could profoundly change our view of the universe.”
In another setting, it is just possible that quantum criticality could lead researchers to a clearer view of particle physics. One prominent idea for extending the standard model of particle physics involves the idea of “supersymmetry”, which proposes that every kind of particle known is actually one of a pair. If true, supersymmetry could show how the four forces we experience emerge from one unified force, something that physicists have long suspected happened in the high-energy conditions of the early universe. Although researchers have not yet found any traces of supersymmetric particles, theorists such as Piers Coleman of Rutgers University in New Jersey and Catherine Pépin of the French Atomic Energy Commission in Saclay suggest that it may be possible to test some aspects of supersymmetric theories in solid materials.
In the world at large, particles come in two types – fermions and bosons – and many exotic materials, they argue, mirror this. In supersymmetry theories, the laws of physics become unified at high energies, at which these fermions and bosons “come together” to make up more fundamental supersymmetric objects. In exotic materials, energy gets carried around in two essentially different ways – through the motion of heavy electrons, which act as fermions, and through other excitations that act as bosons. Coleman and Pépin argue that an essentially similar “unification” process may take place in exotic materials as they approach a quantum critical point. “It would be very exciting if true,” says Schofield. “Given the number of exotic materials we’re finding, there’s a tantalising possibility that supersymmetry could be found in a cryostat before we ever see it in a particle accelerator.”
Schofield thinks quantum criticality might provide a refuge for theorists struggling to produce a “theory of everything” that describes the fundamentals of how the universe works. Many of them are hoping that the next generation of particle accelerators will provide more data to help ground their ideas. But why wait, Schofield says, when quantum critical materials offer so much experimental potential? “Disillusioned string theorists could come to work on this,” he says. “Every new material gives you a new universe.”
