Physics for the 21st Century
Emergent Behavior in Quantum Matter Interview with Featured Scientist Piers Coleman
Interviewer: What is emergence?
PIERS: To understand the concept of emergence, you have to contrast it with the word reductionism. Emergence and reductionism are two counterparts in some sense. So, reductionism is the idea that to understand the world in which we live, you break it down into its constituent parts. You learn the basic laws that control matter on its very smaller scales. And once you know that, you know everything and immediately understand the universe in which we live. But more and more, we’re learning that that’s not enough. In fact, we do understand many of the microscopic laws that govern matter. Once we learned all about them, we didn’t know how to put it all back together again. And what we are discovering increasingly is that as matter comes together it develops new kinds of structures and new forms of collective motion. And the rules that govern that collective behavior have a life of their own.
Interviewer: What is a superconductor?
PIERS: To understand a superconductor, we have to first understand a conductor. When we talk about conductors, a conductor is literally any material that can conduct electricity. Typically when you have a metal, such as copper, it will conduct electricity through the metal, but that electricity will only keep on running so long as I apply a force, a voltage, or a pressure that keeps it running through. And so we say it’s a conductor which has a resistance. A superconductor is a conductor which loses that resistance. And so once you start electricity flowing through a superconductor, it keeps on flowing, not just for a few moments or a few seconds. If you come back a year later, that electricity is still flowing just as it was in its original state of motion. That’s one aspect of superconductors.
Interviewer: Why don’t we use superconductors?
PIERS: Today we don’t use superconductors in our lives in part because most superconductors that we know are metals which go superconducting at very low temperatures.
Interviewer: So is it one of your goals to find a high-temperature superconductor?
PIERS: In our interest in finding materials which have new properties, one of our fascinations and one of our interests is in finding a material that will produce superconductivity at room temperature, or we’d settle for Arctic or even Siberian temperatures. Those would still be fine. Because if we could find a practical material that does that, then we would have a great many electrical applications. Not just in transmitting electricity from one point to another, but superconductors have other practical properties. One of their other practical properties is that they exclude magnetic fields from their interior. And one of the properties this gives them is that they have the ability to levitate magnets, or to be levitated in a magnetic field. And so these properties are extremely useful. One area in which this may be useful is in the development of high-speed rail transport.
Interviewer: Is superconductivity an example of emergent behavior?
PIERS: Superconductivity is a wonderful example of emergent behavior—wonderful in many respects. First of all, it was completely unanticipated when it was first discovered over 100 years ago. Second, it’s an example of a property that you just wouldn’t imagine the metals would develop just by making them colder. And after it was discovered, it took something like 50 years for physicists to understand how a superconductor actually works. It’s a very nice example of emergent behavior because it’s a property of matter that you wouldn’t anticipate from the microscopic properties of the ways electrons interact with each other.
Interviewer: What do you do as a theorist? What are the big questions that are driving you?
PIERS: Well, the canvas that we work with in my part of physics, which is condensed matter physics, is the canvas of the periodic table. And of course we have something like 92 different elements to play with. The amazing thing is that, because of emergence, when we put those atoms together to form crystals, they develop new properties—not just superconductivity, but also magnetism and various other emergent properties that fascinate us. As we go out along the periodic table, the possibilities for new kinds of behavior exponentiate. In fact as we combine the atoms together to form new materials, each new material is like its own mini universe of behavior, and its collective properties need to be understood mathematically and experimentally. We’d like to understand things well enough that we could help people design new materials.
Which direction do you go in this “multiverse” of possibilities when you can combine literally any element with another one and bake it to form a new kind of crystal? What do we have to do to find the ones that are most interesting? How do we transform them from one to the other? What are their basic properties that enable them to develop these emergent properties? To answer those questions requires a combination of experimental work: making the materials and measuring their properties; and theoretical work: understanding the math that describes their collective behavior, making predictions, and helping interpret the experiments that are being made.
Interviewer: What excites you about this?
PIERS: This is literally the frontier beneath our nose. It’s the frontier that comes about from combining the basic elements and producing new collective forms of behavior. And these collective forms of behavior go from the simplest crystals out presumably to life itself. You and I are a consequence of combining inert, inorganic atoms together in a way that produces an incredible collective phenomenon. A collective phenomenon that began 4 billion years ago and is still going strong today. Between biology and the most mundane crystals is a whole panorama of possibilities. And what we’d like to do is understand the principles that govern that emergent collective behavior. In so doing, we’re not abandoning a reductionist point of view. In fact, the two have a synergy between them.
Interviewer: Are you trying to come up with principles that are broadly applicable?
PIERS: Yes. When people imagine physics, they imagine something of great complexity. They imagine that to do physics you need huge banks of computers that will track all the complexity and all of its gothic detail. But actually, the life of physicists is rather different from that. It’s much closer to that of the impressionist painter or the haiku poet. And what they want to do is to condense out of the complexity the essence of the physics. What we want is something that describes the relevant low-energy degrees of physics, which are often the collective degrees of freedom. And to capture those, we can strip away a lot of its complexity and talk about writing down models that contain the relevant degrees of freedom for the low-energy physics.
That’s one of the remarkable things about nature. If you want to understand its collective behavior, you don’t need to keep track of all of the detailed wigglings and nigglings at very high frequency. What you need to capture are the long wavelength slow modes of the behavior. These can be the slow modes of the waves, but also of the electron waves themselves. So we use experimental guidance to give us insight into what those low-energy models actually are. Once we have a good model, we hope that we can actually solve it somehow. Now solving that model may involve a computer, but in an ideal situation the best solutions can be done on the back of an envelope. Our real dream is to use experiments and perhaps computers and their simulations to give us the ultimate simplification of the physics that can be captured just like a piece of haiku poetry in a simple equation. And in that sense, studying emergence is still reductionist. We are still seeking those simple encapsulations of the world around us that will capture all the physics in an extraordinarily simple fashion.
Interviewer: How do you go about trying to get these “ultimate simplifications?”
PIERS: I want to get a few of the buzzwords in and get across the idea that’s particularly exciting to us, not just in condensed matter physics today, about the state that separates stable states of matter. We know that matter can occur in various stable phases, and that these are like the different multiverses of the periodic table. So a metal can just form a simple metal, and we have a name for that particular state of matter. Or it can magnetize different types of magnets. So what we’re discovering more and more is that the point of connection between the stable phases, the so-called critical point that connects them, is particularly fascinating. And critical points seem to be more and more the linking idea for the periodic table. They are like the portals between these different multiverses. And we discover that when we can tune a state of matter close to a critical point, it seems to nucleate many new emergent states of behavior. This is giving us a clue as to where we should start looking. Where should I go? What kind of material should I make to form a high-temperature superconductor? Well, one idea is to tune it to the brink of magnetic instability, which we’re studying. And it’s led to all sorts of new ideas.
Interviewer: Can you talk about something specific you worked on that involved quantum critical points?
PIERS: One example was something we call Omega over T scaling. This was neutron scattering data carried out by friends of mine, an experimentalist called Almut Schroeder, and her collaborator, Gabriel Applei, with a number of other experimentalists. What they’ve done is some very fine sets of neutron scattering of a material called Cerium Copper 6 Gold (CeCu6Au). What is Cerium Copper 6 Gold? Well, the 6 says there are six atoms of Copper combined with one atom of Cerium. It’s an example of an inter-metallic compound. So why is it interesting? Well, Copper on its own is an example of a regular metal. And electrons move around, not so differently to the way they move around in empty space. When you put a little bit of Cerium into it—Cerium has a magnetic moment on it—it’s like a little gyroscope. And it turns out that when you put those gyroscopes into the electric sea, they kind of dissolve. The spins on these gyroscopes dissolve into the fluid and they drive the mass of the electrons up so it’s now a thousand times larger than it was in Copper, meaning they’re much more inertial in the way they move around the metal. We call them heavy fermions or heavy electrons. Now, if you push a bit harder on this by putting in a little bit of Gold into this Cerium Copper 6, you get Cerium Copper 6 Gold. And as you start to put the Gold in, it starts to expand the lattice. As it expands the lattice, it turns out that some of the electrons localize and form a magnet, an anti-ferromagnet. What my colleagues Gabriel Applei and Almut Schroeder did was to actually look at that system at the very point where it went unstable. The quantum critical concentration of Gold: 1% of Gold, and this is 10% Gold, drove it quantum critical. And they were able to make big enough samples of this stuff that they could actually get a decent signal and probe the magnetic fluctuations by putting it in a beam of neutrons.
Interviewer: What did they see?
PIERS: What they saw was remarkable. They found that when they looked at these jigglings of the magnetic order nascently forming, that as they cooled it down, the quantum mechanical fluctuations got slower and slower. We could look at the spectrum of those fluctuations as a function of frequency and see that, as they went to lower temperatures, the width of that spectrum got narrower and narrower.
Interviewer: When you say the “spectrum of the fluctuations,” what is that?
PIERS: The neutrons measure the variations in the magnetism inside the material as a function of time and as a function of space. That’s why neutron scattering is such a valuable way of probing matter. They measured these fluctuations as a function of energy. What they were able to do was to measure the amount of neutrons that were scattered for a given amount of energy transferred to the material. And from the energy transferred, you can convert that to the frequency of the magnetic fluctuations.
Interviewer: What did this experiment tell you?
PIERS: One of the ideas that came out of our conversations—and I wouldn’t say it was the theorists or the experimentalists, but it was the collaboration—was that one should actually look at that and plot the data as a function of omega, the frequency, divided by the temperature. When we did that, a whole bunch of data all collapsed onto one curve, and we could write down a mathematical form for that curve. What this told us was that the characteristic time scale of the fluctuations was determined by the temperature itself. In fact, it was really the inverse of the temperature. So, the lower in temperature you go, the longer the time scale of these quantum mechanical critical fluctuations.
Interviewer: Why is that remarkable?
PIERS: It was remarkable because it wasn’t expected on the basis of the existing models of how magnetism would emerge in this material. And it turned out that this simple behavior is something that had been seen in the context of thermal phase transitions, thermal critical points. What we were seeing is kind of like a spacetime generalization of what we were seeing in thermal critical points. Think of quantum phase transitions as classical phase transitions in spacetime. When you do this, it turns out that temperature acts like the fourth dimension. And the lower the temperature, the wider the universe becomes in that fourth dimension. So what these guys were seeing in that Omega over T scaling was that one over temperature was providing the time scale. And you can see this in this beautiful data. But it turns out that relationship shouldn’t hold, according to our simplest models of quantum phase transitions. This tells us that something more profound and more profoundly simple is taking place at this quantum critical point.
I think what this data told us is that the old paradigm was breaking down—the old paradigm of metals and the nature of the metallic state and the way it transforms could not explain this data. That’s mentally exciting to us. It means that we might have a clue as to more exotic kinds of metallic behavior, more exotic ways in which the electrons can interact to produce new states of matter. This data told us that the mechanism by which magnetism forms within the metal could not explain this particular system; and that perhaps if we could only develop a deeper understanding of the critical magnetic fluctuations that separate the magnet from the metal, we could understand the new strange metals that give rise to new forms of order, such as high-temperature superconductivity. So what did it lead to? It led to recognition that we need to revise our understanding.
Interviewer: Can you define a quantum critical point and compare it to a classical critical point?
PIERS: Critical points are, in the context of matter, the point of a phase transition—a second order phase transition. It’s a continuous phase transition where the order develops continuously as you go beyond that special point. For example, when iron becomes a ferromagnet at quite high temperatures, it does so by a second order phase transition. And the point at which the transition occurs, where the order just starts to develop, is then called a critical point. Now what’s important about a critical point? It’s the point where the order fluctuates on longer and longer length scales. You can think of it as bubbles of order being created, and it turns out that these bubbles of order can be any type of order.
Interviewer: Is water boiling a second order phase transition?
PIERS: Water boiling is an example of a first order phase transition. However, if you increase the pressure of water, it turns out that the boiling point actually goes up in temperature. At higher pressure, it goes at higher temperatures. If you go to a mountain, it goes at lower temperatures. As you increase that temperature by pressurizing it, you can ask, “Well, can that temperature, the transition, go arbitrarily high?” And the answer is no, it can’t. It eventually comes to an end. And the point where it comes to an end is a critical point. It turns out that if you look at water at its critical point, it turns out it goes dark. The steam goes dark at that point because the fluctuations of density actually expand on longer and longer length scales. They become correlated on longer and longer length scales. They become so correlated that they actually start to scatter light. This is called critical opalescence, and it occurs at the critical point of water. So this same opalescent phenomena occurs at all critical points. At a magnetic quantum critical point, you get magnetic opalescence. The fluctuations of the magnetization grow on longer and longer length scales.
Now the interesting thing is that for thermally induced phase transitions, critical behavior only occurs very, very close in to the critical point. Now let’s talk about quantum phase transitions and quantum critical points. These are critical points where thermal motion has been replaced by quantum mechanical fluctuations, which become fierce enough to melt the underlying order. Now what’s different about quantum criticality is that now the fluctuations become opalescent not just in space, but also in time. You can think of them as fluctuations, bubbles of order that bubble up and live for a long time in a very extended space and then disappear again, like a kind of quantum mechanical soda. And at the critical point, those bubbles bubble up on all length scales.
Interviewer: What drives those quantum phase transitions?
PIERS: Conventional phase transitions are driven by thermal motion. Quantum phase transitions are not driven by the thermal jigglings of matter, but by the quantum mechanical jigglings of matter. Now, why does matter have quantum mechanical jigglings? Well, this is connected with the Heisenberg Uncertainty Principle, which tells us that we can measure with arbitrary accuracy the velocity of a particle, but when we do that, we don’t know what its position is. Or we can measure its position with arbitrary accuracy, but we don’t know what its velocity is. So there’s a tradeoff. We can have some partial knowledge of roughly where it is and some partial knowledge of roughly what its momentum is, but the tradeoff is that one or another of those is jiggling around. So when you localize an electron near an atom, it has zero point motion. In fact, the clouds of electrons around an atom can be thought of as a jiggling of the electron in the potential well of that atom. Atoms themselves undergo jigglings. We call it zero point motion. That very same zero point motion might also, some people believe, be responsible for 73% of the dark energy in the universe. We’re trying to understand these jigglings, and when they get too strong, they themselves can melt matter. In particular, when the jigglings of a spin become too great, the magnet melts. And at the point where that magnetic order is released, the metal acquires new properties. It acquires very strange metallic properties which some of us believe are responsible for the fabric that gives rise to high-temperature superconductivity. So, we’re spending a lot of time at the moment studying that very point, that portal between the two multiverses: the point of maximum quantum mechanical jiggling we call a quantum critical point.
Interviewer: Is there an idea that some behavior like superconductivity is to avoid the quantum critical point?
PIERS: Yes. There is an indication from a wide range of experiments that, when you get a magnetic quantum critical point, it tends to nucleate superconductivity around it. This is a new form of superconductivity in which the magnetism plays a major role in forming the [electron] pairs that then condense. And so one of the reasons for being interested in quantum criticality is that we believe that, in the vicinity of a magnetic quantum critical point, the interactions between the electrons give them a marked tendency to want to form cooper pairs that condense into robust high-temperature superconductors. We didn’t have the chance to go back and talk about what causes electrons to form pairs. But in the first generation of superconductors, it was the elasticity of the lattice—the lattice expands slightly to allow them to come together and form pairs. But in this new generation of superconductors, the superconductivity is almost certainly not produced by the deformations of the lattice, and many people believe it’s due to the interplay of the magnetism with the electrons. In a very naïve picture, the magnetism is providing the glue that glues the electrons together into a pair, but the exact nature of that magnetic glue is a matter of great controversy. Whether you can even think of it as electrons glued together into a pair is a matter of great discussion.
Interviewer: Is there anything you would like to mention that we have left out?
PIERS: I think one thing we haven’t touched on is this link between the lab and the universe—it’s one of the amazing things about physics that what we learn in the lab teaches us about things out in the cosmos. And what we learn out in the cosmos teaches us about what’s going on in the lab—and what we mean by the lab today can mean various things. It can mean a cryostat, or it can mean a trap of cold atoms. But the amazing thing is that we learn about principles from the apple, from the cryostat that tells us also about the cosmos. Today we’re at an extraordinary time where there are even people taking ideas from string theory and trying to apply them to the problem of quantum criticality. And so we have this fascinating time where people are seriously discussing whether they can use the tools that were invented to describe the quantum mechanics of gravity to describe the physics of electrons at a quantum critical point. If it’s true, which is not clear at the moment, it would be yet one more example of that tremendous relationship between physics in the lab, in the cryostat, and physics out in the cosmos, in the collider.
8.2 Emergent Behavior in Quantum Matter – Video
Reductionism—breaking things into their component parts to study how they work—is an effective tool in physics. But many real-world challenges resist this approach. All too often, large scale behavior emerges in ways that are difficult to predict from the behavior of individual components. When the computational requirements are too massive or the theories that govern the component parts are inadequate, many complex systems have yielded to the physics of emergence, which seeks organizing principles at the system level. Find out how many different phenomena—superconductors, hydrodynamics, and even the formation of structure in the universe—are all fruitful areas where the physics of emergence is leading to new understanding.
Supplementary: Unit 8: Emergent Behavior in Quantum Matter — Printable Online Text
Supplemental resource for educators and students