The Joy of Condensed Matter

By John C. Baez By John C. Baez February 24, 2021

Everyone seems to be talking about the problems with physics: Peter Woit’s book Not Even Wrong, Lee Smolin’s The Trouble With Physics, and Sabine Hossenfelder’s Lost in Math leap to mind, and they have started a wider conversation. But is all of physics really in trouble, or just some of it? If you actually read these books, you’ll see they’re about so-called “fundamental” physics. Some other parts of physics are doing just fine, and I want to tell you about one. It’s called “condensed matter physics,” and it’s the study of solids and liquids. We are living in the golden age of condensed matter physics.

But first, what is “fundamental” physics? It’s a tricky term. You might think any truly revolutionary development in physics counts as fundamental. But in fact physicists use this term in a more precise, narrowly delimited way. One of the goals of physics is to figure out some laws that, at least in principle, we could use to predict everything that can be predicted about the physical universe. The search for these laws is fundamental physics.

There is still plenty of mind-blowing new physics being done.

The fine print is crucial. First: “in principle.” In principle we can use the fundamental physics we know to calculate the boiling point of water to immense accuracy—but nobody has done it yet, because the calculation is hard. Second: “everything that can be predicted.” As far we can tell, quantum mechanics says there’s inherent randomness in things, which makes some predictions impossible, not just impractical, to carry out with certainty. And this inherent quantum randomness sometimes gets amplified over time, by a phenomenon called chaos. For this reason, even if we knew everything about the universe now, we couldn’t predict the weather precisely a year from now. So, even if fundamental physics succeeded perfectly, it would be far from giving the answer to all our questions about the physical world. But it’s important nonetheless, because it gives us the basic framework in which we can try to answer these questions.

As of now, research in fundamental physics has given us the Standard Model (which seeks to describe matter and all the forces except gravity) and General Relativity (which describes gravity). These theories are tremendously successful, but we know they are not the last word. Big questions remain unanswered—like the nature of dark matter, or whatever is fooling us into thinking there’s dark matter. Unfortunately, progress on these questions has been very slow since the 1990s. Luckily fundamental physics is not all of physics, and today it is no longer the most exciting part of physics. There is still plenty of mind-blowing new physics being done. And a lot of it—though by no means all—is condensed matter physics.

Traditionally, the job of condensed matter physics was to predict the properties of solids and liquids found in nature. Sometimes this can be very hard: for example, computing the boiling point of water. But now we know enough fundamental physics to design strange new materials—and then actually make these materials, and probe their properties with experiments, testing our theories of how they should work. Even better, these experiments can often be done on a table top. There’s no need for enormous particle accelerators here.

The water is always running in Björn Hof’s laboratory. Like a Zen water fountain, it gently flows over the top of a reservoir into a tube, and from there into a glass pipe 15 meters long, but thinner than...READ MORE

Let’s look at an example. We’ll start with the humble “hole.” A crystal is a regular array of atoms, each with some electrons orbiting it. When one of these electrons gets knocked off somehow, we get a “hole”: an atom with a missing electron. And this hole can actually move around like a particle! When an electron from some neighboring atom moves to fill the hole, the hole moves to the neighboring atom. Imagine a line of people all wearing hats except for one whose head is bare: If their neighbor lends them their hat, the bare head moves to the neighbor. If this keeps happening, the bare head will move down the line of people. The absence of a thing can act like a thing!

The famous physicist Paul Dirac came up with the idea of holes in 1930. He correctly predicted that since electrons have negative electric charge, holes should have positive charge. Dirac was working on fundamental physics: He hoped the proton could be explained as a hole. That turned out not to be true. Later physicists found another particle that could: the “positron.” It’s just like an electron with the opposite charge. And thus antimatter—the evil twin of ordinary matter, with the same mass but the opposite charge—was born. (But that’s another story.)

We now live in the era of “designer matter.”

In 1931, Werner Heisenberg applied the idea of holes to condensed matter physics. He realized that, just as electrons create an electrical current as they move along, so do holes—but because they’re positively charged, their electrical current goes in the other direction! It became clear that holes carry electrical current in some of the materials called “semiconductors”: for example, silicon with a bit of aluminum added to it. After many further developments, in 1948 the physicist William Schockley patented transistors that use both holes and electrons to form a kind of switch. He later won the Nobel Prize for this, and now they’re widely used in computer chips.

Holes in semiconductors are not really particles in the sense of fundamental physics. They are just a convenient way of thinking about the motion of electrons. But any sufficiently convenient abstraction takes on a life of its own. The equations that describe the behavior of holes are just like the equations that describe the behavior of particles. So, we can treat holes as if they are particles. We’ve already seen that a hole is positively charged. But because it takes energy to get a hole moving, a hole also acts like it has a mass. And so on: The properties we normally attribute to particles also make sense for holes.

Physicists have a name for things that act like particles even though they’re not: “quasiparticles.” There are many kinds; holes are just one of the simplest. The beauty of quasiparticles is that we can practically make them to order, having a vast variety of properties. As the quantum physicist Michael Nielsen put it, we now live in the era of “designer matter.”

For example, consider the “exciton.” Since an electron is negatively charged and a hole is positively charged, they attract each other. And if the hole is much heavier than the electron—remember, a hole has a mass—an electron can orbit a hole much as an electron orbits a proton in a hydrogen atom. Thus, they form a kind of artificial atom called an exciton. It’s a ghostly dance of presence and absence!

OPPOSITES ATTRACT: This is how an exciton, the binding together of a positively charged “hole” and an electron, moves inside a crystal lattice.Wikipedia

The idea of excitons goes back all the way to 1931. By now we can make excitons in large quantities in certain semiconductors and other materials. They don’t last for long: The electron quickly falls back into the hole. It often takes less than a billionth of a second for this to happen. But that’s enough time to do some interesting things. Just as two atoms of hydrogen can stick together and form a molecule, two excitons can stick together and form a “biexciton.” An exciton can stick to another hole and form a “trion.” An exciton can even stick to a photon—a particle of light—and form something called a “polariton.” It’s a blend of matter and light!

Can you make a gas of artificial atoms? Yes! At low densities and high temperatures, excitons zip around very much like atoms in a gas. Can you make a liquid? Again, yes: At higher densities, and colder temperatures, excitons bump into each other enough to act like a liquid. At even colder temperatures, excitons can even form a “superfluid,” with almost zero viscosity: if you could somehow get it swirling around, it would go on practically forever.

This is just a small taste of what researchers in condensed matter physics are doing these days. Besides excitons, they are studying a host of other quasiparticles. A “phonon” is a quasiparticle of sound formed from vibrations moving through a crystal. A “magnon” is a quasiparticle of magnetization: a pulse of electrons in a crystal whose spins have flipped. The list goes on, and becomes ever more esoteric.

But there is also much more to the field than quasiparticles. Physicists can now create materials in which the speed of light is much slower than usual, say 40 miles an hour. They can even create materials in which light moves as if there were two space dimensions and two time dimensions, instead of the usual three dimensions of space and one of time! Normally we think that time can go forward in just one direction, but in these substances light has a choice between many different directions it can go “forward in time.” On the other hand, its motion in space is confined to a plane.

In short, the possibilities of condensed matter are limited only by our imagination and the fundamental laws of physics.

At this point, usually some skeptic comes along and questions whether these things are useful. Indeed, some of these new materials are likely to be useful. In fact a lot of condensed matter physics, while less glamorous than what I have just described, is carried out precisely to develop new improved computer chips—and also technologies like “photonics,” which uses light instead of electrons. The fruits of photonics are ubiquitous—it saturates modern technology, like flat-screen TVs—but physicists are now aiming for more radical applications, like computers that process information using light.

Then typically some other kind of skeptic comes along and asks if condensed matter physics is “just engineering.” Of course the very premise of this question is insulting: There is nothing wrong with engineering! Trying to build useful things is not only important in itself, it’s a great way to raise deep new questions about physics. For example, the whole field of thermodynamics, and the idea of entropy, arose in part from trying to build better steam engines. But condensed matter physics is not just engineering. Large portions of it are blue-sky research into the possibilities of matter, like I’ve been talking about here.

These days, the field of condensed matter physics is just as full of rewarding new insights as the study of elementary particles or black holes. And unlike fundamental physics, progress in condensed matter physics is rapid—in part because experiments are comparatively cheap and easy, and in part because there is more new territory to explore.

So, when you see someone bemoaning the woes of fundamental physics, take them seriously—but don’t let it get you down. Just find a good article on condensed matter physics and read that. You’ll cheer up immediately.

John Baez is a professor of mathematics at the University of California, Riverside and a visiting researcher at the Centre for Quantum Technologies in Singapore. He blogs about math, science, and environmental issues at Azimuth.

Lead image: Stef Simmons, UCL Mathematical and Physical Sciences / Flickr