## The Joy of Condensed Matter

I published a slightly different version of this article in Nautilus on February 24, 2021.

Everyone seems to be talking about the problems with physics: Woit’s book Not Even Wrong, Smolin’s The Trouble With Physics and 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.

The fine print is crucial. First: “at least 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 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.

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—particles like ordinary matter particles, with the same mass but with the opposite charge—was born. But that’s another story.

In 1931, 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 but 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 really 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 were 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 really 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 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!

This is how an exciton moves through a crystal.

The idea of excitons goes back all the way to 1931. By now we can make excitons in large quantities in certain semiconductors. They don’t last for long: the electron quickly falls back into the hole. It can take between 1 and 10 trillonths of a second for this to happen. But that’s enough time to do some interesting things.

For example: if you can make an artificial atom, can you make an artificial molecule? Sure! 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 create materials called “hyperbolic metamaterials” 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 acts as if there’s a whole circle of directions that count as “forward in time”. The possibilities 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.

### 23 Responses to The Joy of Condensed Matter

1. Bill Bottenberg says:

Thanks John, this was great, and enjoyable analysis of today in physics.

• John Baez says:

2. First Approximation says:

Good article!

There seems to be many ideas that cross between condensed matter physics and particle physics. Quantum field theory is used both. The Higgs mechanism originated in studying superconductivity. Etc.

This alone should kill the “fundamentalist” chauvinism, but do you think these parallels provide a useful hint for beyond-the-stand-model physics?

• John Baez says:

People have tried to use some ideas from condensed matter physics in beyond-Standard-Model physics. An example that leaps to mind is string-net condensation, discussed in this paper and others:

• Michael Levin and Xiao-Gang Wen, Photons and electrons as emergent phenomena.

But the great thing about condensed matter physics is that you can test ideas in the lab much more easily than in particle physics. So I actually think straight condensed matter physics is more interesting than applying ideas from condensed matter to beyond-Standard-Model physics.

• Joe says:

Piggy-backing: Have you checked out Volovik’s “The Universe in a Helium Droplet”? It talks about quantum field theoretic and general relativistic analogies in different condensed matter settings. How likely do you think it is that we can probe these condensed matter analogies to discover something about QFT, GR or quantum gravity? Have you heard of this happening yet? (The book has been around for 2 decades I think now.)

• John Baez says:

I haven’t seen The Universe in a Helium Droplet—it looks like lots of fun, thanks. I’ve seen some work trying to connect superfluidity in helium-3 to ideas about quantum gravity. I think it’s great to pursue these analogies, but everything about beyond-Standard-Model physics is very hard, so at this point the easy way to make real progress is to study condensed matter physics for its own sake, not to use it to study beyond-Standard-Model physics. One should learn to love the stuff one really sees in the lab!

3. anon says:

I feel like it’s worth noting that the hottest topic on the hep-th arxiv for the past couple years is the duality between the SYK model (an important model in condensed matter physics), and JT gravity, a two dimensional model of gravity. The exchange of ideas goes in both directions: insights from gravity are being used to compute observables in the SYK model and, in another direction, insights from the SYK model are being used to learn new things about black holes, like the recent discovery of entanglement “islands” in the black hole spacetime, and the recent calculation of the black hole Page curve using a path integral that includes contributions from wormhole geometries. So the distinction between condensed matter and high energy theory is not completely sharp. (Actually, going further, I think the most interesting thing isn’t the condensed matter side or the hep-th side but the fact of the duality itself– these sorts of holographic dualities remind me of S duality/Langlands duality but they are newer and more mysterious.)

• John Baez says:

All this stuff sounds very neat. I haven’t been following it at all—too busy doing applied category theory and other things!

One of the great attractions of condensed matter physics has always been its close connection to particle physics: they’ve always shared mathematical techniques. I mentioned how Heisenberg introduced holes in condensed matter physics in 1931, one year after Dirac’s use of holes in particle physics. The interplay has been strong ever since. The connection between the Higgs mechanism and the Landau-Ginzburg theory of superconductivity is one famous high point. The whole circle of ideas involving the renormalization group is another. Conformal field theory is a tractable, mathematically beautiful special case of this. Now condensed matter physicists are busy trying to make Majorana fermions in lab! The list goes on and on.

I would call 2-dimensional gravity “math inspired by physics” or maybe “simplified models of quantum gravity”, not “high-energy theory” in the old-fashioned sense of physical theories that can be tested by accelerator experiments. It’s perfectly fine if high-energy theory drifts into this realm as long as the practitioners are honest about it. I think that over time people will come to admit that “math inspired by physics” is a perfectly valid field of study, even if it never makes contact with experiment. It can flourish even if we never make another experimental discovery in high-energy particle physics.

• John Baez says:

And here’s another nice case of ideas from quantum field theory showing up in condensed matter: people are trying to explain the superconductivity in twisted graphene bilayers and trilayers using skyrmions!

• Charlie Wood, A new twist reveals superconductivity’s secrets, Quanta, 16 March 2021.

• anon says:

Another interesting recent example along these lines is the work of Seiberg and Shao. They are using QFT to describe exotic states of matter called fractons. A key part of their story is the need to make sense of QFT with discontinuous fields. So along the way new things are learned about QFT itself.

Another comment about black holes is that part of the reason they blur the line between hep-th and condensed matter is that from one perspective they belong to particle physics (they’re characterized by mass and spin only, GR breaks down at the singularity), but from another perspective they are condensed matter systems (entropy, temperature, evaporation).

4. Wyrd Smythe says:

The nice thing about holes is they flow in the direction the arrows in diode and transistor symbols point. Back when I was learning electronics, it annoyed me that current flowed in the opposite direction of the arrows.

Question: If a hole is due to an absent electron, what gives them greater mass than an electron?

• John Baez says:

The effective mass of an electron in a material is basically the number $m$ that makes the energy $E$ equal to

$E = \frac{1}{2} m v^2$

at low velocities $v$. This depends a lot on the material, because the material affects how much energy an electron moving at some velocity will have: the electron interacts with the material. The ‘actual’ mass of the electron is just one part of this story, and sometimes a very small part.

The same is true for holes. And remember, when a hole (a place where there’s no electron) is moving around, it’s really electrons that are moving around. So there’s no reason for a hole to be lighter than an electron!

From Wikipedia:

For electrons or electron holes in a solid, the effective mass is usually stated in units of the rest mass of an electron, me. In these units is usually in the range 0.01 to 10, but can also be lower or higher—for example, reaching 1,000 in exotic heavy fermion materials, or anywhere from zero to infinity (depending on definition) in graphene.

• Wyrd Smythe says:

(Sorry for the delay in replying. Real life got distracting.) What puzzled me was that, in the post you wrote “if the hole is much heavier than the electron” and I wondered how, in the same material and under the same conditions (?), the hole could be much heavier. Them both having the same mass makes sense, but what makes the hole heavy enough to act like a proton is what I didn’t understand.

• John Baez says:

I tried to answer your question but I’ll say it again, shorter. When a hole is moving, it’s actually a bunch of electrons moving, since a hole is just a place where an electron isn’t. So, there’s no reason to suspect that a hole moving will take less energy than a single electron moving.

• Wyrd Smythe says:

I totally get the “less energy than a single electron” — it’s it taking much more that throws me. If I understand, it’s because one hole has the apparent mass of many electrons? (Apologies if I’m coming off as dim-witted, but I like to be sure I’m 100% clear on things like this.)

• John Baez says:

When a hole moves, it’s really a bunch of electrons moving around, and mass is just a measure of how much energy it takes for something to move around. So it seems quite plausible that a hole would have a larger mass than an electron. It’s actually surprising that sometimes a hole has a smaller mass than an electron. But in fact both the electron mass and the hole mass can vary widely depending on the material they find themselves in. It all depends on how much energy it takes to move around the relevant stuff.

5. Feynman’s last blackboard contained fa list of things to learn, which were all condensed matter topics

Bethe ansatz
Kondo effect
2-D Hall effect
Non-linear classical hydrodynamics

and a line that appears to read “accel. Temp”

• John Baez says:

Neat! My guess about “accel. temp” is that it’s about the Unruh effect:

The Unruh effect is the hypothetical prediction that an accelerating observer will observe a thermal bath, like blackbody radiation, whereas an inertial observer would observe none. In other words, the background appears to be warm from an accelerating reference frame; in layman’s terms, an accelerating thermometer (like one being waved around) in empty space, subtracting any other contribution to its temperature, will record a non-zero temperature, just from its acceleration.

6. H.Z. says:

To me the hardest thing to wrap my brain around is the treatment of identical particles in multibody wave functions. While the mathematics isn’t particularly hard to get since condensed matter physicists don’t particularly care about special relativity, it is still mind-boggling that you and me have electrons that are supposedly anti-symmetric with each other. Even though there shouldn’t be any observable effects given our distance, it nevertheless gives me a slightly nauseous feeling that my feet are on wobbly ground.

7. anon says:

“materials in which light moves as if there were two space dimensions and two time dimensions”

What exactly is this line referring to? I’d love a term for it or a link to where i could read more about.

• John Baez says:

Yes, I should have given the usual name for these materials: “hyperbolic metamaterials”. Here’s an explanation that’s available for free:

• Alexander Poddubny, Ivan Iorsh, Pavel Belov, and Yuri Kivshar, Hyperbolic metamaterials, Nature Photonics 7 (2013), 948–957.

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