What's The Difference Between Particles & Quasiparticles? (SCRIPT) (Patreon)

The device you’re watching this video on is best understood by thinking about positive and negative charges moving around a circuit of diodes and transistors. But the only elementary particle actually flowing in the circuit is the negatively charged electron. And yet those flowing positive charges are there, in the form of a particle you may never have heard of. Your device works because of quasi-particles - a class of strange emergent behaviors of nature that enable our most important technologies and are behind some of the weirdest phenomena we’ve ever encountered

[intro]

Let’s start our discussion of quasiparticles by talking about the particular quasiparticle that lets me talk to you about quasiparticles right now. Electrons, which are regular particles, are pushed around inside electrical circuits, but it’s only half the story. In semiconductors that make up transistors, diodes, and solar cells the pushing around of a quasiparticle is equally important.

Let’s look at the material that is central to all modern electronics - silicon. The silicon atom has 4 electrons in its outer or valence shell. Atoms are most stable with full valence shells, which means 8 electrons. That’s why silicon likes to form covalent bonds with 4 other silicons, and each of those with another 4, forming this tetrahedral crystal structure.

We’re going to depict this as a square grid in 2-D to save on animation costs. These electrons are locked in place in the now-full valence energy level. But they can still get bumped up to a higher energy state - say, by thermal vibrations or in the case of solar cells by a photon, at which point they are free to move from atom to atom - for example if pulled by a voltage applied across the silicon.

Meanwhile, the gap left by this electron allows some movement in the valence shell. A neighboring electron can move there, and its neighbor can fill t he new gap, etc. It looks like the hole moves around, and under a voltage the hole moves in the opposite direction to the flow of electrons.

This is our first quasiparticle - it’s an electron hole. It has an effective positive charge due to the charge of the nucleus not being properly canceled by electrons in that location. It even has an effective positive mass. We can model it as though it’s a real particle.

To see how this quasiparticle is more than just “a way of looking at things”, consider perhaps the simplest semiconductor device - the diode.

Diodes allow current to travel in one direction but not the other. They consist of two layers of silicon - on one side there’s an excess of valence electrons, and in the other a deficit. This is achieved by doping - contaminating each layer by a different element.

On one side we sprinkle the silicon lattice with a tiny number of atoms that have 5 rather than 4 valence electrons. Phosphorus is a popular choice. Those extra electrons are more free to move around because they aren’t part of the crystal bonds. This is an n-type semiconductor - n because the flowing charge is negative.

The other side is doped with atoms that have 3 valence electrons - frequently boron. Now electrons can shuffle to fill the gaps in the underfilled valence shells - so we have flowing positively charged electron holes a nd a p-type semiconductor.

In a diode, n- and p-types are fused together. At the p-n junction, extra electrons in the n-type diffuse into the gaps in the p-type so we end up with a region where all valence shells are filled so charge can’t flow. Apply a voltage in one direction and the holes and electrons flow away from this junction, expanding the non-conductive region and shutting down the current. But apply the voltage the other way and the electrons and holes are driven towards the junction, causing it to narrow and electrons hop across, enabling the flow of electricity. That’s the diode - a valve for electricity. And these p-n junctions also drive solar cells, LEDs, and transistors.

And they all depend on the behavior of these quasiparticles - these holes. You might argue that electron holes are just a convenient way of looking at things, but that they aren’t “real” like electrons are. After all, if you melt the silicon the electrons still exist but the holes don’t.

In a sense that’s right - quasiparticles are emergent from the behavior of a particular configuration of matter. Just like states of matter, which we talked about previously.

OK, let’s explore some other quasiparticles. We’ll stick with our silicon crystal. We have one quasiparticle from making a gap at one spot in the electron energy level. We can make another by making a different local energy tweak. Another way energy can be stored in the lattice is in the vibrational modes of the atoms. Think of the covalent bonds as springs, so when an atom receives pressure it will move, pressing on the springs, and causing other nearby atoms to move as well. In this way vibrational energy can move around the lattice. But this seems a bit more like a sound wave than a particle. In fact sound waves in solids do propagate exactly like this. But remember we’re at the quantum scale here.

Those vibrational modes in the crystal are quantized, similar to electron energy levels. In this case, the crystal lattice can vibrate at any frequency, but the amount of energy at each vibrational mode can only go up in discrete chunks.

That means vibrational energy also gets transferred in discrete packets. So now we have something like a particle - a quantum of vibrational energy moving around the lattice. This new quasiparticle is called a phonon. I said that sound is transmitted through solids via these vibrations - so this makes the phonon a quantum of a sound wave, similar to how a photon is a quantum of light - of an electromagnetic wave.

The analogy is not a shallow one. Phonons behave in many ways like light. They travel at the speed of their wave-type - sound in this case. They have energy equal to the planck constant times their frequency. They are boson-like in that you can stack multiple phonons on top of each other in a single vibration.

Compare that to electron holes, which are fermion-like in that you can only have one in a given spot at one time.

As well as being a quantum of sound in solids, they are also the quantum of heat. After all, heat in solids comes from the vibrational motion of its atoms, and that vibration is transferred around by phonons. You can think of sound as a coherent beam of phonons, like a laser, while heat is a random buzz of phonons.

Understanding the behavior of phonons is critical for the understanding of the behavior of both sound and heat in solids. And the latter is also really important for your computer, which, as you know, can get hot. Energy is often transferred between phonons and other particles - quasi- and real - and modeling this is needed for modeling the behavior of heat on the quantum scale.

For example, electrons traveling through a circuit encounter resistance - basically, they have collisions, which can be electromagnetic interactions with other electrons, falling into a hole, etc. In doing so they can dump its energy into a vibrational mode and create a phonon. This manifests as heat. The heat due to electrical resistance is one of the main limitations on running your computer as fast as you might like to. But quasiparticles can help there too.

But first a recap. We now have two types of quasiparticle - holes, which are like quasi-electrons … or perhaps quasi-positrons, and we have phonons, which are analogous to photons. Now, elementary particles can be combined into composite particles, for example an atom is composed of quarks forming a nucleus and electrons bound to that nucleus by the exchange of virtual photons. Believe it or not we can create composite quasiparticles in a similar way.

And, as it happens, the new quasiparticle we’re going to create can help us with this electrical resistance problem. You may have heard of a little something known as Superconductivity, when you cool a metal near absolute zero and the electrical resistance becomes zero, which in turn creates many cool interactions with electromagnetic fields, like levitating magnets, which you can use to make super fast trains.

We’ll do a deeper dive into superconductivity another time - today I just want to show you how this phenomenon is enabled by quasiparticles. Metals form crystal lattices similar to silicon, but they are much better conductors because they don’t use up all of their valence electrons in the bonds of the lattice. Add a voltage and those electrons are free to travel through the structure as an electrical current.

But of course we have them pesky phonons, which at any significant temperature just add up to a lot of random jiggling of the atoms - AKA heat. That motion, as we know, causes resistance. Electrons are jostled, exchanging phonons in both directions with the atoms, which prevents a smooth, streamline flow

You might think that cooling down the metal alone would be enough to enable higher conductivity. But it’s not the relative stillness of the atoms that does this; it’s something much more interesting. Very low temperature means few random, noisy phonons. Which in turn means that coherent structures of phonons become possible. In fact, it becomes possible for the phonons to take on another property analogous to the photon - it becomes the carrier of a force. In this case a quasi-force that can actually bind electrons together.

Normally we think of electrons as repelling each other via the electromagnetic force - mediated by photons.

At the same time, the negatively charged electrons in a metal attract the positive nuclei. The nuclei get tugged a tiny bit in the direction of a free-moving electron, and that tiny increase in positive charge can in turn attract more electrons.

Ideally that first electron is part of an electric current, so it moves along. The nuclei spring back again, and actually oscillate.

They take a little of the original electron’s energy in a vibration that’s part of a phonon, mixed up and indistinguishable from all the other crazy oscillations across the lattice. Any electrons that were attracted by this momentary convergence of positive charge are jostled so much that this effect is tiny. But if the metal is really, really cold - like, near absolute zero - then the phonons induced by the attraction of nuclei to a passing electron can be a dominant vibrational mode in the lattice.

A stream of electrons in one direction sets up a sort of resonance in the vibrational modes of the lattice, effectively binding pairs of electrons together. These are electrons bound by phonons , and our next quasi-particle - the Cooper pair. Now it’s really a fair bit more complex than this. Pairs are bound over large distances, not separated by single atoms. And it’s not simple to say which electron is bound to which. In fact, a network of electrons move together in the mutually induced resonant oscillation of the metal lattice

An amazing thing about Cooper pairs is that they behave like bosons. Each electron is spin half, so two electron have spin 1 - for reasons we can’t get into, this means they act a bit like photons in that many Cooper pairs can occupy the same quantum state. In fact at very low temperatures all of the pairs in an enormous network of flowing electrons all occupy the lowest energy state. They don’t have the energy to excite new phonons, and so … they don’t. This means they stream through the lattice with zero resistance.

As I mentioned, there is a lot more to the story of superconductivity, and we’ll come back to it. These Cooper pairs are also responsible for superfluidity. They are, in general, pretty super as far as quasi-particles go. There are many quasi-particles beyond the few I had time for today - for example, quasiparticles appear in lattices of quantum spin, like are magnons - quanta of waves in that lattice, or skyrmions, which are localized, stable topological field configurations sort of like knots - all very important for the emerging field of spintronics. In superfluids we have rotons - a quantum of a vortex in the fluid.

The roton is a quasiparticle enabled by a quasiparticle - Cooper pairs - which is in turn enabled by another quasiparticle - the phonon. It seems quasiparticles can build into complex hierarchies, just like regular particles.

Which shouldn’t be so surprising, because quasiparticles are like regular particles in many ways. After all, the elementary particles like electrons, photons, and quarks are just excitations in the elementary quantum fields. But a field is just some property that can vary over space. For example the number of electrons in the valence shell of a block of silicon. It turns out that any field, elementary or not, will give rise to particles as long as that field has quantized energy states. A crystal lattice supports many fields - the quantized number of valence electrons, or the many quantized vibrational modes in its bonds.

We now know of dozens of quasiparticles, but there are no doubt many more waiting to be discovered. And some may enable new technologies just as cool as the superconductor, or as world-changing as the transistor. All part of the magnificent complexity emergent from simple fields spanning space time.