A layperson's introduction to quantum oscillations
Introduction and motivation
In an effort to get more content on Tildes, I want to try and give an introduction on several 'hot topics' in condensed matter physics at a level understandable to laypeople (high school level physics background). Making physics accessible to laypeople is a much discussed topic at universities. It can be very hard to translate the professional terms into a language understandable by people outside the field. So I will take this opportunity to challenge myself to (hopefully) create an understandable introduction to interesting topics in modern physics. To this end, I will take liberties in explaining things, and not always go for full scientific accuracy, while hopefully still getting the core concepts across. If a more in-depth explanation is wanted, please ask in the comments and I will do my best to answer.
Previous topics
Why has it been 100 days since the last post?
I had a different topic planned as a second post, however it turned out I had to explain a lot more concepts that I anticipated so that it would no longer fit this format. Then I got busy. Now I finally found a topic I think I can do justice in this format.
Today's topic
Today's topic will be quantum oscillations.
What are quantum oscillations?
Quantum oscillations are periodic fluctuations in some materials' properties when it is exposed to a strong magnet. As the name suggests, this effect arises from quantum physics. Nevertheless, I think it's relatively easy to give a feel on how it works. In the rest of this post I will focus on one kind of quantum oscillation, the oscillation of a material's resistance (with the very fancy name Shubnikov-de Haas oscillations), because electrical resistance is a concept most people are familiar with. However, there are many other material properties that fluctuate similarly.
What do quantum oscillations look like?
Let's start from the basics, electrical resistance. Electrical resistance tells you how hard it is for an electrical current to flow through a material. Related to this is conductance, which instead tells you how easy it is for a current to flow through a material (so it is the inverse of the resistance). Now, something funny happens to some metals' conductance when you expose them to a strong magnet.
Let's think for a moment on what we expect would happen. Would the conductivity be affected by the magnet? Perhaps a stronger magnet would increase the conductivity, or reduce it. What we most certainly wouldn't expect to happen is for the conductivity to go up and down as we increase the strength of the magnet we aimed at the material. Yet, this is exactly what happens. In this picture we see the conductivity (expressed on the vertical axis) plotted against the magnetic field (expressed on the horizontal axis). The conductivity is going up and down like crazy!
Why is this happening?
One of quantum physics core principle is quantisation (who'd have thought). And as it turns out, this quantisation is at the core of this behaviour. For the purpose of this post, quantisation can be thought of as energies at which the electrons are allowed to have.
Normally, when electrons are in a metal, there are no real restrictions on what energy they are allowed to have. Some electrons will not have a lot of energy and won't move, other electrons will have a lot of energy and be able to move freely around the metal.
However, when metals are put in a strong magnetic field the energies of the low energy electrons are allowed to have changes drastically. The electrons are only allowed to be at certain energies, with a wide gaps in between these energies. Crucially, the exact values of these energies change with the strength of the magnet.
This means that at some magnet strengths, the allowed low-energy energies will nicely line up with the energies the free-flowing electrons have. This means some of those electrons will interfere with the free flowing electrons, making it harder for them to flow freely*. This interference in electron flow means less conductance! Then, when we change the magnetic field so that the energies are no longer aligned, the free flowing electrons no longer get caught and will be able to move freely, so that the conductivity goes up again. This pattern becomes more pronounced as the magnetic field strength increases.
What is it good for?
These oscillations were first noticed in bismuth by Shubnikov and de Haas in the year 1930. It was direct evidence for the quantum mechanics underlying nature. These days quantum oscillations are a popular method to extract information on a metals, alloys and semimetals' properties. These techniques have been used to, for example, further our understanding of high temperature superconductivity.
Sources
D Shoenberg - Magnetic Oscillations in Metals (1984)
*more technically: the probability of scattering is proportional to the number of states into which the electron can be scattered, which is given by the number of available states near the energy surface of the material.
This post seems less popular than the last one. Is the topic I chose too abstract, or not interesting enough?
Would people be interested in posts in the same format that focus on more basic quantum physics? There are already a lot of resources on this, so I feel I might not be adding a lot by writing about it here, but if people are interested I could give it a try.
Alternatively I could give a short introduction on more exciting semiconductor physics, but I would have to forgo the explanation (I have tried explaining several things in draft posts but never got anything coherent) and just focus on why this particular phenomenon is exciting.
Please reply and let me know!
Weekends are generally much less active here than weekdays and my guess would be that this being Halloween weekend probably just exacerbated that. And as to the topic contents itself, even though physics really isn't my thing I was able to follow along just fine and enjoyed reading it. I just didn't really feel I had anything worth commenting on or know enough about the subject to even ask a worthwhile question.
p.s. I definitely appreciate the effort you put into it and hope the lack of activity doesn't discourage you from posting more of these in the future, though. :)
Thank you for the feedback. To be honest I was pretty discouraged by the silence. Next time I will try posting on a weekday.
Do you have any preference in the type of content you'd like to see? Less explanations and more cool modern physics, or more explanations of simpler physics.
Honestly, a decent mix of both sounds most appealing to me. I watch a fair amount of maths/physics/chemistry content on Youtube (e.g. PBS Space Time, Numberperhile, NileRed, etc) and the topics they cover can range from relatively rudimentary stuff to insanely complicated. But so long as it's explained well and in a manner I can actually understand as a layman to all those subjects (similar to what you have also done) I enjoy it regardless of the specific topic.
Thanks for posting. Its a bit beyond the type of physics I have to deal with, but it sounds like an interesting phenomena.
What kind of information is extracted this way from metals?
The most important piece of information we gain from this method is the shape of the so-called Fermi surface. This is rather abstract, but on a basic level we end up with pictures like this. The exact shape of this surface tells us a lot about the properties of the material. For example, the surface that I linked has holes in it, which means the material is conducting. The exact shape and location of the holes tell us how the material interacts with light.
More technically, the Fermi surface shows the separation between occupied and unoccupied energy levels as function of the electrons' momentum for each atom. At the points that look like holes in the surface, the surface is connecting to the next atom's Fermi surface. Which means the occupied states of the two atoms are connected, which means there can flow a current between them.
I'm not sure I understand the interference part. We have low energy and high energy electrons, but only low energy electrons are affected by the magnet? How do the low energy electrons line up with the high energy electrons to interfere with them? Is this anything to do with wave-particle duality and constructive/destructive wave interference?
Thank you for the post, by the way! This is a really interesting topic. :)
This is one of the simplifications I used to make this post understandable. The electrons end up in so-called Landau levels, which is just the fancy name for the allowed energy levels I mentioned. Once one of the Landau levels gets pushed far enough up in energy that it's near the energy of the freely moving electrons, the freely moving electrons can hop into these levels and will then stop moving. This is where the interference comes from. The strength of the interference (or, scattering rate) is dependent on the amount of (energy) states the electron can scatter into (this is called Fermi's golden rule).
Sort of, the Landau levels I mentioned exist at energies where the electron's wave will produce a standing wave. This is true for any energy quantisation in quantum mechanics. The easiest example is the famous particle in a square well. Wiki has a nice illustration of this. Ignore figure A, figures B through D show standing waves, waves that aren't moving sideways and just stand in the same space. Figures E and F show unstable waves, these will interfere with themselves until they extinguish. So the allowed energy states are the states where the electron's wave interferes constructively with itself.
Super appreciative that you tool the time to write this. Small insights into the minutiae of specific fields is always humbling.
I do have one question though: I don't remember learning in high school chemistry about different electron energy states. I know atoms have energy states dictated by their electrons. But what's the deal with per electron energy?
The energy states of the atom as they are treated in chemistry are actually the energy states of the electron orbiting the atom. In chemistry we only look at how atoms' electrons interact with each other.
In nuclear physics, we look at how the atom's nuclei (the heavy part in the centre) interact with each other, this is the origin of things like nuclear radiation and nuclear fusion, but it's not chemistry.
I just found this series . Keep them coming! One question, related to the fluctuations in conductance mentioned here. Is the syncing of phase change due to lining up the electrons in anyway related to superconductance?
Yes. The quantum oscillations at strong fields will produce 0 resistance. This is part of the so called integer quantum hall effect. See the video here for a visual on it https://en.wikipedia.org/wiki/Quantum_Hall_effect#Integer_quantum_Hall_effect_%E2%80%93_Landau_levels. Notice how the resistance goes to 0.
As a general note, these quantum oscillations and thus the superconductivity relies on low temperatures. If the temperature is too high there would be so much thermal energy in the system that the electrons could jump between the Landau levels easily.