A layperson's introduction to quantum oscillations

wanda-seldon
2018-10-27T12:38:05Z

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

Spintronics

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.

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