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What Are Some Strange Phases of Matter?

Leonard Kelley holds a bachelor's in physics with a minor in mathematics. He loves the academic world and strives to constantly explore it.

What Are The Classical Phases of Matter?

In this article, we will be covering unusual phases of matter you may never have heard about. But in order to do so, it would be useful to explain what are “normal” phases are so we have a basis for comparison. Solids are materials where the atoms are locked in and cannot move freely but instead can only wobble slightly because of atomic motion, endowing them with a fixed volume and shape. Liquids also have a set volume (for a given pressure and temperature reading) but can move about more freely but still limited to the near-vicinity. Gases have large spaces between atoms and will fill up any given container until equilibrium is reached. Plasmas are a mix of atomic nuclei and electrons, separated by the energies involved. With that established, lets delve into the mysterious other phases of matter.

Fractional Quantum Hall States

This was one of the first new phases found that had scientists surprised. It was first uncovered via a study on a two-dimensional system of electrons in a gaseous, ultra-cold condition. It led to particles forming which had integer fractions of electron charge that moved about oddly – literally. The proportions were based off odd numbers, falling into quantum states of correlation not predicted by either Bose or Fermi statistics (Wolchover, An, Girvin).

Fractons and the Haah Code

As a whole, this state is beautiful but difficult to describe, seeing as it took a computer to find the Haah Code. It involves fractons, implying a relation to fractals, the endless patterning of shapes associated with chaos theory and that is the case here. Materials that use fractons have a very interesting pattern in that the pattern of the overall shape continues as you zoom in onto any vertex, just like a fractal. Also, the vertices are locked in with each other, meaning that as you move one you move all. Any disruption to a part of the material migrates down and down and down, essentially encoding it with a state that can be easily accessed and also leads to slower changes, hinting at possible applications for quantum computing (Wolchover, Chen).

Quantum Spin Liquid

With this state of matter, a set of particles develops loops of particles that spin in the same direction as the temperature approaches zero. The pattern of these loops changes as well, fluctuating based on the superposition principle. Interestingly, the pattern of the changes in the number of loops remains the same. If any two merge, then an odd or even number of loops would be maintained. And they can be oriented horizontally or vertically, giving us 4 different states this material can be in. One of the more interesting results from quantum spin liquids are frustrated magnets, or a liquid magnet (sorta). Instead of a nice North-South pole situation, the spins of the atoms are arranged in those loops and so get all twisted and…frustrated. One of the best materials to study this behavior is herbertsmithite, a naturally occurring mineral with layers of copper ions contained within it (Wolchover, Clark, Johnson, Wilkins).

The beauty of a quantum spin liquid.

The beauty of a quantum spin liquid.


Imagine a liquid that would move forever if given a push, like stirring a cup of hot chocolate and it continued to spin forever. This no-resistance material was first uncovered when scientists noticed liquid helium-4 would move up the walls of its container. As it turns out, helium is a great material for making superfluids (and solids) because it’s a composite boson because natural helium has two protons, two electrons, and two neutrons, giving it the ability to reach quantum equilibrium rather easily. It’s this feature that endows it with the no-resistance feature of a superfluid and makes it a great baseline to compare with other superfluids. A famous superfluid that one may have heard of is a Bose-Einstein Condensate, and it is very much worth reading about (O’Connell, Lee “Super”).


Ironically enough, this state of matter has many properties similar to a superfluid, but as a solid state. It’s a solid…liquid. Liquid solid? It was uncovered by a team from the Institute for Quantum Electronics and a separate team from MIT. In the seen supersolids, the rigidness we associate with traditional solids was seen but the atoms themselves also moved about “between positions without resistance.” You (hypothetically) could slid a supersolid around with no friction at all because even though the solid has a crystalline structure, the positions inside the lattice can flow with different atoms occupying the space via quantum effects (for the actual temperature is too low to induce enough energy to have the atoms move on their own). For the MIT team, they used sodium atoms near absolute zero (thus putting them into a superfluid state) which were then split into two different quantum states via a laser. That laser was able to reflect at an angle that only a supersolid structure could. The Institute team used rubidium atoms that were coaxed into being a supersolid after waves of light bouncing between mirrors settled into a state whose pattern of movement gave the supersolid state away. In another study, researchers got He-4 and He-3 to the same conditions and found that elastic features associated with He-3 (which cannot become a supersolid because it’s not a composite boson) were not seen in He-4, building the case for He-4 under the right conditions to be a supersolid (O’Connell, Lee).

Time Crystals

Understanding space orientated materials isn’t too bad: It has structure that repeats spatially. How about in the time direction, also? Sure, that’s easy because a material just has to exist and voila, it’s repeated in time. It’s in an equilibrium state, so the big advancement would be in material that repeat in time but never settle into a permanent state. Some have even been created by a team at the University of Maryland using 10 ytterbium ions whose spins interacted with each other. By using a laser to flip the spins and another to change the magnetic field, the scientists were able to get the chain to repeat the pattern as the spins synched up (Sanders, Lee “Time,” Lovett).

The time crystal.

The time crystal.

Lesson One: Symmetry

Throughout all this, it should be clear that the classical descriptions of matter states is inadequate for the new ones we have talked about. What better ways are there to clarify them? Instead of describing volumes and motion, it may be better to use symmetry to help us out. Rotational, reflectional, and translational would all be useful. In fact, some work hints at maybe up to 500 possible symmetrical phases of matter (but which ones are possible remains to be seen (Wolchover, Perimeter).

Lesson Two: Topology

Another useful tool to help us distinguish phases of matter involves topological studies. These are when we look at the properties of a shape and how a series of transformations to the shape can yield the same properties. The most common example of this is the donut-coffee-mug example, where if we had a donut and could mold it like playdoh, you could make a mug without any tearing or cutting. Topologically, the two shapes are the same. One would encounter phases best described topologically when we are near absolute-zero. Why? That is when quantum effects become magnified and effects such as entanglement grow, causing a link to occur between particles. Instead of referring to individual particles, we can start to talk about the system as a whole (much like a Bose-Einstein-Condensate). By having this, we can effect changes to a part and the system doesn’t change…much like topology. These are known as topologically impervious quantum states of matter (Wolchover, Schriber).

Lesson Three: Quantum Mechanics

With the exception of time crystals, these phases of matter all related back to quantum mechanics, and one may wonder how these weren’t considered in the past. Those classical phases are apparent, macro-scale things we can see. The quantum realm is small, and so its effects are only recently being attributed to new phases. And as we further investigate this, who knows what new(er) phases we may uncover.

Works Cited

An, Sanghun et al. “Braiding of Abelian and Non-Abelian Anyons in the Fractional Quantum Hall Effect.” arXiv:1112.3400v1.

Andrienko, Denis. “Introduction to liquid crystals.” Journal of Molecular Liquids. Vol. 267, 1 Oct. 2018.

Chen, Xie. “Fractons, for real?” quantumfrontiers.com. Quantum Information and Matter at Caltech, 16 Feb. 2018. Web. 25 Jan. 2019.

Clark, Lucy. “A New State of Matter: Quantum Spin Liquids Explained.” Iflscience.com. IFL Science!, 29 Apr. 2016. Web. 25 Jan. 2019.

Girvin, Steven M. “Introduction to the Fractional Quantum Hall Effect.” Seminaire Poincare 2 (2004).

Johnson, Thomas. “Basics of Quantum Spin Liquids.” Guava.physics.uiuc.edu. Web. 10 May 2018. Web. 25 Jan. 2019.

Lee, Chris. “Super-solid helium state confirmed in beautiful experiment.” Arstechnica.com. Conte Nast., 10 Dec. 2018. Web. 29 Jan. 2019.

---. “Time crystals make their appearance, no blue police box reported.” Arstechnica.com. Conte Nast., 10 Mar. 2017. Web. 29 Jan. 2019.

Lovett, Richard A. “’Time crystals’ latest quantum weirdness.” Cosmosmagazine.com. Cosmos. Web. 04 Feb. 2019.

O’Connell, Cathal. “A new form of matter: scientists create the first supersolid.” Cosmosmagazine.com. Cosmos. Web. 29 Jan. 2019.

Perimeter Institute for Theoretical Physics. "The 500 phases of matter: New system successfully classifies symmetry-protected phases." ScienceDaily.com. Science Daily, 21 December 2012. Web. 05 Feb 2019.

Sanders, Robert. “Scientists unveil new form of matter: time crystals.” News.berkeley.edu. Berkeley, 26 Jan. 2017. Web. 29 Jan. 2019.

Schirber, Michael. “Focus: Nobel Prize – Topological Phases of Matter.” Physics.aps.org. American Physical Society, 07 Oct. 2016. Web. 05 Feb. 2019.

Wilkins, Alasdair. “A Strange New Quantum State of Matter: Spin Liquids.” Io9.gizmodo.com. 15 Aug. 2011. Web. 25 Jan. 2019.

Wolchover, Natalie. “Physicists Aim to Classify All Possible Phases of Matter.” Quantamagazine.com. Quanta, 03 Jan. 2018. Web. 24 Jan. 2019.

© 2020 Leonard Kelley

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