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Superfluid Helium-3: Clinks like a crystal, flows like a tea?
Here's a beginner-friendly thread on how the ideal fluid can also behave like a solid; a superfluid crystal!
(1/n)
#UAlbertaInnovationShowcase
@ualbertaPhysics @quantumalberta @ABInnovates @UAlbertaFGSR
Here's a beginner-friendly thread on how the ideal fluid can also behave like a solid; a superfluid crystal!
(1/n)#UAlbertaInnovationShowcase
@ualbertaPhysics @quantumalberta @ABInnovates @UAlbertaFGSR
Firstly, what is superfluid Helium-3 (3-He)? 
It's a quantum phase of matter that appears when you cool Helium to within 0.002° of absolute zero - below about â273.148 °C!
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It's a quantum phase of matter that appears when you cool Helium to within 0.002° of absolute zero - below about â273.148 °C!
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The '3' in '3-He' refers to the isotope of Helium with 2 protons + 1 neutron in its nucleus - 3 'nucleons'.
When cooled to this low of a temperature, the atoms pair up to form a state called a 'Cooper Pair'. It's these pairs that form the superfluid phase. (3/n)
When cooled to this low of a temperature, the atoms pair up to form a state called a 'Cooper Pair'. It's these pairs that form the superfluid phase. (3/n)
One of the many bizarre properties of a superfluid is that it can flow without friction! This means you can technically set up an eternally-swirling whirpool in it.
(Look up some videos on YouTube for some of the other wild behaviour of this liquid!) (4/n)
(Look up some videos on YouTube for some of the other wild behaviour of this liquid!) (4/n)
After it was first discovered it in the 1970s, it was found that the 3-He superfluid actually came in 2 'flavours' (or phases). The 'A phase' (shown in red) and the 'B Phase' (in blue).
Both are frictionless but have otherwise different properties! (5/n)
Both are frictionless but have otherwise different properties! (5/n)
In 2007, a theory paper [1] came out saying that if you squished 3-He till it was ~1/100th the thickness of a human hair, a new 3rd phase should show up. And moreoever, it should have a stripey pattern - a stripe phase! (6/n)
![In 2007, a theory paper [1] came out saying that if you squished 3-He till it was ~1/100th the thickness of a human hair, a new 3rd phase should show up. And moreoever, it should have a stripey pattern - a stripe phase! (6/n)](https://pbs.twimg.com/media/E1C44o3UcAM4tB4.png "In 2007, a theory paper [1] came out saying that if you squished 3-He till it was ~1/100th the thickness of a human hair, a new 3rd phase should show up. And moreoever, it should have a stripey pattern - a stripe phase! (6/n)")
This was cool not just because it was a new type of superfluid, but also because liquids aren't supposed to have patterns. Periodic ordering in space is pretty much how physicists define crystalline solids! (think of stuff like graphene) (7/n)
(In physics-speak, you would say that liquids have *continuous* translational symmetry, while solids only have *discrete* translational symmetry. Essentially a fancy way of saying that only solids can be patterned.) (8/n)
If the 2007 prediction was right, this was a new state of matter - a fluid with the spatial structure of a solid, but the frictionless flow properties of a superfluid! 
So the experimentalists got to work designing some beautiful nanoscale devices to find it. (9/n)
So the experimentalists got to work designing some beautiful nanoscale devices to find it. (9/n)
But as you might imagine, precisely squishing something to less than 1 micrometre is not an easy feat. It took till 2019 before a group [2] finally did it and they indeed found a new 3rd phase! (10/n) https://physics.aps.org/articles/v12/20
However, there was a big caveat: their experiment couldn't figure out the exact structure of this new phase, BUT they ruled out a stripe phase! 
It had be a 2D pattern, not a 1D pattern like a stripe. Maybe hexagons, maybe squares. But def no stripes. (11/n)
It had be a 2D pattern, not a 1D pattern like a stripe. Maybe hexagons, maybe squares. But def no stripes. (11/n)
Last year, @5thsound's group did an amazing series of experiments to map out the full phase diagram of this 3rd phase[3].
They found that it (in grey) was stable over a large region of temperature and pressure, as long as you squished the 3-He thin enough. (12/n)
![Last year, @5thsound's group did an amazing series of experiments to map out the full phase diagram of this 3rd phase[3].They found that it (in grey) was stable over a large region of temperature and pressure, as long as you squished the 3-He thin enough. (12/n)](https://pbs.twimg.com/media/E1C46nXVgAMIGQr.jpg "Last year, @5thsound's group did an amazing series of experiments to map out the full phase diagram of this 3rd phase[3].They found that it (in grey) was stable over a large region of temperature and pressure, as long as you squished the 3-He thin enough. (12/n)")
They found that it (in grey) was stable over a large region of temperature and pressure, as long as you squished the 3-He thin enough. (12/n)
So the ball was back in the theorists' court: could we construct a theory which would give rise to a new superfluid phase with a 2D pattern? (13/n)
And this is precisely what we believe we did in our new paper [4]! 
We used an idea called 'Weak Crystallization' from the great Soviet theoretical physicist, Lev Landau, and applied it to superfluid 3-He. (14/n)
We used an idea called 'Weak Crystallization' from the great Soviet theoretical physicist, Lev Landau, and applied it to superfluid 3-He. (14/n)
In the paper, we were able to show that there is phase transition to a 2D patterned superfluid phase in roughly the same region as experiments show! (15/n)
But the true beauty of this idea is that we never assumed the structure of the 2D pattern. Using Group theory, we were able to consider all possible patterns at once and just compute which ones would show up! (16/n)
And since this is a quantum system, it would be silly if only one pattern showed up. In fact, all of the possible patterns show up in this superfluid crystal phase but with different proportions! (17/n)
These 3 crystal structures turn out to be most prominent from our calculations. (For the experts, these are irreducible representations of the D6 symmetry group) (18/n)
This means that depending on how an experimentalist 'looks' at this phase of matter, they could see the crystal having a different pattern. (It's like those lenticular printed pictures, but the quantum version!) (19/n)
But this is just the tip of the iceberg; there should lots of interesting stuff going on inside this unique phase of matter. A whole host of exotic Physics should emerge within this superfluid crystal! That's the task for the rest of my PhD, so stay tuned! 
FIN!
(20/n, n = 20)
FIN!
(20/n, n = 20)
References: [1] https://arxiv.org/abs/cond-mat/0601565,
[2] https://arxiv.org/abs/1805.02053 ,
[3] https://arxiv.org/abs/1908.01779 ,
[4] https://arxiv.org/abs/2104.15125
[2] https://arxiv.org/abs/1805.02053 ,
[3] https://arxiv.org/abs/1908.01779 ,
[4] https://arxiv.org/abs/2104.15125
