I’m always interested in reading about new work being done in theoretical physics.
That being said, I got halfway through this article and I’m still scratching my head as to what is meant by “twisting” here.
From the discussion of sheets lining up with one another, I assume they mean rotating one sheet relative to the other along a shared normal axis. But when I hear “twisting,“ I think of twisting these sheets like you would do to make a Mobius strip.
Neither the article nor the nice-looking illustration make this clear, so I’m off instead on a Google hunt so that I can conceptualize what’s being worked on here.
Edit: OK, this is pretty cool.
It’s always exciting when new theories are required to explain experimental results— doubly so here since this could yield insight into the physics of superconductivity, which we don’t understand all that well yet.
You’re correct. Look up moiré patterns and supercells for more intuition. Also sometimes patterns can require more than two sheets (trilayer graphene is also studied)
Seconded! Great link! Shows geometrically what is going on (the picture presented by the article does not lead to any intuitions of this sort, and might actually serve to (unintentionally) mislead the reader).
A picture, the right picture -- is worth a thousand words, as they say.
There was also an article last month in Quanta Magazine with more back story and some spectacularly done graphics, if you’re interested in getting more visual intuition of the moire pattern appearing between the graphene layers: https://www.quantamagazine.org/how-twisted-graphene-became-t...
Disclaimer: I have no clue about the mathematics and physics behind this to even speculate anything.
Stupid question: could one recursively stack and twist these layers and ultimately join the head with the tail while keeping the property of "each layer is twisted in relation to the previous"?
I mean twisting each layer with the magic angle, and adding on top of the previous, and so on, until the very first layer is a suitable successor of the topmost layer.
This kind of stack could be made into a magically twisted graphene donut.
Maybe the construction would be completely useless, but a research paper with a title containing "magically twisted graphene donut" is a win nevertheless.
If you imagine this torus with flat sheets projected out from the innermost annulus, then the distance between the sheets would increase as you get further out. I wonder how far apart the sheets can be before the effect breaks down.
To avoid the sheets being too far apart, the torus would have to have a big radius. And then the non-torus stack of sheets would have to repeat many times i.e. it would have to be very long.
Maybe there's a better topology to make some kind of a loop of the twisted stacks...
I'd really love to know if this has any (remote, or even indirect) connection to the very special & cool irrational (one might say 'magic') angles described in this (Open Access, HTML!) paper:
I wanna know this, among other reasons, because no other paper cites this one, nor does any other paper describe these angles, yet, when one plugs the closest IEEE single/double float numeric approximation of the absolute numeric value of these angles into Google Scholar (in quotes), one can find numerous, but not staggeringly numerous, occurrences of these in the mathematics, physics, & biology literature.
All of these seem to so far have gone unidentified as linked to the rather generalized constructions from the above paper, because the obviousness of how to derive it seems somewhat unidirectional. I'd explain what I mean by that more specifically, but I actually struggle rather hard with finding the right words for it, so, for now I can only suggest trying it out yourself and seeing what you find!
I'll give you the IEEE float approximations I have at hand, which only cover the 2D case derived from the golden ratio, and not the 3D case derived from the plastic number (personally, I'd prefer if we started calling it the radiant ratio, but I don't think that'll catch on). Note that I don't have have single and double float values for them at hand right now, and that if one wanted to thoroughly check the literature for unnoticed occurrences of this, one'd have to factor in:
1. the two possible representations of each type of float. I forgot the term, but, the 'short' version typically returned by most but not all software, and the 'long' version actually stored, which /some/ software actually outputs. Both get accepted as the same value, of course)
2. each form of float rounding behavior
Anyway, here:
golden morphic angles (see the paper for why there exist two, tl;dr: intervals):
Circle, Ellipse:
degrees: 76.34541
radians: 1.3324789
turns: 0.2120706
Ellipse, Parabola, Hyperbola:
degrees: 126.869896
radians: 2.2142975
turns: 0.3524164
And just for completeness sake, the classic (not-generalizing-to-conic-sections) golden angle:
I believe the use of the term "magic angle" in this article is at least partially a reference to the technique whose actual technical name is "magic angle spinning" NMR spectroscopy[0]. If course, the angle used in MAS is not related to the angle used in these twisted graphene bilayer structures, but in both cases there appear to be "magical" results that appear only at the specific angle in question.
That being said, I got halfway through this article and I’m still scratching my head as to what is meant by “twisting” here.
From the discussion of sheets lining up with one another, I assume they mean rotating one sheet relative to the other along a shared normal axis. But when I hear “twisting,“ I think of twisting these sheets like you would do to make a Mobius strip.
Neither the article nor the nice-looking illustration make this clear, so I’m off instead on a Google hunt so that I can conceptualize what’s being worked on here.
Edit: OK, this is pretty cool.
It’s always exciting when new theories are required to explain experimental results— doubly so here since this could yield insight into the physics of superconductivity, which we don’t understand all that well yet.