
What’s the Magic Behind Graphene’s ‘Magic’ Angle? - pseudolus
https://www.quantamagazine.org/whats-the-magic-behind-graphenes-magic-angle-20190528/
======
oliveshell
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.

~~~
selimthegrim
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)

~~~
oliveshell
Thanks! Makes perfect sense in the context of moiré patterns. I was mostly
thrown off by the fancy 3-D illustration in the article.

For anyone in a similar boat, here’s an image I found much more helpful:

[https://images.app.goo.gl/74xuavy8Nun67FTQ8](https://images.app.goo.gl/74xuavy8Nun67FTQ8)

~~~
SmokeGS
Yup! This image from a nature really helped me

[https://media.nature.com/w800/magazine-
assets/d41586-018-078...](https://media.nature.com/w800/magazine-
assets/d41586-018-07848-2/d41586-018-07848-2_16357200.jpg)

paper:
[https://www.nature.com/articles/d41586-018-07848-2](https://www.nature.com/articles/d41586-018-07848-2)

------
laser
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...](https://www.quantamagazine.org/how-twisted-graphene-became-the-
big-thing-in-physics-20190430/)

Moire pattern:
[https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/04/Magic-...](https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/04/Magic-
Graphene-Graphic-560px_v03.jpg)

and
[https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/04/Graphe...](https://d2r55xnwy6nx47.cloudfront.net/uploads/2019/04/Graphene_Angle_Mobile.gif)

------
jnurmine
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.

~~~
AaronFriel
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.

~~~
jnurmine
I see what you mean.

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...

------
Cogito
Things I haven't yet been able to determine, noting that I haven't dived into
the paper yet, are:

\- What temperature range does this happen at?

\- Is the resistance measured edge-to-edge across the sandwich, or between the
layers?

------
Crystalin
At what scale does this work? Are the layers limited to a height of 1 atom ?

~~~
garmaine
Layers always have a height of 1 atom.

------
no_identd
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:

[https://link.springer.com/article/10.1007/s00004-015-0285-1](https://link.springer.com/article/10.1007/s00004-015-0285-1)

Vanderroost, Mike - Morphic Angles (2016)

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:

degrees: 137.50777

radians: 2.3999631

turns: 0.38196602

~~~
plus
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.

[0]
[https://en.m.wikipedia.org/wiki/Magic_angle_spinning](https://en.m.wikipedia.org/wiki/Magic_angle_spinning)

