Can someone steer me toward a clear and self-contained explanation of what’s geometrically special about an angle of 1.1°, understandable by nonphysicists?https://www.quantamagazine.org/how-twisted-graphene-became-the-big-thing-in-physics-20190430/ …
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Replying to @JimPropp
I don't think any such explanation is known. The original calculation by Bistritzer and MacDonald, in 2011, gave 1.05° as the largest of several "magic angles": https://www.pnas.org/content/108/30/12233 … It required diagonalization of a 10x10 matrix, not shown in the paper.
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Replying to @johncarlosbaez @JimPropp
A more recent, more accurate, more complicated calculation gave 1.08°. I can imagine writing a nice essay that explains *what happens* at this angle, but not why it's this angle.
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Replying to @johncarlosbaez @JimPropp
re: explaining what happens -- You probably would mean this paper then: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.106405 … (there are multiple magic angles)pic.twitter.com/uqm450g9MD
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Neat! It looks like the root of their explanation is that the magic angles allow them to construct "flat-band" wavefunctions on the torus in terms of a ratio of theta functions (Eq. 6). The magic angles theta are encoded in the "double-periodic Moiré" boundary conditions (Eq. 4).
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