Frontiers in Synthetic Moiré Quantum Matter Proceedings of a Workshop (2022) / Chapter Skim
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3 Topological Twistronics
3 Topological Twistronics
Pages 21-28
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From page 21... ...
His group started from the insight that the flat bands in bilayer graphene appear because of a quantum interference effect. "It is not simply that
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From page 22... ...
"The question," Vishwanath said, "is can we control either one of them? " If so, it could be possible to balance them in such a way that it creates the flat bands seen in magic-angle twisted bilayer graphene.
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"We're going to use this to design moiré lattices." As an example Vishwanath should a twisted bilayer where the lattices in the two layers had rectangular symmetry. The areas where tunneling vanishes end up being quasi one-dimensional structures -- long narrow parallel lines crossing the structure -- along which where the electrons find it easiest to move, as opposed to moving perpendicular to those lines.
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From page 24... ...
"We still don't quite know what the ground state is for the spin model," he said, "and, beyond that, what happens when you dope electrons." It is a huge open problem, he said, "and it would be wonderful to realize this." In fact, Vishwanath said, there is a recent nice paper by Allan MacDonald and his group in which the researchers used ab initio calculations to describe the band structure of a twisted transition metal dichalcogenide material such as WS2. In the band structure of this moiré material, the first and second valence bands realized an s-orbital model and a p-orbital model, respectively, on a honeycomb lattice, while the third band realized a single-orbital model on the Kagome lattice.
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From page 25... ...
"Both of these are extremely special when it comes to the twisted bilayer graphene," he said. "How do we going about trying to engineer this in future setups?
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From page 26... ...
2019. "Flat Band in Twisted Bilayer Bravais Lattices." Physical Review Research 1:033076.
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From page 27... ...
"If we could get a flat band in this system," she asked, "then would we be able to realize topological superconductivity, something that's been sought after for a long time and is very difficult to realize? That's our motivation." Among the various differences between twisted bilayer graphene and this 3D TI system, one in particularly important, Cano said: It is impossible to realize isolated flat bands in the 3D TI system.
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From page 28... ...
"That's one of the fundamental principles of being a topological phase." Still, she continued, it might be possible to engineer this Dirac cone -- to flatten it or rearrange it in some way -- and that could be interesting. From a mean field perspective, there is evidence that if the Dirac cone could be flattened -- that is, if the velocity of the Dirac cone was reduced, thus enhancing the density of states near the charge neutrality point -- "then you would have an increased propensity of moving into an interacting phase." A number of papers have suggested the possibility of su perconducting and magnetic phases driven by interactions on the surface of a 3D TI, and those phases are more likely with a more shallow Dirac cone (Baum and Stern 2012; Das Sarma and Li 2013; Marchand and Franz 2012; Santos et al.
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