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2 Theoretical Considerations Concerning Moir Quantum Materials
Pages 18-26

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From page 18...
... To begin, Vishwanath offering some context for moiré quantum materials by looking back to an earlier breakthrough in condensed matter physics. The invention of transistors and other semiconductor devices, Vishwanath said, made it possible to replace the much bulkier, more expensive, and more energy-intensive vacuum tubes, which up to that point had been the main option for using an electric current to modulate a second current.
From page 19...
... And finally, he said, he would talk about some new models that arise from thinking about moiré physics. UNDERSTANDING FLAT BANDS Vishwanath began his discussion of design flat bands with a basic explanation of why flat bands appear in the magic-angle twisted bilayer graphene.
From page 20...
... graphene except that now! at the magic angle the band is perfectly flat 0 (third energy band structure D⇤ (−r)
From page 21...
... A group in Vishwanath's lab led by postdoctoral fellow Eslam Khalaf explored the properties of multiple layers of graphene and, in particular, examined trilayer graphene where the top and bottom layers were aligned and the middle layer was twisted. Remarkably, Vishwanath said, what they found was that, with a particular twist angle, the electronic structure was equivalent to a magic-angle twisted gra phene bilayer plus a single graphene layer, so the electronic structure contained a flat band plus a Dirac band, as Jarillo-Herrrero had explained in his talk.
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.
From page 23...
... As a recent review article detailed, there are good reasons to believe that twisted van der Waals heterostructures can be used as a platform for simulating various quantum phenomena of interest (Kennes et al.
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.
From page 25...
... FUTURE DIRECTIONS To finish his presentation, Vishwanath listed some future directions for research into moiré quantum materials. One area would be to carry out a systematic study of materials -- beyond graphene and transition metal dichalcogenides -- that can be stacked and twisted.
From page 26...
... The natural question is whether one can also see fractional quantum Hall effects. What about fractional Chern insulators or quantum spin liquids?


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