Frontiers in Synthetic Moiré Quantum Matter Proceedings of a Workshop (2022) / Chapter Skim
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Pages 29-36
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From page 29... ...
"And if this 2D layer is an insulator, then we can integrate out the gap degrees of freedom, and we will be left with a super-lattice potential on the surface of the 3D TI." From a theoretical perspective, the two approaches provide basically the same Hamiltonian, which is a combination of the Hamiltonians of the 3D TI and the Hamiltonian of a potential on the surface of that topological insulator. "So that's the basic Hamiltonian we want to study," she said, and to do that she would analyze the Hamiltonian with a continuum model, a tight-binding model, and ab initio calculations.
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From page 30... ...
These are the same things that you see in twisted bilayer graphene, Cano said, but with a major dif ference: in this system, Dirac cone velocity can never be equal to zero. "If we ramp up the potential, we will just start slowly decreasing the velocity." It is also possible to use perturbation theory to compute the energies and ve locities of the various satellite cones, Cano noted.
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From page 31... ...
SOURCE: Jennifer Cano, Stony Brook University, presentation to the workshop, May 18, 2021.
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From page 32... ...
Finally, Cano described the results of ab initio calculations for such a twisted heterostructure. She chose to examine hexagonal boron nitride (hBN)
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From page 33... ...
"The con is there are limitations on what you can do in practical terms." To carry out her ab initio calculations of the bismuth selenide on a patterned dielectric, Cano chose to model a slab of Bi2Se3 that was five quintuple layers thick. "That's about as many as you need for the Dirac cones on opposite surfaces to remain gapless," she said.
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From page 34... ...
Then the Dirac cones of gra phene and the Dirac cones of bismuth selenide can interact with each other, and there we can get a more legitimate twisted heterostructure." FUTURE DIRECTIONS Cano spent the remainder of her talk speaking of future directions in the field beyond her work that she had described and beyond twisted bilayer graphene. "One of the things that could be interesting is how can we manipulate the surface states of 3D materials with these sorts of hetero structures?
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From page 35... ...
"So there's an analogy to be made there," she said, "and the reason I think this is interesting is if we fractionally fill these flat bands, what we know from quantum Hall physics is that fractionally filling flat bands at higher magic angles gives you different phases than if you fractionally fill the first flat band coming from the first Landau level." This in turn leads her to speculate that fractionally filling the flat bands coming at the second or third magic angle might lead to different correlated phases. This is something her team plans to pursue in the future.
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From page 36... ...
Finally, although she said she was not sure whether it would actually lead to anything interesting, Cano suggested looking at "proper 3D materials" with a twist. One could, for example, put two blocks of materials together that were offset by a twist and look at the interface to see if anything happened that was not seen in twisted bilayers of graphene or other two-dimensional materials.
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