Frontiers in Synthetic Moiré Quantum Matter Proceedings of a Workshop (2022) / Chapter Skim
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3 Topological Twistronics
3 Topological Twistronics
Pages 27-37
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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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From page 29... ...
ANALYZING A TWISTED HETEROSTRUCTURE As context for analyzing a twisted heterostructure using those three approaches, Cano briefly reviewed the situation with twisted bilayer graphene, as had been described earlier in the workshop by Pablo Jarillo-Herrero. According to the Bistritzer–MacDonald model, the appearance of flat bands in twisted bilayer graphene can be understood through the leading order in perturbation theory.
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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... ...
In this situation there will be a Dirac cone on the surface of the topological insulator, and the two-dimensional material will have valence band that does not cross through the Dirac cone but is somewhat close. By integrating out the two-dimensional degrees of freedom to get the superlattice potential, one is left with a potential on the surface of our 3D TI whose strength depends not only on interlayer coupling but also on the separation between the top of the 2D valence band and the charge neutrality point of the Dirac cone.
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From page 32... ...
In one case, Cano noted, the fifth-order perturba tion calculation showed the velocity of a satellite cone going to zero, indicating a magic angle, but the numerical calculations showed that the velocity of the Dirac cones never went to zero, so there were no magic angles for the original Dirac cone or the satellite cones. Cano also showed a second plot, this one of the Dirac cone velocity as a func tion of the twist angle, Q (right-hand side of Figure 3-3)
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From page 33... ...
"This is quite neat because this is a real model which is actually using the surface states of bismuth selenide," she said. "We don't assume anything about them." So it is possible to significantly change the velocity of the Dirac cones by adjusting the superlattice potential even though it is not possible to gap the material or make flat bands.
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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 a second prediction we are making is there will be a circulation current which is coming from the wave function winding around these zeros and that circulating current increases as you go from first to second to third magic angle." Another set of issues arises from comparing superlattice potentials versus twisted heterostructures. Both of these things can give rise to extremely flat bands, Cano said, and both of them are also highly tunable, albeit in different ways.
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From page 36... ...
" Cano answered that she does not believe there is a simple way to understand it, but she added that she does not believe the behavior is particularly unusual because something very similar happens in twisted bilayer graphene, a completely different system.
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From page 37... ...
2013. "Many-Body Effects and Possible Superconductivity in the Two Dimensional Metallic Surface States of Three-Dimensional Topological Insulators." Physical Review B 88:081404(R)
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