Frontiers in Synthetic Moiré Quantum Matter Proceedings of a Workshop (2022) / Chapter Skim
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1 Setting the Stage
1 Setting the Stage
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One can, under the proper conditions, be a superconductor, but it can also be a Mott insulator, a strange metal, a Fermi liquid, or exist in antiferromagnetic phase or a pseudogap phase. This richness in the properties of a material is often seen when the interactions between the individual constituents -- electrons, in the case of high-temperature superconductors -- are very strong, Jarillo-Herrero said.
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A NEW PLATFORM This is where moiré quantum matter comes in, Jarillo-Herrero said. It is a new platform for studying strongly correlated materials and topological physics.
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"Imagine what we can get," Jarillo-Herrero said, "if we start playing with a little more exotic building blocks and different strategies to arrange them." With that detailed introduction, he then launched into the main part of his talk. MAGIC-ANGLE GRAPHENE AND THE RISE OF MOIRÉ QUANTUM MATTER Jarillo-Herrero began with a description of graphene and its electronic structure (see Figure 1-1)
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As the twist angle gets closer and closer to zero, the wavelength goes toward infinity. So this is what happens in real space, Jarillo-Herrero said, but what happens in momentum space and what happens to the electronic structure?
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. "Then we say that a flat band condition has been realized," Jarillo-Herrero said, and the angle at which this flat band condition is reached is called the "magic angle." For two single layers of graphene, that magic angle is about 1.1°.
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(C) FIGURE 1-4 Flat bands in momentum space imply localization in physical space.
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All of this physics happens in a relatively narrow twist angle range around 1.1°. In particular, the magic-angle twisted bilayer graphene system is an electrically tunable superconductor.
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To begin with, his own group has reproduced the findings, as have several other groups, even extend ing them to other systems. Various phenomena that are characteristic of quantum materials have been observed in the magic-angle twisted bilayer graphene system, such as strange metal behavior and nematicity.
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The electronic structure of the new material can be thought of as being equivalent (in terms of the material's Hamiltonian) to magic-angle twisted bilayer graphene plus a single graphene layer (see Figure 1-6)
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FIGURE 1-6 The electronic structure of magic-angle twisted trilayer graphene. NOTE: MATBG = magic-angle twisted bilayer graphene; MATTG = magic-angle twisted trilayer graphene.
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High-temperature superconductors have higher critical temperatures than conventional superconductors and lower electron densities. The magic-angle bilayer and trilayer graphene materials have low critical temperatures -- around 2 K -- but they have extremely low electron densities, so that the critical temperature relative to the electron density is higher than for other superconductors, and, in particular, magic-angle twisted trilayer graphene is the strongest coupled superconductor that exists, he said.
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Applying a small twist angle between the two layers of the bilayer hBN leads to AB and BA stacking domains just as with twisted bilayer graphene, and the AB and BA stacking domains in the hBN material have different dipole moments, creating a moiré ferroelectric pattern in which the moiré pattern can be controlled with an electric field. "This thing works at room temperature," he said, "and, who knows.
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"Something that is very interesting happens when you go beyond three layers," Jarillo-Herrero said. "You have now different first magic angles." Noting that twisted bilayer graphene actually has different magic angles -- a first magic angle, a second magic angle, and so on -- he said that this is not what is going on here.
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Since the size of the moiré pattern of each is tun able, the two moiré bilayers can be tuned to have the same moiré wavelength, and they can be placed so that the moiré patterns match up and so that the AB and BA domains of the twisted bilayer graphene have opposite electric dipole moments from the domains in the twisted bilayer hexagonal boron nitride directly below (see Figure 1-8)
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Finally, he said, it may be possible to create moiré quantum materials using non-van der Waals substances. One way to do this would be to grow layers of the non-van der Waals materials epitaxially on top of graphene and then pull them off to create an ultra-thin film of the non-van der Waals material.
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In the case of the twisted stacked graphene, the electronic structures are clearly distinct up to at least six layers, but after that the first magic angle changes by smaller and smaller amounts with each additional layer, he said, "so I think probably six to seven layers is a realistic number." Kapitulnik then passed along two questions about the specific properties of electrons in the twisted multilayer graphene materials: Are spin interactions between the electrons important, and what is known about the type of superconductivity? Jarillo-Herrero answered that at this point there are no known mechanisms that would generate a large spin coupling between electrons, so "we suspect that for graphene-based moiré structures spin–orbit coupling is very small.
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2019. "Magic Angle Hierarchy in Twisted Graphene Multilayers." Physical Review B 100:085109.
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