Frontiers in Synthetic Moiré Quantum Matter Proceedings of a Workshop (2022) / Chapter Skim
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Unfortunately, the properties of such strongly correlated systems are very hard to solve theoretically, he continued, and he used the case of high-temperature superconductors as an example of how physicists try to understand the behaviors of these systems. In copper-oxide superconductors, copper-oxygen planes hold the key to the superconducting behavior.
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Associated with the length scales are energy scales or temperature scales, and these scales for moiré quantum matter are also intermedi ate between the other two: about 1–10 Kelvin for the new moiré materials -- which is a very convenient energy scale to explore in a laboratory, he said -- versus 0.1–1 nano Kelvin for cold atoms and 100–1,000 Kelvin for quantum materials. A key to the creation of this moiré quantum matter is two-dimensional twist ronics, in which a pair of twodimensional crystal lattices are placed one on top of
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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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. With two graphene sheets on top of each other, if the twist angle is small, the energy–momentum dispersion can be captured in terms of the Dirac cone for
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layer 1 and the Dirac cone for layer 2, and the separation in momentum space is proportional to the twist angle (far left image in Figure 1-3)
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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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In particular, the tunneling strength effectively differs by a factor of √2, so, electronically, the new material can be thought of as the bilayer material with a higher tunneling strength plus a single graphene layer. Because of the difference in tunneling strength, the magic angle for the trilayer material is a factor of √2 greater than the magic angle of the bilayer material, or about 1.56°.
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This transverse field provides a "new tuning knob" with which the twisted trilayer graphene can be tuned -- in particular making it more tunable than the twisted bilayer graphene. It is possible with these trilayer materials, Jarillo-Herrero said, to control the appearance of superconductivity by controlling the charge density and the displacement field.
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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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