National Academies Press: OpenBook
« Previous: Front Matter
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

1

Setting the Stage

In the workshop’s first session, Pablo Jarillo-Herrero of the Massachusetts Institute of Technology, whose research findings triggered the current interest in moiré quantum matter, offered a look at the past, present, and future of the field, describing the original discovery, the current state of the field, and where he expects it to be going.

He began with some general comments on strongly correlated quantum materials. These materials, he said, “give us some of the most fascinating states of matter we have in the universe.” A well-known example is the family of high-temperature cuprate superconductors, originally discovered in the late 1980s. Depending on the level of doping and on the temperature, these superconductors can exist in a variety of different phases. 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.

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. In the undoped version of the materials, electrons cannot move around in the planes because there is a very strong repulsion between the electrons that holds them in place. Thus, they behave as insulators. However,

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

when the material is doped with holes (i.e., some electrons are removed from the system), the electrons can move from site to site, although they have to do it in a correlated fashion, moving in pairs, because there is still a competition for the sites. Then, when the temperature drops below a certain critical level, the resistance to electron flow disappears, and the material behaves as a superconductor.

The physics of such a material, Jarillo-Herrero said, is believed to be described by the Hubbard model, which takes into account the energy penalty for double occupancy of a site and also the hopping between empty and occupied sites. However, while physicists believe that the Hubbard model describes what is going on, they cannot be sure because they cannot theoretically solve the model for more than just a few particles.

This is true in general for strongly correlated systems, Jarillo-Herrero said. Solving them theoretically is very hard. And this has led to alternative approaches to investigating these types of systems and behaviors.

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. In particular, it offers a different scale of study from traditional materials with correlated behavior. Quantum materials, such as high-temperature superconductors, have a lattice scale of a few angstroms, while an alternative platform that has emerged in the past 20 years—ultra cold atoms in optical lattices—has a lattice scale of around 1 micron. In cold atom optical lattices, lasers are used to create the lattice that holds the atoms, and it is possible to have exquisite control over the parameters of the system, making it possible to control and tune the interactions between the atoms and investigate the correlated physics of the system.

Moiré quantum matter, which has emerged in the past 3 years, offers scales that fall between the scales of these more traditional systems. The typical scale of moiré quantum matter, known as the moiré wavelength, is about 10 nm, or a couple of orders of magnitude removed from both the scale of the atomic lattice of quantum materials and the scale of optical lattices. Furthermore, the degree of control that can be exerted over moiré quantum matter is intermediate between the other two—not as much as with the cold atoms in optical lattices but more than with quantum materials. Associated with the length scales are energy scales or temperature scales, and these scales for moiré quantum matter are also intermediate 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 twistronics, in which a pair of twodimensional crystal lattices are placed one on top of

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

the other with their axes of orientation offset by a certain angle. This offset angle can be controlled, Jarillo-Herrero said, and varying it can lead to dramatic changes in the electronic properties of the twisted material. This ability to tune the angle between two crystalline materials is something that did not exist before, he said. “It is unprecedented.”

This new moiré quantum matter has a number of attractive aspects. First, it can be created with relatively simple building blocks. Jarillo-Herrero’s original work, for instance, was done with sheets of graphene—pure carbon—which makes it possible, to a certain extent, to ignore chemistry in analyzing the materials’ behavior. But despite their simplicity, these materials can give rise to a wide variety of behaviors, and studying these behaviors in the relatively simple moiré systems allows one to ask the question: What are the key ingredients needed for complex emergent behaviors in physical materials?

Another attractive aspect is that moiré quantum matter is highly tunable in situ. There is a lot of control compared with other materials. In particular, there are many parameters that can be changed—the electric field applied to the material, electrostatic doping, strain, pressure, magnetic field, temperature, and others—in order to observe how the properties of the material change.

Third, these new moiré quantum materials may make it possible to explore vast new families of hybrid materials based on non-equilibrium growth and assembly. Even the simplest such materials—those made with graphene—give rise to a great deal of complexity and emergent behavior. “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). Graphene is pure carbon, with the atoms arranged in a twodimensional honeycomb structure (upper left corner in Figure 1-1). Although all of the carbon atoms are identical from a chemical point of view, from the crystalline point of view there are actually two types of atoms—A and B, indicated as red and green in the figure—and the basic building block of the lattice structure is an A–B pair.

When one calculates the electronic structure of graphene, it results in a “very peculiar energy–momentum structure dispersion,” Jarillo-Herrero said (lower left corner in Figure 1-1), which near the Fermi energy has a linear energy–momentum expression. “This is very unusual in condensed matter physics,” he said. It is actually more characteristic of massless particles such as photons.

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Image
FIGURE 1-1 Electronic structure of graphene.
SOURCE: Pablo Jarillo-Herrero, Massachusetts Institute of Technology, presentation to the workshop, May 18, 2021.

If one looks at the Hamiltonian equation describing graphene (upper right corner in Figure 1-1), it shows a linear relationship between energy and momentum, and it is essentially the Dirac equation in two dimensions for massless particles. In the usual Dirac equation the spinor (αk, βk) specifies the particle spin (i.e., whether it is up or down), but in the case of the equation for graphene, the spinor specifies whether the wave function is on the A or the B (red or green) sublattice.

Another characteristic of graphene’s energy-momentum structure is the existence of two types of valleys (labeled K and K’ in the lower left corner of Figure 1-1). Part of the richness of the graphene structure arises from the four-fold degeneracy of its electrons—spin up/spin down combined with valley K/valley K’—which gives the electrons multiple degrees of freedom.

When one puts two layers of graphene on top of one another but offset by a particular angle rather than perfectly lined up, it creates a moiré pattern (see Figure 1-2). Furthermore, as the twist angle changes, the moiré pattern changes as well, with larger angles producing moiré patterns with smaller moiré wavelengths. 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? To answer that, he illustrated the electron structure in terms of Dirac cones (see Figure 1-3). 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

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Image
FIGURE 1-2 Graphene–graphene moiré structure.
SOURCE: Pablo Jarillo-Herrero, Massachusetts Institute of Technology, presentation to the workshop, May 18, 2021.

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). This actually would be the situation if the electrons in one graphene sheet did not know that the other graphene sheet exists, but because the two Graphene sheets are just 3 angstroms apart, the electrons can tunnel between the layers. This interlayer tunneling leads to a bonding–antibonding state (middle image in Figure 1-3), which is the same as the bonding–antibonding states in a hydrogen molecule but for a giant graphene “molecule,” he said. The result is that the bonding band gets pushed down a little bit in energy.

This situation occurs when the crossing points match at much higher energy than the inter-layer tunneling, but as the twist angle is decreased, the Dirac points get closer and closer and the band gets pushed down until it reaches zero (right-hand image in Figure 1-3). “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°.

Taking a closer look at the behavior of electron in magic-angle graphene, Jarillo-Herrero began by showing an energy–momentum calculation for graphene (see Figure 1-4, leftmost image). The existence of flat bands along E = 0 means that the kinetic energy of the electrons is quenched—that is, the electrons have very little kinetic energy—and so the interactions between the electrons acquire a disproportionally large effect.

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Image
FIGURE 1-3 Graphene–graphene moiré structure.
SOURCE: Pablo Jarillo-Herrero, Massachusetts Institute of Technology, presentation to the workshop, May 18, 2021; reprinted with permission from Springer Nature: Y. Cao, V. Fatemi, A. Demir, S. Fang, S.L. Tomarken, J.Y. Luo, J.D. Sanchez-Yamagishi, et al., 2018, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556:80–84, https://www.nature.com/articles/nature26154, © 2018.
Image
FIGURE 1-4 Flat bands in momentum space imply localization in physical space.
SOURCES: Pablo Jarillo-Herrero, Massachusetts Institute of Technology, presentation to the workshop, May 18, 2021; (A) Courtesy of Pablo Jarillo-Herrero; (B–C) reprinted with permission from Springer Nature: Y. Cao, V. Fatemi, A. Demir, et al., 2018, “Correlated Insulator Behaviour at Half-Filling in Magic-Angle Graphene Superlattices,” Nature 556:80–84, https://www.nature.com/articles/nature26154, © 2018.
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

So where are the electrons in this system? Moving from momentum space to physical space requires performing a Fourier transform, Jarillo-Herrero noted, and a Fourier transform of a flat object is a highly peaked object. In particular, the electrons in magic-angle graphene all congregate in those spots where an A carbon atom in graphene layer 1 sits above an A carbon atom in graphene layer 2 (see Figure 1-4C). These are referred to as AA stacking regions. By contrast, the electrons tend to avoid the AB and BA stacking regions, where an A carbon atom from one layer is above (or below) a B carbon atom from the other layer. The result is a collection of AA regions where the electrons like to sit, surrounded by AB and BA regions (see Figure 1-4B). As illustrated in Figure 1-4B, the electrons congregate in those sections of the moiré structure where the hexagons in one layer line up approximately with the hexagons in the other layer (i.e., in the AA regions). Those AA regions are 13.4 nm apart, center to center.

The result is a “triangular” Fermi-Hubbard lattice, Jarillo-Herrero said, where it is not quite triangular because the AB and the BA regions are not identical, which leads to some very interesting topological properties, he said.

What Jarillo-Herrero’s group showed 3 years ago, he said, is that you can produce a special type of correlated insulators by putting an integer number of electrons per moiré unit cell into the system, and as you dope away from that state, you get superconductivity. 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. By varying an electric voltage across the layers, it is possible to add either electrons or holes to the system, which can transform it from an insulator to a superconductor.

The phase diagram of the magic-angle twisted bilayer graphene system looks very much like the phase diagram of, for instance, a copper-oxide high-temperature superconductor, he noted (see Figure 1-5). A major difference between the phase diagrams, he noted, is that the phase diagram for the high-temperature superconductor shows a spectrum of different materials, with each one having to be created with a particular chemical composition to get the desired amount of electron or hole doping. By contrast, the bilayer graphene’s different data points are reached by changing the gate voltage across the system—something that can be done in a few seconds, rather than by having to create entirely new chemical compositions. That makes Jarillo-Herrero’s system exceptionally convenient for studies.

“So this is something that attracted a lot of attention,” he said. He posted his paper in March 2018, and within a few weeks a “theory tsunami” arrived with dozens of papers in which people were trying to explain various aspects of the magic-angle twisted bilayer graphene material. There was particular interest in the origin of the correlated insulator state and the superconducting order parameter, he said. “All kinds of proposals have been put forward. We don’t know the answers yet.” But the point is that this is a very rich system that opens up many theoretical possibilities.

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Image
FIGURE 1-5 The phase diagram of magic-angle twisted trilayer graphene compared with a phase diagram for cuprate superconductors.
SOURCES: Pablo Jarillo-Herrero, Massachusetts Institute of Technology, presentation to the workshop, May 18, 2021; (A) reprinted with permission from Springer Nature: Y. Cao, V. Fatemi, S. Fang, et al., “Unconventional Superconductivity in Magic-Angle Graphene Superlattices,” Nature 556:43–50, © 2018; (B) reprinted with permission from A. Damascelli, Z. Hussain, and Z.-X. Shen, 2003, “Angle-Resolved Photoemission Studies of the Cuprate Superconductors,” Reviews of Modern Physics 75:473, © 2003 by the American Physical Society.

Since April 2018, much has happened in the field, he said. To begin with, his own group has reproduced the findings, as have several other groups, even extending 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. His group has discovered several other correlated systems based on this twistronics platform, such as magic-angle twisted bilayer–bilayer graphene, which has interesting magnetic properties although it is not a superconductor. Because the systems are two-dimensional, it is possible to access them directly with scanning probe microscopy, such as scanning tunneling microscopy. “Plenty of local techniques are being applied, and we are finding more and more information about the system,” he said.

Another interesting set of discoveries had found ferromagnetism, anomalous Hall effect, and quantum anomalous Hall effect in the system, “which brings topology front and center to the system,” Jarillo-Herrero said. One of the nicest things that has happened to him, he said, is that he has had a chance to work with and learn from people in a number of different physics communities. These materials have brought together physicists from such areas as two-dimensional van der

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

Waals materials and heterostructures, strongly correlated materials, and topological condensed matter physics. “They all three come together in this moiré quantum matter,” he said. “That is something which is very rich.”

CURRENT NEXT-GENERATION MOIRÉ QUANTUM MATTER

One other thing that has happened since April 2018, Jarillo-Herrero said, is that people have begun to create what he called “next-generation moiré quantum matter” or “moiré magic 3.0.” And in this portion of his presentation he discussed this second generation that has appeared since the original discovery.

In February 2021 Jarillo-Herrero’s group published an article in Nature describing a new type of moiré superconductor, magic-angle twisted trilayer graphene (Park et al. 2021). A paper by a second group who had produced the same material appeared the same week in Science (Hao et al. 2021). The system, which Jarillo-Herrero said is much more tunable and much richer than the magic angle bilayer graphene, has three layers of graphene, with the top and bottom layers aligned and the middle layer offset by a magic angle.

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). In this case, however, the magic angle is different from the one in the bilayer graphene, Jarillo-Herrero explained, because the magic angle depends on the interlayer tunneling between the layers, and the tunneling behaves somewhat differently when there are three layers than when there are two. In particular, the tunneling strength effectively differs by a factor of Image, 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 Image greater than the magic angle of the bilayer material, or about 1.56°. This means that the moiré wavelength is a bit shorter, he said—about 9 nm instead of 13 nm, which in turn implies that the interactions will be stronger between the electrons.

Next Jarillo-Herrero displayed the calculated electronic structure of this new trilayer material at zero electric displacement field (see Figure 1-6B). It shows two flat bands (the orange bands in the middle) and a massless Dirac fermion band (the purple X shape) corresponding to the single graphene layer in the decomposition of the Hamiltonian that he had described. This is what creates the much richer structure of the new material—in the same structure there are massless Dirac fermions as well as strongly correlated flat band electrons.

When Jarillo-Herrero’s team works with this trilayer material, it has a system with electrodes attached to its top and bottom, which forms a parallel-plate capacitor with the trilayer graphene. They can apply the same polarity to the two electrode

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Image
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. SOURCES: Pablo Jarillo-Herrero, Massachusetts Institute of Technology, presentation to the workshop, May 18, 2021; (A) courtesy of Dr. Eslam Khalaf, Harvard University, with left image reprinted with permission from E. Khalaf, A.J. Kruchkov, G. Tarnopolsky, and A. Vishwanath, 2019, “Magic Angle Hierarchy in Twisted Graphene Multilayers,” Physical Review B 100:085109, © 2019 by the American Physical Society; (B) reprinted with permission from Springer Nature: J.M. Park, Y. Cao, K. Watanabe, et al., 2021, “Tunable Strongly Coupled Superconductivity in Magic-Angle Twisted Trilayer Graphene,” Nature 590:249–255, © 2021.

to add charge density to the system or opposite polarity, which creates a transverse electric field. Such a transverse electric field breaks the symmetry of the trilayer graphene’s electronic structure and leads to the hybridization of the massless Dirac band and the flat band. 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. But it is not just any superconductivity, he said, the system exhibits ultrastrong coupling superconductivity. That refers to the relationship between the critical temperature at which a material becomes superconducting and the Fermi temperature (i.e., the charge density, of the system). In a typical conventional superconductor, such as aluminum, the critical temperature is mod-

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

est—about 1 K—while the electron density is very large. Given that huge electron density, the superconductivity is quite modest, he said. 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. If the cuprate superconductors had the same coupling strength as this twisted trilayer graphene, he added, their critical temperature would be well above room temperature.

Switching gears, Jarillo-Herrero next explained why magic-angle twisted trilayer graphene is not a spin-singlet superconductor. This can be seen by applying a magnetic field parallel to the layers of graphene. In conventional superconductors this magnetic field breaks apart the Cooper pairs (i.e., the pairs of opposite-spin electrons that make superconductivity possible in conventional superconductors), creating an energy difference between the spin-up and spin-down electrons in each pair. If the gap between the energy levels becomes too large relative to the critical temperature, the superconductivity disappears.

For the spin-singlet superconductors described by the traditional Bardeen-Cooper-Schrieffer (BCS) theory, one can calculate the so-called Pauli limit to determine at what magnetic field strength the superconductivity will disappear, and for the magic-angle twisted trilayer graphene, superconductivity should disappear when the in-plane magnetic field reaches about 5 Tesla, but in reality the superconductivity does not disappear until the field is about 10 T. This violates the Pauli limit by a factor of three, so the superconductivity in the trilayer graphene material cannot be the spin-singlet superconductivity described by traditional BCS theory.

Noting that magic-angle twisted bilayer graphene exhibits a large number of interesting behaviors, Jarillo-Herrero said that researchers have discovered yet other interesting behaviors in some of the new moiré heterostructures that have been developed and explored in the past few years. For instance, a few months earlier several groups had reported seeing a new type of ferroelectricity in these systems, which he called “moiré ferroelectricity.” This ferroelectricity comes from the non-equilibrium stacking of twodimensional materials, he said, and it has been seen in particular in bilayer hexagonal boron nitride (hBN). In regular hBN, the hexagonal planes are stacked on top of each other in such a way that layer 2 is rotated 180° and then placed on top of layer 1 so that the boron atoms in one layer line up with nitrogen atoms in the next layer, and vice versa. This material in non-ferroelectric. In non-equilibrium parallel stacking, the two layers are oriented

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

in the same direction with the boron atoms in the top layer lining up directly above the boron atoms in the layer below, and the same for the nitrogen atoms. “This is a very uncomfortable situation for the system,” he said. “It doesn’t want to have the same atoms on top of each other,” so the layers shift relative to one another AB or BA stacking (i.e., boron sitting on top of nitrogen or nitrogen sitting on boron). In this nonequilibrium configuration there is a permanent electric dipole moment between the layers whose direction depends on whether it is AB or BA stacking (see Figure 1-7).

Using this material along with a layer of graphene, Jarillo-Herrero’s team is making a ferroelectric field effect transistor in which switching the polarization of the ferroelectric hBN leads to different conduction in the graphene channel.

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. maybe one day it will be useful for applications. There are many, many more things one can do that I don’t have time to tell you about.”

Image
FIGURE 1-7 Equilibrium and non-equilibrium stacking of hexagonal boron nitride.
SOURCE: Pablo Jarillo-Herrero, Massachusetts Institute of Technology, presentation to the workshop, May 18, 2021.
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

NEXT NEXT-GENERATION MOIRÉ QUANTUM MATTER

From there Jarillo-Herrero moved to a discussion of what he called “the next, next-generation moiré quantum matter,” offering a number of examples of the sorts of moiré quantum materials he expects to see in the next few years.

He began by describing a number of potential approaches to creating new types of moiré quantum matter. First, one could increase the richness of the materials by adding more layers while keeping the building blocks simple—for example, by moving to magic-angle twisted four-layer graphene or even five-layer or more. Alternatively, instead of adding layers, one could increase the complexity or richness of the materials by using more exotic building blocks while keeping the number of layers small—for example, with twisted bilayer cuprates. Another approach would be to use more complex architectures, and he mentioned what he calls “moiré on moiré” structures, which he described a bit later. A fourth approach to increasing the richness of the structures would be to move in the direction of three-dimensional moiré structures—having flat bands not just in two dimensions but in all three. Or one could increase the complexity and richness by expanding beyond van der Walls systems—for example, with twisted remote epitaxy of non-van der Waals materials.

Jarillo-Herrero then went into more detail on each of these possible approaches to adding complexity and richness.

Adding layers while keeping the building blocks simple is the approach that was used in going from bilayer to trilayer graphene; adding a fourth layer would be the obvious next step. To do this, he said, one would also continue the pattern of alternating twists seen in the trilayer system: layer 2 twisted +θ from layer 1, layer 3 twisted –θ from layer 2, and layer 4 twisted +θ from layer 3 so that layer 1 and layer 3 are lined up, as are layers 2 and 4.

“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. With four layers of graphene and beyond, there are multiple first magic angles, multiple second magic angles, and so on. Furthermore, as the number of layers increases, so does the number of magic angles, and at some point “almost any angle will be a magic angle.”

There are a number of questions to be explored with these systems, he said. For instance, the group that suggested the structure for the twisted four-layer graphene also proposed a totally new mechanism for superconductivity called skymionic superconductivity where the Cooper electron pairs are actually pairs of skyrmions (Khalaf et al. 2019). If that is actually the mechanism behind the superconductivity of these materials, they must have a particular sort of symmetry called C2zT,

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

and so far the only magic-angle twisted multi-layer graphene materials that have been superconducting have had this symmetry. “So is this symmetry essential?” he asked “We have to explore experimentally, but this is a very suggestive theoretical proposal.”

Next he noted that as the number of layers increases in these twisted multi-layer graphene materials, the first magic angle also increases, so the moiré wavelength and the size of the moiré pattern get smaller and smaller. That raises the question of whether it could be possible to get stronger interactions and higher critical temperatures as the number of layers increases. “We need to determine this,” he said.

The second way to increase complexity and richness is by using more exotic building blocks and keeping the number of layers small. There are hundreds of two-dimensional van der Waals materials that could serve as building blocks, he said, including insulators such as hexagonal boron nitride, various metals and semimetals, semiconductors, superconductors, ferroelectrics, and magnets and quantum spin liquids. “We can play with all of them.” One recent publication, for example, reported on monolayer copper oxides used in a twisted double-layer structure which result in high-temperature topological superconductivity (Can et al. 2021). A second group put two-dimensional magnets on top of each other with a twist to create a special type of moiré magnets (Hejazi et al. 2021).

The third approach to increasing complexity is to use more complex architectures. To explain what he meant by that, Jarillo-Herrero offered the example of twisted homo-moiré bilayers. That is, take two magic-angle twisted bilayer graphene structures and put them on top of each other but with a twist that can take on various values. This would couple two strongly interacting systems (i.e., the two twisted graphene bilayers, and there would be various ways to tune this system). One simple way would be to vary the angle between the two bilayers. Another would be to place one or a few hexagonal boron nitride layers between the graphene bilayers as spaces. Or the carrier density could be tuned separately in each of the graphene bilayers.

“You can also do something perhaps even more exotic,” he said: twisted hetero-moiré bilayers. Take magic-angle twisted bilayer graphene and place it on top of twisted hexagonal boron nitride. Since the size of the moiré pattern of each is tunable, 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). “You can tune the properties of the system in a way that is impossible to do with regular materials,” he said.

As he was closing, Jarillo-Herrero mentioned two other approaches to increasing complexity in moiré structures. One approach would be to create moiré structures in a third dimension by working with units of twisted moiré layers stacked

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Image
FIGURE 1-8 New moiré heterostructures created by twisted hetero-moiré bilayer stacking.
SOURCE: Pablo Jarillo-Herrero, Massachusetts Institute of Technology, presentation to the workshop, May 18, 2021.

on top of each other. This can result in flat bands in the electronic structure in the third direction in addition to the flat bands in the planes of the two-dimensional moiré structures. These materials have been studied theoretically, and different correlated phases have been predicted, and because of the flat bands in all three dimensions, it is possible the materials would have very strong correlations.

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. This has been done with silicon and many other materials, and it would be interesting to create new moiré structures with some films of exotic quantum materials that were not originally van der Waals materials. “You can play a lot of games with this moiré and with twisted structures,” he said.

In a brief question-and-answer session following his presentation, Jarillo-Herrero offered some more details about his studies. The workshop chair, Aharon Kapitulnik, who was moderating the session, first asked how robust the process is and whether relaxation affects the material after the layers have been stacked.

When his group first started working with trilayers, Jarillo-Herrero responded, they were expecting that it would be difficult to get the top and bottom layers

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

exactly aligned, but it turns out that this is actually the most favorable stacking orientation—the material wants the top and bottom layers to be exactly on top of each other. “So in terms of fabricating magic-angle trilayer graphene, we have 100 percent success,” he said. The group made four devices, and every one displayed superconductivity. In this sense, relaxation is actually very useful, he added. “It is something we can engineer and tune by choosing what type of twist angles we want for our structures.

In terms of the twist angle, he added the control is quite good—within about 0.1° with modern stackers, and many groups are able to achieve this.

Next Kapitulnik asked whether there is a limit to the number of twisted graphene layers that can be added and at what point bulk effects come in.

Jarillo-Herrero answered that the main limit to the number of layers is “the patience of your graduate students and postdocs.” In practice, he said, his group will try to make twisted four-layer graphene and maybe even five-layer, but perhaps not six layers because it takes more and more work to keep adding layers. “My hope is that we will develop automatic robotic stackers and schemes,” he said, “because robots have a lot more patience than people.” If so, they should be able to do many more layers.

Calculations of electronic structures of graphene and graphite have shown that after about 10 layers, the stacked graphene layers start to look very similar to graphite, he said, but below 10 layers the materials with different numbers of layers have clearly distinct characteristics. 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. As for the type of superconductivity, the magic-angle twisted trilayer graphene is not a spin singlet superconductor, as he had said in his presentation, so it is likely that the superconductivity is unconventional in nature. Typically electron-phonon coupling gives rise to spin singlet superconductors. So the majority of the theoretical community believes that the superconductivity in bilayer and trilayer graphene materials are unconventional.

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×

REFERENCES

Can, O., T. Tummuru, R.P. Day, I. Elfimov, A. Damescelli, and M. Franz. 2021. “High-Temperature Topological Superconductivity in Twisted Double-Layer Copper Oxides.” Nature Physics 17:519–524.

Hao, Z., A.M. Zimmerman, P. Ledwith, E. Khalaf, D.H. Najafabadi, K. Watanabe, T. Taniguchi, A. Vishnawath, and P. Kim. 2021. “Electric Field Tunable Superconductivity in Alternating Twist Magic-Angle Trilayer Graphene.” Science 371(6534):1133–1138.

Hejazi, K., Z.-X. Luo, and L. Balents. 2021. “Heterobilayer Moiré Magnets: Moiré Skyrmions, Commensurate–Incommensurate Transition, and More.” arXiv 2009.00860v2.

Khalaf, E., A.J. Kruchkov, G. Tarnopolsky, and A. Vishwanath. 2019. “Magic Angle Hierarchy in Twisted Graphene Multilayers.” Physical Review B 100:085109.

Park. J.M., Y. Cao, K. Watanabe, T. Taniguchi, and P. Jarillo-Herrero. 2021. “Tunable Strongly Coupled Superconductivity in Magic-Angle Twisted Trilayer Graphene.” Nature 590(7845):249–255.

Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 1
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 2
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 3
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 4
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 5
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 6
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 7
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 8
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 9
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 10
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 11
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 12
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 13
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 14
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 15
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 16
Suggested Citation:"1 Setting the Stage." National Academies of Sciences, Engineering, and Medicine. 2022. Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26594.
×
Page 17
Next: 2 Theoretical Considerations Concerning Moir Quantum Materials »
Frontiers in Synthetic Moiré Quantum Matter: Proceedings of a Workshop Get This Book
×
Buy Paperback | $26.00 Buy Ebook | $20.99
MyNAP members save 10% online.
Login or Register to save!
Download Free PDF

On May 18-19, 2021, the Condensed Matter and Materials Research Committee of the National Academies of Sciences, Engineering, and Medicine convened a public workshop to examine the frontiers of research on moiré quantum matter. Participants at the workshop discussed the challenges and possibilities that this new material presents. This publication summarizes the presentations and discussion of the workshop.

  1. ×

    Welcome to OpenBook!

    You're looking at OpenBook, NAP.edu's online reading room since 1999. Based on feedback from you, our users, we've made some improvements that make it easier than ever to read thousands of publications on our website.

    Do you want to take a quick tour of the OpenBook's features?

    No Thanks Take a Tour »
  2. ×

    Show this book's table of contents, where you can jump to any chapter by name.

    « Back Next »
  3. ×

    ...or use these buttons to go back to the previous chapter or skip to the next one.

    « Back Next »
  4. ×

    Jump up to the previous page or down to the next one. Also, you can type in a page number and press Enter to go directly to that page in the book.

    « Back Next »
  5. ×

    Switch between the Original Pages, where you can read the report as it appeared in print, and Text Pages for the web version, where you can highlight and search the text.

    « Back Next »
  6. ×

    To search the entire text of this book, type in your search term here and press Enter.

    « Back Next »
  7. ×

    Share a link to this book page on your preferred social network or via email.

    « Back Next »
  8. ×

    View our suggested citation for this chapter.

    « Back Next »
  9. ×

    Ready to take your reading offline? Click here to buy this book in print or download it as a free PDF, if available.

    « Back Next »
Stay Connected!