4
Discussion Period
Joe Checkelsky of the Massachusetts Institute of Technology moderated the discussion period that capped off the first day of the workshop. The period started with Checkelsky providing an overview of the day’s presentations, and then the floor was opened to questions directed at Checkelsky and the day’s three presenters along with committee member Claudia Felser of the Max Planck Institute in Dresden, Germany.
OVERVIEW
In his overview, Checkelsky first offered a historical comparison and then listed some of the challenges and opportunities in working with quantum moiré systems.
The historical comparison was with a transformation that took place in thin film technology. Thin films are close cousins of the van der Waals systems being discussed at the workshop, he noted, and they had been around for a very long time before a few developments in the 1950s and 1960s led to a revolution in the development of molecular beam epitaxy (MBE). The key developments had seemed to be disparate technological ideas—the ability to make very effective yet affordable high-vacuum seals, the development of effusions cells, and the development of reflection high-energy electron diffraction (RHEED)—that led to a new synthesis ability of layer-by-layer growth where a kinetic reaction at the surface was controlling the growth process.
Among the things that were enabled by this new process were in situ monitoring of growth, high-quality interfaces with low interdiffusion, and, eventually, things like modulation doping and very precise control of the layers’ thickness, composition, and doping. This ability to make better two-dimensional materials led to a vast array of discoveries and technologies, including the development of the quantum cascade laser, the discovery of the fractional quantum Hall effect, the development of the high-electron-mobility transistor, and the development of semiconductor optoelectronics, all of which had far-reaching implications and applications.
Over the years, Checkelsky said, MBE has been used to create thin films out of a large range of materials: semiconductors of various types, halides, heuslers, pnictides, organics, magnetic semiconductors, silicides, nitrides, metals, intermetallics, chalcogenides, and oxides, among others. The oxide thin films in particular have been shown to have a large array of exotic properties: high mobility, metal–insulator transition, superconductivity, ferroelectricity, piezoelectricity, ferromagnetism, and many others.
One thing that becomes clear from taking such a look back, he said, is that after some years there was a well-established process with which one thought about these thin-film systems. “You choose a substrate … you learn how to prepare that substrate in a very clean way, and then you have choices that are not dissimilar to things one can do with van der Waals structures”—things like homoepitaxy, heteroepitaxy, layers that are matching, strained, relaxed relative to the substrate. Eventually, he added, one builds toward device structures. At the same time that the process was being developed and refined, researchers were also developing a collection of theory tools, including the rational design of structures, simulations of growth kinetics, calculations of defect densities, and electronic structure calculations. There have also been new deposition methods and new characterization tools developed over time.
Thinking about the lessons from this history that might apply to the new work in van der Waals materials, Checkelsky said that the most important thing for these thin films was the substrate and the ability to find different substrates and understand what the different substates would mean for the film grown on them. In the case of the van der Waals materials, the lesson might be the importance of learning how to make one really good substrate and one really good layer and then connect them in a meaningful way.
One can observe a number of parallels between the development of thin film technologies in the 20th century and the work with the van der Waals materials in the early part of the 21st century. For instance, again it has been a number of seemingly disparate ideas and technological advances that led to an explosion of activity. In the 21st-century case it was the development of exfoliation to be able to make
monolayers out of layered crystals and the ability to make edge contacts, which make it possible to make rather complex structures but still allow one to home in and measure the particular layer of interest. This led to another entirely new synthesis regime with minimal kinetics and the ability to segregate contaminants, which in turn enabled atomically sharp interfaces with almost no cross-contamination because the construction is done at room temperature. It also led to the ability to make a wide variety of moiré lattices, and researchers have observed a number of interesting phenomena in the materials, such as superconductivity.
One difference between the two periods of development and discovery, Checkelsky said, is that there are far more question marks related to today’s materials because, at this time, the field is not nearly so well developed. For instance, the processes that are now most effective at producing the new materials and devices are mechanical, such as the layer transfer technique, but already in the literature there are a number of other suggested processes, some of which have already been used to produce moiré structures, such as folding and chemical vapor deposition. Among the questions are: Can you do it in a tunable way? What is the role of strain? Is there a way to do it with thin film, even with direct synthesis? For characterization, there are a number of outstanding challenges, including those involving scattering experiments, specific heat, and magnetization.
“We have a lot of question marks here, and we’re also trying to understand what is the next key target,” he said. “Is it correlated building blocks? Is it other moiré patterns? Is it better moiré materials? What are we trying to do?”
From there Checkelsky offered some thoughts as to how to go to the next generation of moiré systems. There are many possibilities, he said. People have already used a materials database approach in which they go through the database and think about which things can be exfoliated. From this perspective there are hundreds of potential source materials one could try. Once one has decided on a source material, there are a number of parameters that one could vary: the number of layers in the structure, how the source material is synthesized, how to exfoliated and place each layer, and the angle of the twist, among others. The number of possibilities is almost endless.
An important issue is the types of technical challenges that will be encountered in trying to fabricate devices using materials beyond what has already been tried—graphene, hexagonal boron nitride (hBN), and transition metal dichalcogenides? And would those technical challenges be outweighed by the benefits of the materials?
One potentially useful approach, Checkelsky said, would be to work with more complex starting materials than the ones that come up in a search on materials that can be exfoliated. For instance, it is possible to grow thin films on dissolvable substrates so that once the substrate has been dissolved away, one is left with a freestanding thin film of a material that has not been exfoliated but rather grown
(Lu et al. 2016). Researchers have shown that this technique can be used to grow monolayers even. In short, he said, by using thin-film techniques it may be possible to dramatically expand the number of materials for exploration even beyond the already very large number one gets when focusing on exfoliation.
In terms of improving the materials, he continued, there is a report from a group in Tokyo about having automated the stacking process (Masubuchi et al. 2018). The group said they put together 29 layers of graphene and hBN—which is quite a lot compared with what had been typically been able to be done to date.
These are promising approaches, he said, “but I wonder if there could be something very different.” Perhaps one could use three-dimensional materials, for instance, or may there are other things that could be combined or things that could be combined in new way. He mentioned in particular Jennifer Cano’s talk in which she discussed using topological surface states. “I think there could be a lot of possibilities.”
In closing his short presentation, Checkelsky brought up the issue of exactly how these moiré systems should be thought about. In many ways they inhabit a space that is between quantum materials and quantum simulators. In terms of length scale, for instance, the lattice constant for a moiré system (generally on the order of 10 nm) tends to be intermediate between the lattice constants of a crystalline system (a few angstroms) and an optical lattice system (closer to a micron). The same thing is true, he said, for the thermal scale and the number of lattice sites for these systems—the moiré systems are between the other two. “An interesting question in terms of the approach to thinking about developing these materials is, Is it going to be better to treat them like quantum materials and use the approach we are used to? Is it going to be better to design them the way the optical lattices are designed? Are we going to be able to use both in some synergistic way?” That will be an important question to address going forward, he said, because the ways one studies quantum materials and quantum simulators are quite different.
QUESTION-AND-ANSWER PERIOD
After finishing his short overview, Checkelsky asked each of the day’s panelist to make a few general comments, beginning with Jennifer Cano of Stony Brook University.
From a theoretical perspective, Cano said, there are three different directions to go in the future. One is working with the systems that already exist and really understanding the phase diagrams—for example, where a chiral spin liquid is found. The second is working with design principles to decide where to search in the huge phase space—a space that is far too large to search through systematically either experimentally or with theory. So a key to this sort of exploration will be deciding which sorts of phases are most interesting to look at. The third
aspect, particularly for theorists, is to go beyond what is known and come up with “crazy ideas” to look into. “There is so much to explore, but maybe there is some whole other regime of phase space that we haven’t started to look at,” she said. “What are the new ingredients we can put together and go beyond the van der Waals materials?”
Felser was next, and she spoke about “wishes” for the future—areas in which she would like to see improvements or more exploration. “One is it would be good to have bigger areas,” she said. “I would like to have a big twisted graphene to do catalysis on.” It would be particularly interesting to study as a catalyst, she said, because one can design a chiral structure on graphene. She would also like to see some focus on one-dimensional systems instead of the two-dimensional systems such as graphene. There are two-dimensional materials that show modulation in only one direction, and it would be particularly interesting, she said, to combine two such materials.
Pablo Jarillo-Herrero of the Massachusetts Institute of Technology then offered a few thoughts. Given that there is a phase space of essentially infinite size of different possibilities for these materials, he said, he believes it is important to explore areas of that phase space that have not been looked at before. If one only looks in areas that people suggest are likely to be important, it is difficult to find big surprises. “I think it’s good to also be a little bit adventurous,” he said. “Systems are so complex that every time you look in a place where people have not looked before, you find new surprises and interesting behavior.” So, on the one hand, it can be valuable to listen to theorists and look in places they believe might be useful to explore, it can also be good to look in places no one has suggested, which may hold the biggest surprises. In terms of a specific area to examine, Jarillo-Herrero said that chirality is an interesting phenomenon that should be explored further and that work should be done on developing better systems to create chiral structures.
Finally, Ashvin Vishwanath of Harvard University offered his thoughts. What his experience has shown to him, he said, is how much condensed matter physics is one subject despite the enormous phase space that it explores. There is no obvious reason that should be true, he said. People study whatever phenomenon appear in materials that seem to be of interest—high-temperature superconductivity, the quantum Hall effect, and so on—and “we’re seeing all of that coming together in this completely new system.” So someone who is interested only in, say, superconductivity will be missing a lot about these new materials by not being familiar with the other pieces. It is an indication that the research that materials scientists have been doing over the past decade has not been some sort of a random walk, although at times it might have seemed that way, but that the research has uncovered various things about many-body systems that are fundamental to those systems and that have equipped materials scientists to deal with these new discoveries being discussed at the workshop.
A second issue that Vishwanath addressed was the matter of scale. “We’re finding ourselves in a new plateau of energy scales,” he said. “Could that be useful for something?” One obvious observation, he added, was that if one looks at the energy scales of the bandgap, which are in the range of 10 meV, which corresponds to a terahertz frequency range, which is a regime that is somewhere between optics and electronics. “This is sort of the missing part of the spectrum,” he said, “so that is something that will be extremely interesting going forward.” Researchers should be thinking what they would like to accomplish with devices in the terahertz range.
And a third issue involved tools. An entire suite of tools was build up over decades to work in solid state physics, he noted, but when researchers started working with optical lattices, while they were inspired by some of the probes that had been developed for the earlier area, “at the end of the day you do something completely different.” Researchers developed and used tools that were more natural at that scale, thus gaining some new tools while also losing some earlier ones that had been developed for solid state physics. “So what are the analogous tools we will need to develop at the moiré scale?” he asked. Many of the spectroscopy tools, such as neutron scattering, will not be as useful, but surface-related probes will still provide valuable information. “Now the surface is pretty much everything, so nobody can complain you’ve just observed a surface feature,” he said, and thus scanning probes may be more relevant. But, he added, researchers need to think about new probes that can be deployed to examine these new materials.
After the four panelists had made their general comments, Checkelsky opened the question-and-answer portion with a question of his own. In the quantum materials world, he said, database approaches have been effective at providing us a certain sense of, for example, what materials might be topological insulators or pointing to materials that may have certain other properties. Could there be a useful database approach with these new materials? It would not be exactly the same as with quantum materials databases, but perhaps it might work in other ways, he said, mentioning, for example, materials with a particular symmetry, and he asked Vishwanath in particular about a symmetry search.
The problem is that there are many more moving parts than just symmetry, Vishwanath responded. There are such things to consider as the materials, can the materials be stacked together, and what sort of coupling there is between them. It short, it seems that there are new degrees of freedom that are not encountered in regular solid state physics. This is not necessarily a problem—it can be an advantage—but any search strategy will have to take into consideration these new degrees of freedom.
Felser agreed with Vishwanath that there is not yet enough known about these new materials to do valuable predictions using a database. There are many, many new materials that researchers are examining in this field, and it will take time
before they accumulate enough data on a large enough collection of materials to make such a database effective for making predictions.
Checkelsky asked Cano to respond to the same question, perhaps from the perspective of her work on topological surfaces. She answered that at present there seems more to be gained from making simple models than doing database searches. “I think the most fruitful thing to start out,” she said, “might be to identify a few classes of simple low-energy physics, like Dirac cones, quadratic band touching, and maybe quadratic insulators and then identify a few low-energy k∙p models and then see which of those puts you in the right place. I think material search is too much to ask right now.”
Turning to Jarillo-Herrero, Checkelsky noted that he has more experimental experience in this area than the other panelists, and he asked him what he would tell his graduate students to help them identify good targets for research. “Is it still based on intuition, or can you imagine something a theorist could tell you?” he asked. “Do you need the twist angle and the compound? What do you think is the key information?”
Jarillo-Herrero said he had two types of answers for the question which were almost contradictory. On the one hand, in the discovery of the properties of magic-angle twisted bilayer graphene it was very important that they had guidance from theorists, such as the approximate angle to work with. Otherwise his group might have been exploring randomly and never discovered the magic angle. On the other hand, he urges his students to look where no one else has looked because that is where truly important discoveries can be made. Before he did the experiments that uncovered the properties of magic-angle twisted bilayer graphene, he said, it was clear to him that putting two layers of graphene together at a certain angle was unexplored territory and that it might hold some interesting physics. “So I give a lot of freedom to my graduate students and postdocs to explore things,” he said. “I tell them, don’t do what everyone else is doing. Try to do something a little bit different and look especially for unexplored territory.” So it is a little bit of both, he concluded—use what the theorists say as inspiration, but at the same time explore areas that not everyone else is exploring.
Ramamoorthy Ramesh of the University of California, Berkeley, who would be one of the presenters on the workshop’s second day, offered an observation concerning the idea of searches. The abilities of artificial intelligence (AI) and machine learning are exploding, he said, and in the not-too-distant future it may well be possible to load all of the data about this new class of materials into a database and let AI programs make predictions. “I think this is going to happen,” he said. “AI machine learning is just exploding. This is a ship you cannot turn back.”
Next Checkelsky changed the subject and noted that one of the main themes of the workshop was thinking about building blocks that are strongly correlated, which present huge challenges. With graphene, for instance, there is a good under-
standing of the starting blocks, so the main question is what happens when they are put together. But with strongly correlated building blocks, he said, “now we don’t understand the starting blocks.” So, he asked the panel, what should be the first step in that direction?
Vishwanath answered that in the case of the cuprates, there has actually been an enormous amount of work, and “we actually may understand them better than people as a community are willing to admit. We understand the magnetism. We understand the basic energy scales.” And the new work with the cuprates is an opportunity to test that understanding, he said. “Can you predict what happens when you put a pair of these cuprate superconductors together at various angles, various doping regimes?” The work may offer an opportunity to probe the inner workings of the cuprates as opposed to just what is going on on the surface. “To me, that would be the first place to begin,” he said. “And these are also materials that can be stacked and twisted and so on. That seems to me the ideal starting point.”
Noting that graphene is actually an organic material—since it is made of carbon—Felser suggested that it might be valuable to look for other organic materials that could be used to construct quantum moiré materials. Building on that, Jarillo-Herrero spoke about metal-organic frameworks which, he said, have a “moiré flavor” because they are superstructures made out of smaller atoms and molecules. Many of them are actually two-dimensional, which means that adjacent layers can be twisted relative to each other. In addition, it is possible to create links between the layers in pretty much any desired positions. Noting that researchers would like to be able to strengthen the coupling between layers of the various moiré materials, he suggested that in these metal-organic frameworks, it may be possible to strengthen the coupling between layers chemically. Indeed, he added, even in magic-angle twisted bilayer graphene, people have suggested it may be possible to establish particular chemical links in a moiré structure to, for instance, stabilize an angle. Given all these possibilities, he suggested that researcher might want to explore twisted structures made with metal-organic frameworks.
Checkelsky then asked a question about characterization based on a question that had been posed in the chat: What are the most important tools for studying moiré materials? What is missing? Is there something that needs to be developed, some key tool that would open up the ability to make better systems by being able to better characterize them?
Jarillo-Herrero said that 15 to 20 years ago interest in gaining a better understanding of the cuprates led to enormous advances in various measurement techniques, such as X-ray scattering techniques. The lesson is that the desire to better characterize a system can help justify the investments needed to develop and improve the sorts of technologies that could be useful in that characterization. In the case of magic-angle graphene, the energy scales are much smaller, so some of the current technologies are not particularly useful in characterizing it, “but I see
that as a motivator,” he said. There are no fundamental principles preventing the development of the necessary technologies, he added. “We just needed to have a problem that was important enough to justify trying to push the frontier of energy resolution” in the various technologies. “And I hope,” he said, “that moiré systems are going to play a substantial role in pushing the frontier in terms of tools for systems.”
Checkelsky then asked Felser if there is one obvious tools that is missing from the toolbox she uses to study moiré systems. She answered that since she is particularly interested in the chemistry of these systems, she would like better tools that use light–matter interactions to study the materials. She is particularly interested in chiral light–matter interactions, she said.
Pivoting from characterization tools to computational tools, Checkelsky asked Cano and Vishwanath about any analytical or computational tools that need to be developed in order to advance the field. Cano replied that one of the major challenges in the area is the ab initio calculation of band structures because the unit cells are so big. So it would be valuable to have a machine learning approach to ab initio calculations or perhaps some other approach to making the calculations more tractable. “Tricks or tools to getting low-energy physics out of ab initio calculations of these huge moiré cells might be a theoretical advance worth pursuing.”
Vishwanath added that it is common today to use an effective low-energy model to calculate twisted band structures, and it has been found that by and large calculations with the low-energy model agree reasonably well with ab initio calculations, so people will often rely just on the low-energy model. “The thing I would like to know is, are they cases where it does not check out, where you can’t get away with using the effective low-energy model and you really need the full calculation with all the atoms? Where do the errors start getting out of hand?”
Checkelsky then asked if, in the moiré systems under discussion, there are any fundamental limitations to the lattices that one can realize. “Is it just arbitrary? Can you make any lattice you want out of these systems?” Felser said that there are always chemical limitations of one sort or another and that there are likely to be electronic limitations as well in how the two layers interact with one another. The question is, she said, how big the bandgap of a compound can be and the compound still be useful as a moiré lattice. There must be tunneling between the layers, for instance.
Vishwanath added that it is very difficult to predict a priori what is going to happen with a given structure. One can do calculations of what to expect, but the calculations can be wrong in unexpected ways.
Stuart Parkin of the Max Planck Institute suggested that a fundamental limitation is the slippage of the layers. If one orients the two layers at an angle but that configuration is unstable, the layers will have a tendency to move into a more stable orientation.
Jarillo-Herrero responded that in the case of graphene nature has been kind. One can orient two single layers of graphene at essentially any angle and they will stay in that orientation unless the system is heated to a high temperature, at which point it will relax and the two layers will slip back to zero twist angle, which is thermodynamically what the system wants to do. It’s not clear exactly why the system stays at the magic angle until it is heated up, he said. One possibility is that there are some residues between the two layers and that if the surfaces were super-clean, they might slip past each other and reorient at zero degrees. “This deserves more attention,” he said, “because it’s good to know either way. If we can pin certain structures, it’s good to know it—how to pin them, how to control them.”
In response, Parkin commented that the question of residue—or “dirt”—between the layers of the bilayer graphene is an interesting one. In contrast to molecular beam epitaxy, where layers are laid down in a vacuum chamber that essentially eliminates any contaminants, the single layers of graphene created by exfoliation are products of “lousy conditions, so it seems like dirt must play some role in these materials, he said, and this should be taken into account. Not only may this dirt be responsible for keeping layers from slipping past each other, it may also cause a deterioration in various properties of the system, such as mobility, although the electronic structure may not be so greatly affected.
Jarillo-Herrero answered by saying that graphene is something of a special case because it is so inert and does not react much with any contaminants. Thus, for example, graphene structures made at room temperature and normal atmosphere have extremely high mobility. Furthermore, people have experimented with making graphene in vacuum conditions and have not seen any obvious improvement in its properties.
Checkelsky next asked an open-ended question of the panel: In terms of fundamental science, what do people think are the most important problems—or maybe the most important problem—that moiré materials are uniquely positioned to address? Is there something that these materials can do that nothing else can? Additionally, he asked, how could expanding the class of moiré systems affect the answer to that question?
Jarillo-Herrero answered that magic-angle twisted bilayer graphene exhibits characteristics that are normally seen only in much more complex systems. “This is about as simple as it gets—just carbon, and its graphene on top of graphene,” he said. “The fact we can realize this complex phenomenology, all this emergent behavior, just in graphene on top of graphene tells you to some extent that there’s some fundamental principles there which do not depend on details of the chemistry but rely on very basic, simple things like, for example, what is the ratio of kinetic energy to interaction energy?” General symmetry properties may also come into play. Among the members of his group, this was a major motivation for studying the material, he said. By exploring this simple and highly tunable system, they
hoped to extract the key essential ingredients responsible for, say, strong coupling superconductivity and see the lessons learned from that can be applied in engineering regular materials at atomic-scale lattices to get some desired properties—room-temperature superconductivity, perhaps. However, after some time had passed—6 months to 1 year or so—he and others began to realize that the graphene system is also unique in that it brings together topology and correlations, so it may be difficult to gain fundamental understandings that can be applied to other systems. Now a major motivation among his group has changed somewhat with the realization of what a rich problem the system represents, and “we are having fun exploring it,” he said. Still, he added, the first motivation is still there, and his group is still looking for fundamental insights that can be applied to other materials.
Felser said that to her the most exciting aspect of the materials is that one gets modulation of charge on a nanometer scale. It may be possible to use this property to build devices, such as data storage devices.
From his perspective, Vishwanath said, there are two key questions in condensed matter research that might be addressed by work on the twisted bilayer graphene system. The first is how electrons pair in superconductors. It is known that in traditional superconductors electron pairing is mediated by phonons, but that is not the case in, for example, high-temperature superconductors, and it does not appear to be the case in magic-angle twisted bilayer graphene either. Because twisted bilayer graphene is a simple, tunable system, it may make it easier to establish exactly what the electron-pairing mechanism is in this material. “I think establishing a new route to superconductivity would be a really big advance,” he said. The second area where twisted bilayer graphene might help answer some unresolved questions, he said, is related to the existence of various exotic phases of matter that have been predicted but not observed.
Cano added that tunable correlation strength is unique to this platform because usually when researchers are looking for spin liquid candidates, they are working with a phase diagram where each point represents an individual material that has been synthesized and tested, and adding points to the phase diagram means synthesizing and measuring new sample, while the tunable correlation strength of twisted bilayer graphene makes it possible to explore a large phase diagram within one material. “I think that’s one of the things that makes this platform really unique for exploring fundamental physics,” she said.
In response to a question from Checkelsky about possible applications of quantum moiré materials, Jarillo-Herrero said that, at a very simple level, magic-angle graphene is a superconducting field-effect transitor—something that with a gate can be switched among being a superconductor, being an insulator, and being a regular metal. “So anything where you might want to have a superconducting field-effect transistor, you could use magic-angle graphene,” he said. This could include such things as the superconducting elements in classical cryogenic computing to
quantum computing. And because magic-angle graphene is by far the lightest of any superconductor, it could be used in a wide number of applications, such as superconducting single-photon detectors. There are many such types of quantum sensing and quantum computing applications that one could imagine, he said. A different sort of applications could use hexagonal boron nitride, which is the thinnest of all out-of-plane ferroelectric materials. Assuming the material could be fabricated at scale, he said, it is possible it could be used in applications right away. More generally, he cautioned, all of the possible applications rely on developing the ability to mass-produce structures made out of these materials.
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