background introduction
Graphene is a component of graphite, which is composed of one carbon atom and three adjacent carbon atoms. It is a single-layer carbon atom with hexagonal honeycomb network structure, and its thickness is equivalent to one carbon atom. The existence of single-layer graphene has been predicted for decades, and it has been successfully grown on the surface of other materials, but the academic interest in graphene research broke out in 2004, because it was the first time that graphene could be separated from graphite flakes by mechanical means (mechanical stripping method).
Graphene is often described as a magical material with transparency, excellent conductivity and strong flexibility. But some people are interested in some more basic problems. Graphene, as a two-dimensional conductor material, shows unusual electrical and magnetic properties, and has great research value in quantum confinement effect and electronic interaction, and has application prospects in electronic components and equipment. The 20 10 nobel prize in physics was awarded to two professors, Andre Geim and Konstantin Novoselov, from the university of Manchester, England, in recognition of their outstanding contributions in the field of graphene research.
When two graphene sheets are close enough to interact, their wonderful characteristics will be further amplified. It is particularly striking that the electronic properties of graphene may depend on the relative angles of graphene sheets, that is, the arrangement between two layers of honeycomb lattices. The superposition of two honeycomb lattices may produce a "superlattice" structure: the regularity between lattices is more obvious after a certain angle matching, even stronger than the influence brought by lattice spacing. This is the well-known "Moire effect"-when you look at two closely spaced grids from a distance, you can observe this optical phenomenon.
The electronic characteristics of twisted double-layer graphene (TBG) require that the position and angle of two graphene sheets can be accurately controlled. These phenomena are now considered to be common in other two-dimensional materials, such as hexagonal boron nitride (h.BN) sheets. These studies have opened up a fertile ground for the study of condensed matter physics, and the magic angle twisted double-layer graphene (MATBG) with certain twist angles shows more fascinating electronic properties.
Pablo Jalillo-herrero's team took the lead in manufacturing the magic horn graphene material.
Allen MacDonald was one of the first scientists to theoretically predict the existence of the magic horn.
NSR: How to find the abnormal electronic behavior in twisted double-layer graphene? Were these effects predicted by theory before they were discovered?
PJ-H: From about 2007, many theoretical groups began to study twisted double-layer graphene. By the end of 2009, Eva Andrei's team reported the research on twisted double-layer graphene by scanning tunneling microscope (STM) [G. Li et al., NAT Phys 2010; 6: 109] 。 They observed that the peak in the data seems to change with the twist angle, and this peak is considered to be the characteristic of the electronic structure of the van Hove singular peak. In particular, for a torsion angle of about 1. 16, the peak spacing between two van hoof peaks is close to zero. At almost the same time, two other groups studied twisted double-layer graphene at a very small angle: Eric Suá rez Morell of Chile [E.S. Morell et al., Phys Rev B 2010; 82: 12 1407] and the team of Rafi bicester Rize and Allen MacDonald [R. bicester Rize and A. MacDonald, Procnatl acad sci USA 2011; 108: 12233] 。 Both groups predict that the twisted double-layer graphene has a flat electronic band at the angle of 1. 1 to 1.5. Bistritzer and MacDonald coined the term "magic angle", which refers to the angle at which the electron velocity at Fermi level becomes zero (Fermi level is the highest energy level that an electron can occupy at absolute zero).
AM: "My understanding of history goes beyond academic publications", this sentence comes from Eva Andre's article. Eva was the first person to measure the magical change of electronic structure, and she discovered the characteristic that double-layer graphene sheets unexpectedly produced Moire effect in STM density measurement. Eva told me that observation comes first, which inspired Antonio Castro-Neto and Joe? The theory of Lopez dos Santos.
My interest in graphene Moore superlattices began with a conversation with Ed Conrad of Georgia Institute of Technology. He showed me some angular resolution photoelectron spectroscopy data, which I couldn't understand. When my postdoctoral fellow Rafi Bistritzer and I started the calculation, we found that the calculation results showed that the speed of graphene electrons would drop to zero under a set of discrete distortion angles. We call these horns magic horns, and the maximum magic horn is about 1. This was completely unexpected, and we immediately realized that it meant a strong interactive electronic platform with unlimited prospects. After a while, we noticed that a research group in Chile also independently turned on some twilight of magic angle physics. But at that time, it was not clear whether any experimenter could set samples to observe this physical phenomenon under the condition of controllable torsion angle. My colleague Emmanuel Tutuk has done a lot of work in this direction and provided some information for Pablo's work.
NSR: What prompted you to study this system? Now it seems that observing the phenomenon of electronic correlation in a controllable way has become a scenic spot-is this result expected or unexpected?
PJ-H: At first, my motivation for studying twisted double-layer graphene was intuition. This "new knob" in condensed matter physics, that is, changing the twist angle, is likely to bring interesting physical phenomena. The system in condensed matter physics is usually very complex, and there are often unexpected gains when exploring unknown fields. As far as Magic Horn Graphene is concerned, my motivation is to find interesting related insulation states. I think that when the Fermi level in graphene moves to the Van Hoff singularity, it may show the related insulation state. [NSR: When Fermi can approach this singularity, new electronic phases, such as superconductivity, have been observed. We did find insulation-but to our surprise, they are completely different types. The insulation behavior occurs in an integer number of electrons per molar unit, not because of the Van Hoff singularity. This is a big surprise. The bigger surprise is the discovery of superconductivity, which is even more unexpected.
AM: The theory of magic horn effect that we first discovered did not meet the expectations of early experiments. Therefore, it is difficult for us to publish this article, because the reviewers think that we must be wrong. Coincidentally, I happened to be elected as an academician of the American Academy of Sciences at that time, and I was allowed to publish my inaugural article in PNAS, with very loose comments. So I decided to give up the tug-of-war with the reviewers and publish our findings directly on PNAS.
After that paper, I tried to find other examples where interesting Mohr superlattice phenomena could be observed. I put forward the possibility of realizing topological exciton band [F. Wu et al., phys rev lett 2017; 118:147401] and many suggestions related to optical properties. I also propose that the Moire system of layered transition metal disulfide (TMD) will produce completely different physical properties from the graphene structure. This part of Moore's research has now really begun to be put into practice.
Promised land of new material principles
NSR: From insulators to superconductors to magnetic materials, the electronic states produced by these graphene systems seem to be very diverse. What is the physical basis for producing such diverse states and what are the key factors that determine these properties?
PJ-H: We are still trying to fully understand these systems. But your basic observation is correct-magic horn graphene and several other molar systems now show a very rich set of related behaviors. The origin seems to be that these systems have very narrow electron bands (meaning that the kinetic energy of electrons is very small), so the interaction between electrons can play a leading role. Once there is a strong interaction between electrons, the possible multi-body ground state (such as superconductivity, related insulators, magnetism, etc. ) is possible. We can browse all these modes, thanks to the high adjustability of Moore system.
AM: There are many similarities between the strong correlation in multilayer graphene and the strong correlation in quantum Hall effect. The work of Eslam Khalaf, Ashvin Vishwanath and Mike Zaletel illustrates this connection. Fundamentally speaking, it is related to the topological characteristics of electronic energy bands. At the same time, these systems have the characteristics of quasi-two-dimensional Hubbard model (one of the simplest lattice models of strongly correlated electronic systems). Magic horn graphene seems to be a combination of quantum Hall effect and high temperature superconductivity, and it is a very magical system.
NSR: Can you explain the magic horn effect? What makes graphene layers "special" in some orientations?
PJ-H: Magic horn effect is a state of "* * * vibration". This magic horn-driven electronic structure makes it so easy for electrons to cross the graphene layer, just like providing a "direct tunnel" for these electrons to another graphene layer. In simpler terms, one explanation for the changeable behavior of electrons in MATBG is that when electrons have great kinetic energy (moving very fast), they have little time to interact. But in MATBG, electrons move slowly, so when they pass by, they will have more opportunities to interact.
NSR: In this system, the interaction between insulation and superconductivity seems to be close to that observed in the high temperature superconductivity of copper oxide. Is there an approximate physical law at work between the two? Will these behaviors really help us understand the origin of superconductivity in such materials?
The phase diagrams of PJ-H: Matbg and cuprate superconductors do have many similarities, but there are also many differences. For example, their lattice symmetry and topological properties of electronic structures are quite different. In addition, the electrons in cuprate are degenerate spins, while the spin states in MATBG are more abundant. Therefore, it is not clear whether the understanding of MATBG will help us understand the origin of superconductivity in copper oxides. Although my intuition will help, it's too early to say.
AM: We don't have completely confident answers to these questions, but we are making progress. There are many similarities between high-temperature superconductors and MATBG systems, among which the critical point of magnetic sequence and fermi surface reconstruction attract the most attention. In my opinion, by conducting new experiments and theoretical scene tests, we may further enhance our understanding of MATBG superconductivity, and the progress will also help us understand the emergence of high-temperature superconductivity. Possibility of modulating system characteristics by in-situ modulation of charge carrier density or other means (for example, by changing grid spacing, dielectric environment and plane magnetic field, etc.). ) is an important advantage of MATBG.
NSR: What role does the dimension play here? Do these behaviors depend on the basic fact that this is a quasi-2D system? Is this behavior related to the study of low-dimensional quantum multibody systems such as quantum Hall effect?
PJ-H: Dimensions are very important for various reasons. Among them: MATBG has high electrical adjustability because of its two-dimensional geometric structure; The electronic structure (such as the density of electronic states) depends on the dimension; The interaction effect may also be strongly dependent on the dimension (for example, the electron shielding effect varies greatly in 1D, 2D and 3D); As for quantum Hall physics, the electronic energy bands in QHE and MATBG (and several other related Mohr systems) are topological in nature, and they are deeply related. This is why the latter can show interesting quantum Hall effect, even in zero magnetic field (unlike standard QHE).
AM: The electron correlation in low-dimensional systems is often stronger, resulting in surprising multi-electron states in a wider range, including fractional quantum Hall effect (FQHE) systems, MATBG, double-layer or triple-layer graphene. The topological diagram of QHE constitutes the physical connection between MATBG and f QHE. An experimental proof of this connection is the universal appearance of abnormal quantum Hall states (QHE without magnetic field) in MATBG.
Challenges, applications and opportunities.
NSR: How to study these systems through experiments? Is the production of high-quality single-layer graphene a routine now? How to control the relative orientation of graphene sheets?
PJ-H: The production of ultra-high quality single-layer graphene has been very standardized, such as graphite mechanical stripping method, and thousands of teams around the world can do this. The tricky thing is to accurately control the rotation angle and stack two graphene sheets together, especially at a small angle like Magic Angle 1.5438+0. At present, only 15 team in the world can do MATBG, but the team has been growing, because the technology is easy to learn as long as someone demonstrates it. Before the outbreak of COVID-19, many teams came to MIT to learn about MATBG, and many of them have now copied and expanded many of our achievements.
AM: The achievements we have made are amazing, but if we can develop the technology to control the torsion angle more finely and make the distribution of the torsion angle more uniform, it will accelerate the progress in this field.
NSR: What are the key issues to explore in these systems? Personally, what are you most eager to learn now?
PJ-H: There are still many key issues to be explored. Perhaps one of the most important problems is the exact mechanism of superconductivity and the symmetry of order parameters. The current experiments and theories seem to point to an unconventional superconducting origin mechanism (some people think that MATBG may be an electron-phonon mediated superconductor in a very special parametric state, although not everyone agrees). We need to study this point in more detail. I personally look forward to discovering and studying new Mohr systems, new superconductors and their related topological behaviors. I think we have only scratched the surface of hundreds of possible Mohr systems. These systems are different in composition, geometric properties and complex states.
AM: I think it is very important to determine the origin mechanism of superconductivity in MATBG. I am solving this problem. An important expectation is that we will be able to realize the fractional anomalous quantum Hall system (also called fractional Chen insulator) in MATBG or transition metal disulfide (TMD) Moire diagram to show the quantum anomalous Hall effect. In view of the flexibility of moire superlattice, we will be able to find and design favorable conditions. Fractional quantum Hall (FQH) state is also one of the possible research objects of topological quantum computation.
NSR: There seem to be many potential degrees of freedom when exploring these systems. For example, now some research interests are to expand the two-tier system to three-tier, so what can we predict or observe? For another example, what will be gained from the heterogeneous double-layer structure composed of other two-dimensional materials such as boron nitride?
AM: I am very interested in finding other layered materials that can be used to build new moire superlattices. Every discovery will bring a new physical universe. In the case of TMD and twisted graphene-based Moore system, we have a case of cruise electronic ferromagnetic system-only the magnetic sequence temperature is quite low. It will be very interesting to find ways to improve the ordered temperature and explore its limit. Because the Mohr superlattice system can be modulated in many ways, the prospect is relatively optimistic. This is a brand-new example of making artificial tunable crystals, and we have only touched the surface. We will witness what happened-this is the charm of science.
PJ-H: Indeed, the possibilities are almost infinite. Just earlier this year, Philip Kim's team and my team independently discovered superconductivity in magic corner twisted three-layer graphene (MATTG). The magic horn is slightly different (about 1.6). This data was actually predicted in theory a few years ago, so we know where to go. It turns out that superconductivity in MATTG is more interesting than that in MATBG, because it is more powerful and adjustable. However, the use of heterogeneous bilayer structure can indeed bring many new things, and the discovery of quantum anomalous Hall effect (QAHE) in the bilayer graphene/boron nitride molar system is one of the earliest examples.
NSR: More generally, MATBG system reflects the explosive growth of academic interest in the study of strongly related electrons in the past two decades, which has spawned the discovery of a number of sub-materials, such as topological insulators, majorana zero modes, foreign semi-metals, etc. What prompted the explosion of research interest? Is there a new theory to unify the quantum and electronic phase states of matter? Or are we still in the stage of discovery and surprise to a considerable extent?
PJ-H: Condensed matter physics experienced two revolutions in 1980s, namely, the discovery of integer/fractional quantum Hall effect (bringing topology into this field) and the discovery of high-temperature superconductivity (pushing strongly correlated systems to the forefront of the discipline). Since then, the research field of topology is not closely related to the strongly correlated system, because the field is completely different. After 2000, there were three subversive discoveries: the discovery of graphene and two-dimensional crystal materials; Theoretical prediction and experimental findings of topological insulators: the second group of high temperature superconductors, namely iron phosphide materials, have been discovered. However, these areas are still largely independent. It is MATBG that integrates the three research fields because it has all the characteristics. The topic of "Moire quantum matter" has aroused heated discussion in all these fields.
AM: In my opinion, we are still in the stage of discovery and surprise, but I am very optimistic that these new strong correlation systems will lead to a broader and deeper understanding of strong electron correlation physics.
NSR: Is it possible to apply these systems in practice, especially in equipment technology?
PJ-H: It's always hard to predict. At present, my team and even researchers in the whole field are encouraged to explore the charm of basic physics in these systems. Actually, as an electrically tunable superconductor, MATBG (called superconducting field effect transistor in engineering) is easy to imagine if it can be manufactured on a large scale. Include superconducting qubits, quantum photodetectors and low-temperature classical calculations.
Amy: Personally, I am very interested in finding potential applications-maybe optical properties, maybe spintronics. The interface with TMD may be useful in adjusting the spin-orbit interaction force, which is very important for spintronics.
The magic horn is in China
NSR: What's your impression of China's research in this field?
PJ-H: From the perspective of theoretical physics, the academic circles in China are very interested in this research. In terms of experimental work, only a few teams with nano-manufacturing experience in China (the most famous of which is Professor Zhang from Fudan University) can produce high-quality Moire quantum systems, and they are doing excellent research. In view of the recent rapid development of domestic scientific research, it is estimated that more experimental groups will begin to study this topic in the next few years.
My former student Cao Yuan was a great scientist in many ways. He is smart, diligent, creative and efficient. He is not only the first author of the two discovery papers I mentioned earlier, but also a young leader in this field, and has made outstanding contributions in this field since then. He won many awards at a very young age, including the McMillan Prize (the most prestigious award for young condensed matter physicists) and the recent sackler Prize in Physics. I feel lucky to work with him. I think I learned as much from him as he learned from me. I believe he will be the leader of his generation of scientists.
AM: Wu Fengcheng, a former student in our group, has done important preliminary work for TMD Moore system, involving its optical and electrical characteristics. He has also made contributions to the research of MATBG superconductivity. Now he is a professor at Wuhan University and a leading talent in this field. Yao Wang of HKU is the main scientist who studies the optical characteristics of TMD Moire system. The quantum anomalous Hall effect was first observed in Tsinghua University's magnetic topological insulator. MATBG provides a second example and some interesting similarities and differences.
NSR: What (or who) inspired you to do this job? What advice would you give to young researchers entering this field?
PJ-H: Many of my colleagues are very creative, and their condensed matter physics experiments have inspired my team. These include Paul McEwan (Cornell University), Andre Geim (Manchester University) and Amir Jacob (Harvard University). Of course, Leo Kouwenhoven, my doctoral supervisor at Delft University of Technology, and Philip Kim, my postdoctoral supervisor at Harvard, have great influence on the formation of my research ideas. For young researchers, I will say: Take risks, follow your own interests, and don't let others limit your ambitions.
AM: I've been doing this for a long time. I really enjoy the ability to surprise experiments. I do the basic theory and method of materials science, trying to find stimulation in the phenomena that have been observed in those experiments. My intuition largely comes from the known experimental results and the reflection on the success or failure of different theoretical models to describe nature. It is also very interesting to deepen the theoretical understanding of observed but still mysterious phenomena.
I suggest that young researchers develop their own unique ways to think about problems in their research fields. Whenever you encounter something you don't understand, please break the casserole and ask to the end until you know everything. Many times, new ideas are just details of predecessors' ideas-but they are not sure, and sometimes they will become really new things.
This article is translated from the interview article "The New Turn of Graphene: An Interview with Pablo Jalillo-Herrero and Allen MacDonald" in National Science Review, written by Philip Bauer and compiled by Zhishe.
Original link:/nsr/advance-article/doi/10.1093/nsr/nwac005/6506475.