Beyond twisted bilayer graphene and beyond

项目背景{石墨烯具有卓越的电子和机械性能，有着广泛的应用前景。不止一个碳原子层可以通过货车德瓦尔斯力结合，形成一个相干晶格，用于电子运动，从而产生新的性质。最近，实验表明双层石墨烯已经产生了显着的特性。两层之间1.1的小扭曲使半金属变成临界温度为1.7K的超导体。在库仑排斥导致电子交通堵塞和系统电绝缘的地方也可以发现莫特绝缘体。人们认为，这种扭曲会在费米能级附近产生窄的电子带。这意味着电子的动能被抑制，库仑相互作用变得重要。事实上，这让人想起了铜氧化物超导体，它们在超导相附近也表现出Mott绝缘反铁磁态。在这种情况下，库仑相互作用主导了CuO平面上单个电子带的性质。在第一年的专题中，我们将研究双层的能带结构，并推广到多层。目的是研究双层膜的窄带物理是否也可以在多层膜中发现。我们将从系统的一个简单的紧绑定模型开始。数值解将帮助我们探索系统的微妙之处。这可以通过分析狄拉克点附近的能带结构来实现。人们也可以使用群论来探索狄拉克点在不同的多层结构中是否稳定。该项目的首要目标是在最近的实验中探索石墨烯物理学。我们研究多层石墨烯的初步阶段将开辟新的研究途径。一个与关联电子物理有关的问题是，费米能级附近窄带的数量和性质是否可以被设计。这可能会导致在其他电子材料中发现的相关物理学的新类似物，其中d带和f带电子的多轨道产生了丰富的现象。帝国理工学院托马斯杨中心的其他研究人员对石墨烯和相关系统的电子结构感兴趣。我们的建议可以通过更复杂的电子结构计算得到证实，另一个可能的方向是研究双层石墨烯物理是否可以在其他领域重现，例如，使用冷原子中的光学晶格和微柱极化激元晶格。例如，在石墨烯中很难检测到的强自旋轨道耦合可以在这些系统中模拟，而在碳中很难实现。在一个非常快速发展的领域中，很难预测研究方向。然而，很明显，在未来的几年里，这些系统将受到强烈的实验关注，理论家们将面临大量的挑战。Mathieu dos桑托斯有理论物理学的背景，但没有专门从事凝聚态物理学。这个项目的目的是提供一个温和的介绍该领域的路线，可以导致有趣的物理没有最初太多的技术知识在该地区。

Project Background { Graphene has remarkable electronic and mechanical properties that promise awide range of applications. More than one of these sheets of carbon atoms can bind by van der Waals forcesto form a coherent lattice for electronic motion giving rise to new properties. More recently, experimentshave shown that bilayer graphene has yielded remarkable properties. A small twist of 1.1 between thetwo layers turns the semimetal into a superconductor with a critical temperature of 1.7K. A Mott insulatorcan also be found where Coulomb repulsion causes a traffic jam of electrons and the system becomeselectrically insulating.It is believed that the twist gives rise to narrow electronic bands near the Fermi level. This means thatthe kinetic energy of the electrons is suppressed, and Coulomb interaction becomes important. In fact, thisis reminiscent of the cuprate superconductors which also exhibit Mott insulating antiferromagnetic statenear a superconducting phase. In that case, Coulomb interactions dominate the properties of a single band of electrons on the CuO planes.First year project. In the first-year project, we will investigate the band structure of bilayer andgeneralise to multiple layers. The aim is to investigate whether the narrow-band physics of the bilayercan also be found in multiple layers. We will start with a simple tight-binding model of the system. Anumerical solution will help us explore the subtleties of the system. This can be followed by analyticalanalysis of the band structure near the Dirac points. One can also use group theory to explore whetherDirac points are robust in different multilayer settings.PhD project objectives. The overarching goal of the project is to explore graphene physics in a newavenue recently made possible in experiments. Our initial stage to study multilayer graphene would openup new avenues of research. One question that relates back to the correlated electron physics is whether the number and the natureof narrow bands near the Fermi level can be engineered. This can give rise to new analogues of correlatedphysics found in other electronic materials where multiple orbitals in d-band and f-band electrons give risea rich variety of phenomena.There are other researchers at the Thomas Young Centre at Imperial interested in the electronic structureof graphene and related systems. Our proposals can be confirmed with more sophisticated electronicstructure calculations.Another possible direction is to study whether bilayer graphene physics can be reproduced in other fields,for instance, using optical lattices in cold atoms and micro-pillar polariton lattices. For instance, strongspin-orbit coupling, which is so small that it is undetectable in graphene, can be simulated in these systemsthat is hard to achieve in carbon.It is hard to predict the direction of research in a very fast moving field. However, it is clear that therewill be intense experimental attention in these systems in the next few years and plenty of challenges fortheorists to address.Student Background. Mathieu dos Santos has a background in theoretical physics but has notspecialised in condensed matter physics. This project is designed to provide a gentle introduction to thefield with a route that could lead to interesting physics without initially too much technical knowledge inthe area.