Interactions and symmetry breaking in Dirac systems

石墨烯是一种更常见的石墨层，只有一个原子厚，它于2004年被制造出来，并于去年将诺贝尔奖颁给了它的发明者。它是一种极其坚固但可变形、导电性良好的碳原子膜。它的发现有望给电子学带来革命性的变化，并已迫使物理学家修改和重新审视他们珍视的许多关于固体如何导电的理论。我建议从理论上研究电子之间的库仑相互作用如何影响石墨烯和其他密切相关的新材料的导电性能。事实证明，这个看似简单的问题实际上隐藏着一个困难而普遍的物理问题。已经有一些在磁场或机械应变下观察到的石墨烯中出现的鲜为人知的反常现象。在过去的六年里，我在西蒙·弗雷泽大学的团队一直在开发一种通用的数学形式主义，它应该描述电子之间排斥的影响。该提案的一部分是使用我们的计算工具来设计和理解控制石墨烯导电性能的方法，包括通过机械变形等方法。这应该会使石墨烯在导电性能上更接近硅，硅是目前商业电子的阿尔法和欧米伽。另一个部分是探索石墨烯独特的电子结构，以研究石墨烯变成绝缘体甚至超导体时发生的新的物理现象。这里的希望是，人们可以通过这种方式学习的新物理学可能适用于整个类别的新材料，这些新材料共享石墨烯的某些方面，甚至可能有助于我们理解高能物理中的一些基本问题，比如基本粒子如何获得它们的质量。

Graphene, one-atom-thick layer of the more familiar graphite, has been fabricated in 2004, and has brought the Nobel prize last year to its inventors. It is an extremely strong, yet deformable, well-conducting membrane of carbon atoms. Its discovery promises to revolutionize electronics, and has already forced physicists to revise and reexamine many of their cherished theories of how solids conduct electricity. I propose to theoretically study how the Coulomb interaction between electrons affects the conducting properties of graphene and other closely related new materials. It turns out that this seemingly straightforward question in fact hides a difficult and general physical problem. There is already a number of poorly understood anomalies that occur in graphene, observed in magnetic field or under mechanical strain. In the last six years my group at Simon Fraser University has been developing a general mathematical formalism that should describe the effects of the repulsion between electrons. One part of the proposal is to use our calculational tools to devise and understand the ways of controlling conducting properties of graphene, by mechanical deformations, among other methods. This should make graphene closer in its conducting properties to silicon, the current alpha and omega of commercial electronics. The other part is to explore the unique electronic structure of graphene to study novel physical phenomena that occur when graphene is turned into an insulator, or even into a superconductor. The hope here is that the new physics one may learn this way may apply to the whole class of new materials that share certain aspects of graphene, and may even help our understanding of some fundamental issues in high-energy physics, such as how elementary particles acquire their mass.