Interactions and symmetry breaking in Dirac systems

石墨烯，一个原子厚的层更熟悉的石墨，已在2004年制造，并带来了诺贝尔奖，去年它的发明者。它是一种非常坚固，但可变形，传导良好的碳原子膜。它的发现有望彻底改变电子学，并已迫使物理学家修改和重新审视他们所珍视的许多固体导电理论。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。在磁场或机械应变下观察到的石墨烯中已经出现了一些知之甚少的异常现象。在过去的六年里，我在西蒙弗雷泽大学的研究小组一直在发展一种通用的数学形式，它应该能描述电子之间的排斥效应。该提案的一部分是使用我们的计算工具来设计和理解通过机械变形等方法控制石墨烯导电性能的方法。这将使石墨烯的导电性能更接近硅，而硅是目前商业电子产品的阿尔法和欧米茄。另一部分是探索石墨烯独特的电子结构，研究石墨烯变成绝缘体甚至超导体时发生的新物理现象。我们希望通过这种方式学习的新物理学可以应用于与石墨烯具有某些方面的整个新材料，甚至可以帮助我们理解高能物理学中的一些基本问题，例如基本粒子如何获得质量。

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.