Correlations and phase transitions in Dirac systems

狄拉克系统中的相关性和相变

• 批准号: RGPIN-2017-04167
• 负责人: Herbut, Igor
• 金额: $ 2.62万
• 依托单位: Simon Fraser University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=686565
• 关键词: Correlations; phase; transitions; Dirac; systems

The electrically insulating or conducting behavior of many solid materials, such as cooper or aluminum, may be well understood by a quantum mechanical model which almost entirely neglects the repulsive interaction between the constituent electrons. However, there are also many known materials where such a simple picture fails, and the inclusion of interactions between electrons becomes paramount. This is particularly true in the so-called Dirac materials, which have their electronic structure similar to graphene; a truly two-dimensional single layer of carbon which holds a promise to revolutionize today's electronics. These Dirac solids have their number of electrons that can react to external probes reduced, which diminishes the usual "screening" of the electron-electron repulsion, and makes them more vulnerable to its feedback effects on the electrons themselves. These features are not necessarily detrimental to their conducting, magnetic, and other properties, but they do necessitate a new theoretical approach to this type of materials. ****** I propose a theoretical study of the qualitatively new effects of the interactions between electrons and of the impurities on the electronic properties of the Dirac systems in both two and three dimensions. The proposal builds on a number of recent studies performed by my own and by other research groups which indicate that interacting Dirac systems may show interesting new ordered low-temperature phases which share some similarity with then so-called nematic phases of, otherwise physically entirely different, liquid crystals. Other possibilities abound; most importantly, a long-sought phase that is by its physical characteristics somewhere in between a normal metal and an ordered insulator is also thought to be possible. A formulation of the physical mechanism that decides which of the multitude of the electronic phases is ultimately the one to be realized is one of the principal goals of the proposed research. Achieving this goal requires improved mathematical understanding of the main theoretical tool for the studies of interacting quantum systems, the so-called renormalization group, and the various possibilities that it allows. The hope is that such a deepened understanding might also lead to advances on other formally similar problems, which, for example, occur in high-energy physics.

许多固体材料（例如铜或铝）的电绝缘或导电行为可以通过量子力学模型得到很好的理解，该模型几乎完全忽略了组成电子之间的排斥相互作用。然而，也有许多已知的材料，这样一个简单的图片是失败的，并且包含电子之间的相互作用变得至关重要。在所谓的狄拉克材料中尤其如此，该材料的电子结构与石墨烯相似。真正的二维单层碳有望彻底改变当今的电子产品。这些狄拉克固体的可对外部探针发生反应的电子数量减少，这减少了电子-电子斥力的通常“屏蔽”，并使它们更容易受到电子本身反馈效应的影响。这些特征不一定会损害它们的导电、磁性和其他特性，但它们确实需要一种新的理论方法来研究此类材料。 ****** 我提出了一项理论研究，研究电子和杂质之间的相互作用对二维和三维狄拉克系统的电子特性的新的定性影响。 该提案建立在我自己和其他研究小组最近进行的多项研究的基础上，这些研究表明，相互作用的狄拉克系统可能会显示出有趣的新有序低温相，这些相与当时所谓的向列相（否则物理上完全不同）液晶具有一些相似之处。其他可能性还有很多；最重要的是，人们一直寻求一种介于普通金属和有序绝缘体之间的物理特性的相，也被认为是可能的。本研究的主要目标之一是制定物理机制，以决定最终要实现的众多电子相中的哪一个。 实现这一目标需要更好地理解用于研究相互作用的量子系统的主要理论工具，即所谓的重正化群及其所允许的各种可能性。希望这种加深的理解也可能导致其他形式上类似的问题取得进展，例如发生在高能物理学中的问题。