Strongly Correlated Quantum Materials

今天的工业很大程度上依赖于先进材料，这些材料从发现到商业产品的发展需要几十年的时间。美国正在资助“材料基因组计划”，以“加快我们对材料科学基础的理解，提供丰富的实用信息，企业家和创新者将能够利用这些信息开发新产品和新工艺”。特别是，“该计划资助计算工具、软件、材料表征的新方法，以及开放标准和数据库的开发。”这类基础研究对加拿大、对美国和世界同样重要。参与基础知识发展的学生将特别有能力认识到这些知识带来的机会，并了解应用基础研究所需工具的优点和局限性。我们将通过专注于材料的计算工具来为这一努力做出贡献，这些材料的惊人特性是物质的非平凡量子力学性质的结果。量子力学允许电子同时定位为粒子，或者以波的形式传播。它还允许在一块物质中相互作用的电子以高度有组织的集体方式行为。具有这些特性的材料被称为强相关量子材料。惊人的集体电子特性的例子包括高温超导性和完美的金属行为在拓扑绝缘体的表面。高温超导体在绝对零度和室温之间的温度下无电阻地导电。室温超导体将引发一场技术革命，从电力线到交通和电子。这个为期五年的研究计划有两大类目标。首先，我们将继续从非常普遍的角度开发高温超导体的计算工具。这些材料有很强的相关性。更具体地说，强相关超导性将理论方法推向了最困难的领域，即在相互作用诱导的金属-绝缘体跃迁附近，在那里电子的局域化和波图同样重要。强相关超导性对于这种转变的临界相互作用强度是最强的，无论它是通过添加/去除传导电子引起的，如在基于铜氧平面（铜酸盐）的陶瓷中，还是由压力引起的，如在层状有机化合物中。通过保持这一总体观点，将铜酸盐和层状有机物放在同一框架内考虑，我们相信我们可以坚定地确定，这些方法为我们提供了具有预测能力的强相关超导理论的主要成分。另一大类目标是开发强相关量子材料的计算工具。例如，我们将在计算机代码中包括为模型开发的软件，旨在从第一原理对材料进行现实的预测。我们还将开发新的方法，使我们能够包括以前在第一性原理代码中无法考虑到的物理效应，从而大大提高预测的可靠性。

Much of today’s industry relies on advanced materials whose development from discovery to commercial product takes decades. The United States is funding the “Materials Genome Initiative” to “speed up our understanding of the fundamentals of material science providing a wealth of practical information that entrepreneurs and innovators will be able to use to develop new products and processes”. In particular, “The initiative funds computational tools, software, new methods for material characterization, and the development of open standards and databases.” This type of fundamental research is as important for Canada as it is for the United States and the world. The students that will participate in the development of fundamental knowledge will be especially skilled to recognize the opportunities brought about by this knowledge and to understand the advantages and limitations of the tools necessary to apply the fundamental research. We will contribute to this effort by focusing on computational tools for materials whose spectacular properties are consequences of the non-trivial quantum mechanical nature of matter. Quantum mechanics allows electrons to be at the same time localized as particles, or propagating as waves. It also allows interacting electrons in a piece of matter to behave in a highly organized, collective way. Materials with these properties are called strongly correlated quantum materials. Examples of spectacular collective electronic properties include high-temperature superconductivity and perfect metallic behavior at the surfaces of topological insulators. High-temperature superconductors carry electricity without resistance at temperatures half-way between absolute zero and room temperature. A room temperature superconductor would lead to a revolution in technology, from power lines to transport and electronics. There are two broad classes of objectives for this five-year research program. First, we will continue to develop computational tools for high-temperature superconductors from a very general perspective. These materials are strongly correlated. More specifically, strongly correlated superconductivity pushes theoretical methods in the most difficult regime, namely in the vicinity of the interaction-induced metal-insulator transition, where the localized and wave picture of electrons are equally important. Strongly correlated superconductivity is strongest for the critical interaction strength of this transition, whether it is induced by adding/removing conduction electrons, as in ceramics based on copper-oxygen planes (cuprates), or by pressure, as in layered organic compounds. By keeping this general point of view, were cuprates and layered organics are considered within the same framework, we believe we can firmly establish that these methods give us the main ingredients for a theory of strongly correlated superconductivity that has predictive power. The other broad class of objectives is to develop the computational tools for strongly correlated quantum materials. For example, we will include software developed for models in computer codes that aim at making realistic predictions of materials from first principles. And we will also develop new methods that will allow us to include physical effects that could not be taken into account before in first-principle codes, increasing significantly the reliability of predictions.