Superconductivity and competing states: the role of the electron-phonon and Coulomb interactions

超导和竞争态：电子声子和库仑相互作用的作用

• 批准号: RGPIN-2022-03295
• 负责人: Marsiglio, Frank
• 金额: $ 3.64万
• 依托单位: University of Alberta
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=762532
• 关键词: Superconductivity; competing; states; role; electron

Much of what we understand about the electronic properties of simple metals and semiconductors is based on a single-particle picture. That is, once we determine what one electron does, then any macroscopic current or response is determined by this single-particle behaviour, with slight modifications to account for the statistics of the many electrons. While this simple idea allows us to understand the properties of simple metals, it provides limited understanding for metals with correlated properties, and for the possible transitions to states with correlated electron behaviour. One such state, discovered more than a century ago, is superconductivity. It has dramatic properties, not least of which are infinite conductivity and perfect diamagnetism. The theory for this remarkable state of matter has been "understood" for more than 50 years now. I use "understood" in quotations to emphasize that it is understood at a certain level, but we need to go beyond this level, to achieve a truly predictive theory, and one which will delineate superconductivity from other instabilities. That is what the work described in this research proposal will accomplish. Past work has focussed on the mechanism for superconductivity itself, the electron-phonon interaction. It largely ignored the competitor states in the explanation, and it largely ignored (or at least oversimplified) the role of direct Coulomb interactions in the explanation as well. We will formulate a theory that is self-regulating, i.e. the theory will tell us that too strong a coupling strength will result in states other than superconductivity. This self-regulating Eliashberg theory will not only predict other states, but will signal the limitations of the electron-phonon interaction. These limitations come from a variety of possible sources, including both single-electron effects (the electron acquires a very large effective mass through the electron-phonon interaction), and through direct repulsive interactions between two electrons. This work will require input from frameworks more amenable to exact results (e.g. Quantum Monte Carlo) so that control over the approximations required in other frameworks (e.g. Eliashberg theory) can be exercised. And once this level of control is achieved, we expect the theory to work with experiment in a much more transparent way than is currently done i.e. with Density Functional Theory (DFT). In fact, we hope to improve DFT formulations through insights gained in this research. In this way we will hopefully have a more unified and complete description of superconductivity and its competitor states, amongst different families ranging from the simple metals, and including the cuprates and the pnictides, right through to the high-pressure hydrides.

我们对简单金属和半导体的电子特性的理解大部分是基于单粒子图片的。也就是说，一旦我们确定了一个电子的作用，那么任何宏观电流或响应都是由这种单粒子行为决定的，并进行了轻微的修改以说明许多电子的统计数据。 尽管这个简单的想法使我们能够理解简单金属的属性，但它为具有相关特性的金属以及向具有相关电子行为的状态的过渡提供了有限的理解。一个多世纪以前发现的一个这样的状态就是超导性。它具有戏剧性的特性，其中尤其是无限的电导率和完美的磁性磁性。 现在已经“理解”了这种非凡的物质状态的理论已有50多年了。我在引文中使用“理解”来强调它在一定层面上是可以理解的，但是我们需要超越这个层次，以实现一种真正的预测理论，并从其他不稳定性中划出超导性。这就是本研究建议中描述的工作将实现的目标。过去的工作集中在超导性本身，即电子相互作用的机制上。它在很大程度上忽略了竞争对手在解释中的国家，并且在很大程度上忽略了（或至少过度简化）直接库仑相互作用在解释中的作用。我们将制定一种自我调节的理论，即该理论会告诉我们，太强的耦合强度将导致除超导以外的其他状态。这种自我调节的伊利亚斯贝格理论不仅可以预测其他状态，而且会预示电子相互作用的局限性。这些局限性来自各种可能的来源，包括单电子效应（电子通过电子 - 光子相互作用获得非常大的有效质量），以及通过两个电子之间的直接排斥相互作用。这项工作将需要从框架中获得更加适应至确切结果的输入（例如量子蒙特卡洛），以便可以控制对其他框架中所需的近似值的控制（例如，埃利亚斯贝格理论）。一旦达到了这种控制水平，我们希望该理论能够以一种透明的方式与实验合作，即使用密度功能理论（DFT）。实际上，我们希望通过在这项研究中获得的见解来改善DFT配方。通过这种方式，我们有望对超导性及其竞争对手国家进行更统一，更完整的描述，包括从简单的金属，包括丘比特和pnictides在内的不同家庭中，到包括高压液体。