Resolving superconductivity and pseudogap physics in oxides: beating the sign problem

解决氧化物中的超导性和赝能隙物理：解决符号问题

• 批准号: EP/W022982/1
• 负责人: Adrian Wasgen Daniel Kantian
• 金额: $ 50.14万
• 依托单位: Heriot-Watt University
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW022982%2F1
• 关键词: Resolving; superconductivity; pseudogap; physics; oxides

Superconducting (SC) materials, which transport currents without losses, are the basis of advanced medical imaging and energy transmission. They are intensely researched for applications such as circuitry, motors and generators far more efficient than any today. But these applications need strong cooling - at 'best' to about -160 C - as superconductivity requires electron pairs in a collective quantum state, easily disrupted by thermal energy. A central goal of materials theory is thus to systematically design superconductors working at higher temperatures.Yet this has been impossible so far, as for the best superconductors today, based on oxide ceramics, we still do not understand how electron pairs form. Dynamical Mean Field Theory (DMFT) could predict SC properties in the oxides, yielding insight into pair formation, and thus allow designing better superconductors. Yet, DMFT currently cannot do so as it uses Quantum Monte Carlo (QMC) algorithms that suffer from the so-called sign-problem. This project aims to solve key models of SC oxides, especially the high-temperature cuprates, as well as strontium ruthenate. Treating much larger Anderson impurity problems (AIPs) - the basis of DMFT - at much lower temperatures than possible before will allow modelling these oxides in their SC state for the first time, as well as the mysterious pseudogap (PG) and strange metal (SM) states, which precede superconductivity at higher temperature. Understanding these as well is crucial for revealing why electrons pair in the oxides.The project will build on a major advance in so-called parallel density matrix renormalization group (pDMRG) numerics, co-developed by the PI recently. The pDMRG code outperforms QMC for interacting electrons at low temperatures as it does not suffer the sign-problem. The pDMRG is also much more powerful than regular DMRG, distributing a calculation too demanding for single-CPU calculations across many compute nodes of a supercomputer. We will thus re-implement DMFT numerics using pDMRG. The outcome will be a DMFT superior to previous implementations not just quantitatively, but qualitatively. Using it, we will solve AIPs derived from the extended Hubbard model of cuprates as well as multi-orbital AIPs for strontium ruthenate. For strontium ruthenate, we will also be the first to simulate the crossover from the SM state to a near-perfect metallic state around 25 K, which has also been impossible with QMC. For the extended Hubbard model, we will seek to replicate the experimentally found emergence of two separate pseudogaps, one large and one small. This project would yield important insight into the nature of electron-pairing in high-temperature oxide superconductors, by solving the extended 2D Hubbard model for unprecedented system sizes und temperatures. It could be a significant step towards being able to engineer high-temperature superconductors on purpose. This project could further deliver a breakthrough in the understanding of a key model-material for superconductivity, strontium ruthenate. Neither its SM state nor its crossover into a perfect metal is currently understood. This project could thus yield a long-necessary 'sorting' of the competing theories for this model material, with broad impact for the theory of superconductivity, due to this particular material being a clean, near-ideal testing ground for the whole class of phenomena.

超导(SC)材料可以无损耗地传输电流，是先进的医学成像和能量传输的基础。它们在电路、电机和发电机等应用领域得到了深入的研究，其效率远远高于当今的任何应用。但这些应用需要很强的冷却--最好的情况是大约零下160摄氏度--因为超导需要处于集体量子态的电子对，很容易被热能破坏。因此，材料理论的一个中心目标是系统地设计在更高温度下工作的超导体。然而，到目前为止，这是不可能的。至于今天最好的基于氧化物陶瓷的超导体，我们仍然不知道电子对是如何形成的。动力学平均场理论(DMFT)可以预测氧化物中的Sc性质，从而洞察成对的形成，从而可以设计出更好的超导体。然而，DMFT目前无法做到这一点，因为它使用的量子蒙特卡罗(QMC)算法存在所谓的符号问题。该项目旨在解决Sc氧化物的关键模型，特别是高温铜酸盐，以及Ruthenate锶。在比以前更低的温度下处理更大的安德森杂质问题(AIP)-DMFT的基础-将使这些氧化物首次能够在其SC态以及神秘的赝隙(PG)和奇怪的金属(SM)态下建模，这两种态在更高的温度下具有超导电性。理解这些也是揭示为什么电子在氧化物中配对的关键。该项目将建立在所谓的平行密度矩阵重整化群(PDMRG)数值计算的重大进展的基础上，该数值计算是由PI最近共同开发的。PDMRG代码在低温下与电子相互作用的性能优于QMC，因为它不存在符号问题。PDMRG也比常规的DMRG强大得多，它将计算过于苛刻，无法在超级计算机的许多计算节点上进行单CPU计算。因此，我们将使用pDMRG重新实现DMFT数值。其结果将是DMFT不仅在数量上，而且在质量上都优于以前的实施。利用它，我们将求解由扩展的Hubbard铜酸盐模型导出的AIPs以及Ruthenate锶的多轨道AIPs。对于Ruthenate锶，我们还将第一个模拟在25K左右从SM态到近乎完美的金属态的跃迁，这在QMC中也是不可能的。对于扩展的哈伯德模型，我们将试图复制实验中发现的两个单独的伪隙的出现，一个大，一个小。这个项目将通过求解扩展的2D Hubbard模型来解决前所未有的系统大小和温度，从而对高温氧化物超导体中电子配对的本质产生重要的见解。这可能是朝着能够有目的地设计高温超导体迈出的重要一步。该项目可能进一步突破对一个关键模型--超导材料--Ruthate锶的理解。无论是它的SM状态，还是它与完美金属的交叉，目前都还不清楚。因此，这个项目可能会对这种模型材料的相互竞争的理论进行长期必要的“分类”，并对超导理论产生广泛的影响，因为这种特殊的材料是整个现象类别的干净、近乎理想的试验场。