Discovering twisted bilayer materials with strong electron correlations

具有强电子相关性的材料在能源和信息技术中具有潜在的应用前景，但理解和定量预测它们的行为仍然是凝聚态物质和材料物理学的重大挑战之一。以高转变温度（high-Tc）超导铜酸盐为例，尽管经过几十年的研究，人们对超导的机理仍然没有明确的共识，甚至对超导状态产生的正常状态也没有完全了解。近年来，扭曲双层石墨烯（TBG）的绝缘性能和非常规超导性的发现引起了极大的兴奋，并为二维材料的扭曲双层建立了一个研究“强相关难题”的新平台。特别是，这些系统允许前所未有的控制水平（例如，与铜酸盐等氧化物材料相比），因为电子相关性的强度可以通过扭曲角度调节，电子密度可以通过施加电场来修改。除了TBG，还有一个巨大的、几乎完全未开发的潜在有趣的强相关扭曲双层材料的化学空间，它是由大约1825种可能可剥落的二维材料组合而成的。强相关扭曲双层材料的研究领域尚处于萌芽阶段。已经提出了许多不同的机制来解释实验中观察到的TBG中的绝缘行为，但没有任何明确的共识。同样，关于超导态的起源和性质也没有一致的看法。这些理论预测之间的差异是由于在描述电子-电子相互作用时使用了简化的哈密顿量和/或近似。因此，有一个明确的和当前的机会，以发展一个微观的，无参数的和基于第一线原理的理解，在现有的扭曲双层材料的强相关性，并探索二维材料的化学空间，新的扭曲双层系统具有强的和可调的电子相关性。在本提案中，我们将开发一种新方法，将第一流的密度泛函理论计算与最先进的功能重整化群方法相结合，在没有可调参数的情况下，计算扭曲双层材料的相图作为掺杂，温度和扭转角的函数。首先，我们将把我们的方法应用于氮化硼（TGBN）上的TBG和扭曲石墨烯，目的是解决目前关于这些系统中绝缘行为和超导性起源的争议。然后，我们将用它来创建一个高通量的计算工作流程，以发现具有强电子相关性的新型双层材料，这些材料会产生非常规相，包括超导性、电荷和自旋密度波、自旋液体或莫特绝缘体。这将使我们能够在最有前途的候选系统方向上指导实验工作，并可能导致将二维材料的优势与强相关系统的可调性相结合的新型能源和信息技术设备。

Materials with strong electron correlations exhibit fascinating properties with potential applications in energy and information technology but understanding and quantitatively predicting their behaviour remains one of the grand challenges of condensed matter and materials physics. Taking the high-transition-temperature (high-Tc) superconducting cuprates as an example, despite several decades of study there is still no clear consensus on the mechanism of superconductivity and even the normal state from which the superconducting state arises is not fully understood. The recent discovery of insulating behaviour and unconventional superconductivity in twisted bilayer graphene (TBG) has generated tremendous excitement and established twisted bilayers of 2d materials as a new platform for studying the "strong-correlation puzzle". In particular, these systems allow for an unprecedented level of control (eg, compared to oxide materials such as the cuprates) as the strength of electron correlations is tunable via the twist angle and the electron density can be modified through application of an electric field. Besides TBG, there exists a large and almost entirely unexplored chemical space of potentially interesting strongly correlated twisted bilayer materials that result from combinations of the approximately 1,825 2d materials that are potentially exfoliable. The field of strongly-correlated twisted bilayer materials is nascent. Many different mechanisms have been proposed to explain the experimentally-observed insulating behaviour in TBG, without any clear consensus. Similarly, there is no agreement regarding the origin and properties of the superconducting state. The discrepancies among these theoretical predictions arise from the use of simplified Hamiltonians and/or approximations in the description of electron-electron interactions. There is, therefore, a clear and present opportunity to develop a microscopic, parameter-free and first-principles-based understanding of strong correlations in existing twisted bilayer materials and to explore the chemical space of 2d materials for new twisted bilayer systems with strong and tunable electron correlations.In this proposal we will develop a new method that combines first-principles density-functional theory calculations with state-of-the-art functional renormalisation group methods to calculate, with no adjustable parameters, phase diagrams of twisted bilayer materials as a function of doping, temperature and twist angle. First, we will apply our method to TBG and twisted graphene on boron nitride (TGBN) with the aim of resolving the current controversies regarding the origin of the insulating behaviour and superconductivity in these systems. Then we will use it to create a high-throughput computational workflow to discover new bilayer materials with strong electron correlations that give rise to unconventional phases, including superconductivity, charge and spin density waves, spin liquids or Mott insulators. This will enable us to guide experimental efforts in the direction of the most promising candidate systems and could potentially result in novel devices for energy and information technology that combine the advantages of 2d materials with the tunabiliy of strongly correlated systems.