Exploring the plethora of possibilities provided by solid-state systems to realize exotic many-body phases is not only motivated by fundamental questions but also by potential quantum technological applications. In both cases, it is important to have control over the properties of the system in order to engineer the phase of interest, to have a clear theoretical understanding of the microscopic physics, and to be able to probe it. In this regard, superlattice systems have recently brought many exciting results: e.g., the moire lattice that emerges when two layers of graphene are twisted induces correlated phenomena, akin to high-temperature superconductors. Furthermore, artificially arranged atoms on surfaces have become popular tools to design electronic bands. SuperCorr will explore the vast set of possibilities provided by these tunable systems to engineer novel correlated many-body physics, propose ways to probe it, and advance our understanding of the complex phase diagrams of quantum matter. More specifically, we will address key questions related to several different graphene moire systems, such as the origin and form of superconductivity, its relation to the correlated insulator, the interplay of topological obstructions and correlations, and the microscopics of their nematic phases. We will work on the impact of spin-orbit coupling and on a theoretical description of twist-angle disorder, viewing inhomogeneities as a blessing in disguise that can also be used to probe and realize interesting physics. Finally, we will develop a theoretical framework for the design of atom arrangements on the surface of complex host materials, in order to create or simulate a quantum many-body system on demand. To this end, we will employ and further extend a variety of analytical and numerical methods of many-body physics and field theory, and combine it, in some projects, with machine-learning techniques, while keeping a close connection to experiment.

Metal-ligand multiple-bonds represent fundamental aspects of chemistry and underpin chemical structure, bonding, reactivity, and catalysis. Indeed, transition metal-carbon multiple bonds are the basis for the 2005 Nobel Chemistry Prize and transition metal-nitrogen triple bonds are well established and important intermediates in biological processes (nitrogenases) and ammonia synthesis. For uranium, the heaviest naturally occurring element, double bonds to oxygen, exemplified by the ubiquitous linear uranyl dication, and nitrogen are well known, and the area of uranium-carbon double bonds is burgeoning. A molecular uranium-nitrogen triple bond, known as a uranium nitride, was for decades the ultimate target in synthetic actinide chemistry; however it eluded all attempts to prepare it. Very recently, we made a landmark advance and prepared the first example of a molecular uranium-nitride triple bond (Science, 2012, 337, 717). Our breakthrough method utilises a very bulky ligand which generates a pocket at uranium in which to install the nitride, coupled to stabilisation during synthesis using a sodium cation, followed by gentle removal of the sodium to furnish the terminal nitride linkage. This project aims to exploit our advance in order to develop this exciting area so that we may map out the intrinsic structure and reactivity of the uranium-nitride triple bond. We will expand the range of uranium-nitride triple bonds with our proven method to generate a family of compounds so that meaningful comparisons can be made. Surprisingly, the 1909 Haber-Bosch patent for ammonia synthesis, where nitrides are implicated, clearly references uranium as the best catalyst. We therefore seek to assess the role of uranium-nitrides in ammonia synthesis to answer long-standing questions regarding the role of uranium. Furthermore, we will assess the potential of uranium-nitrides in atom-efficient N-atom transfer reactions which may straightforwardly be 15N-isotopically labelled. We will establish the intrinsic reactivity character of the uranium-nitride linkage and will test the hypothesis that our nitrides represent a hitherto unavailable entry point to long-targeted, high value uranium-carbon triple and heteroatom-free double bonds that have no precedent. We also seek to extend this chemistry to heavier analogues where the nitride nitrogen is replaced by a phosphorus or arsenic atom which will afford an opportunity to compare trends within a chemical group. We will combine synthetic and structural studies with interdisciplinary magnetometric, computational, and spectroscopic studies (EPSRC EPR National Service at Manchester University, far-IR at Stuttgart University, and XANES at Canberra University) to give a comprehensive understanding of uranium-nitrogen bonding. Our uranium-nitride linkage provides a unique opportunity to probe the nature and extent of covalency in uranium-ligand bonding. The issue of covalency in uranium chemical bonding is long-running, still hotly debated, and important because of the nuclear waste legacy which the UK already has. Spent nuclear fuel is ~96% uranium and the official Nuclear Decommissioning Authority figure for nuclear waste clean-up bill is 70 billion pounds. If we can better understand the chemistry of uranium this higher platform of knowledge may in the future contribute to ameliorating the UK's nuclear waste legacy.

Phase diagrams have revolutionized materials development by providing the conditions for phase stabilities and transformations, and thereby a thorough thermodynamic understanding of materials design. However, the majority of today’s phase diagrams are based on scarce experimental input and often rely on daring extrapolations. Every multicomponent phase diagram relies on a fragile set of phase stabilities as very recent studies show. Materials 4.0 will change this. It will raise materials design to the next level by providing a highly accurate first principles thermodynamic database. First principles, alias ab initio, approaches do not require any experimental input and can operate where no experiment is able to reach. However, they have been limited to zero Kelvin or low temperature approximations which are not representative of phase diagrams. Materials 4.0 reaches far beyond this by utilizing my unique expertise in high-accuracy finite-temperature ab initio simulations. We will develop novel methods accelerated by machine learning potentials that facilitate a highly efficient determination of Gibbs free energies and migration barriers including all relevant finite-temperature excitation mechanisms. The methodology will be implemented in an easy-to-use open-source integrated development environment and made accessible to the community. Materials 4.0 will consider materials relevant to current scientific developments and of technological interest, such as hydrides, lightweight alloys, superalloys, MAX phases, and high entropy alloys. A large ab initio thermodynamic database will be computed for elements across the periodic table. The main focus will be on phase stabilities of various phases, including dynamically unstable ones, and importantly liquids as well; all fully from ab initio. The phase stabilities will be put into practice by re-parametrizing binary phase diagrams and studying the implications on multicomponent phase diagrams.