Discovering twisted bilayer materials with strong electron correlations

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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.