Discovering twisted bilayer materials with strong electron correlations

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.

Twisted bilayers are an emerging class of materials featuring strong and tunable electron correlations. The field is scientifically nascent (strong correlation effects in TBG were only experimentally discovered in early 2018), but the potential applications are numerous, including energy conversion materials and data storage for information communications technologies. The proposed research will enhance UK's research capacity, knowledge and skills in the exciting field of twisted bilayers and in advanced electronic structure theory and simulation, building on the UK's broader strengths in 2d materials and computational condensed matter and materials physics, respectively. The potential applications promise future economic and societal impact and would contribute towards wealth creation in the UK.
Specifically, the new computational framework that combines first-principles effective Hamiltonians with functional renormalization group calculations will enable the parameter-free calculation of phase diagrams of strongly correlated materials, such as magic-angle twisted bilayer systems. This much-needed capability will facilitate the analysis and interpretation of spectroscopic and transport experiments on such systems and will help to resolve the current debate in the theory literature about the microscopic mechanisms that give rise to the experimentally observed strong-correlation phenomena. Moreover, the predictive capability of this method enables the computational discovery of novel twisted bilayer systems with interesting strong-correlation effects opening up new avenues for designing nanomaterials with tailored properties. For this, we will combine the approach with state-of-the-art high-throughput techniques and screen more than 33,000 twisted bilayer systems. The abstraction of a complex chain of calculations into a set of sophisticated workflows that can be used reliably by non-technical specialists will significantly widen the audience that is able to study such systems and use our methods to accelerate discovery in this field.
The insights from this study will be disseminated through publications in high-impact journals, talks at conferences and at local events of the Thomas Young Centre and the London Centre for Nanotechnology. In addition, we will organize a workshop in the last year of the funding period that will showcase our achievements and bring together theorists and experimentalists working on twisted bilayer materials.