Beyond twisted bilayer graphene and beyond

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Project Background { Graphene has remarkable electronic and mechanical properties that promise awide range of applications. More than one of these sheets of carbon atoms can bind by van der Waals forcesto form a coherent lattice for electronic motion giving rise to new properties. More recently, experimentshave shown that bilayer graphene has yielded remarkable properties. A small twist of 1.1 between thetwo layers turns the semimetal into a superconductor with a critical temperature of 1.7K. A Mott insulatorcan also be found where Coulomb repulsion causes a traffic jam of electrons and the system becomeselectrically insulating.It is believed that the twist gives rise to narrow electronic bands near the Fermi level. This means thatthe kinetic energy of the electrons is suppressed, and Coulomb interaction becomes important. In fact, thisis reminiscent of the cuprate superconductors which also exhibit Mott insulating antiferromagnetic statenear a superconducting phase. In that case, Coulomb interactions dominate the properties of a single band of electrons on the CuO planes.First year project. In the first-year project, we will investigate the band structure of bilayer andgeneralise to multiple layers. The aim is to investigate whether the narrow-band physics of the bilayercan also be found in multiple layers. We will start with a simple tight-binding model of the system. Anumerical solution will help us explore the subtleties of the system. This can be followed by analyticalanalysis of the band structure near the Dirac points. One can also use group theory to explore whetherDirac points are robust in different multilayer settings.PhD project objectives. The overarching goal of the project is to explore graphene physics in a newavenue recently made possible in experiments. Our initial stage to study multilayer graphene would openup new avenues of research. One question that relates back to the correlated electron physics is whether the number and the natureof narrow bands near the Fermi level can be engineered. This can give rise to new analogues of correlatedphysics found in other electronic materials where multiple orbitals in d-band and f-band electrons give risea rich variety of phenomena.There are other researchers at the Thomas Young Centre at Imperial interested in the electronic structureof graphene and related systems. Our proposals can be confirmed with more sophisticated electronicstructure calculations.Another possible direction is to study whether bilayer graphene physics can be reproduced in other fields,for instance, using optical lattices in cold atoms and micro-pillar polariton lattices. For instance, strongspin-orbit coupling, which is so small that it is undetectable in graphene, can be simulated in these systemsthat is hard to achieve in carbon.It is hard to predict the direction of research in a very fast moving field. However, it is clear that therewill be intense experimental attention in these systems in the next few years and plenty of challenges fortheorists to address.Student Background. Mathieu dos Santos has a background in theoretical physics but has notspecialised in condensed matter physics. This project is designed to provide a gentle introduction to thefield with a route that could lead to interesting physics without initially too much technical knowledge inthe area.