Beyond twisted bilayer graphene and beyond

Lead Research Organisation: Imperial College London
Department Name: Dept of Physics

Abstract

Project Background { Graphene has remarkable electronic and mechanical properties that promise a
wide range of applications. More than one of these sheets of carbon atoms can bind by van der Waals forces
to form a coherent lattice for electronic motion giving rise to new properties. More recently, experiments
have shown that bilayer graphene has yielded remarkable properties. A small twist of 1.1 between the
two layers turns the semimetal into a superconductor with a critical temperature of 1.7K. A Mott insulator
can also be found where Coulomb repulsion causes a traffic jam of electrons and the system becomes
electrically insulating.
It is believed that the twist gives rise to narrow electronic bands near the Fermi level. This means that
the kinetic energy of the electrons is suppressed, and Coulomb interaction becomes important. In fact, this
is reminiscent of the cuprate superconductors which also exhibit Mott insulating antiferromagnetic state
near 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 and
generalise to multiple layers. The aim is to investigate whether the narrow-band physics of the bilayer
can also be found in multiple layers. We will start with a simple tight-binding model of the system. A
numerical solution will help us explore the subtleties of the system. This can be followed by analytical
analysis of the band structure near the Dirac points. One can also use group theory to explore whether
Dirac points are robust in different multilayer settings.
PhD project objectives. The overarching goal of the project is to explore graphene physics in a new
avenue recently made possible in experiments. Our initial stage to study multilayer graphene would open
up new avenues of research. One question that relates back to the correlated electron physics is whether the number and the nature
of narrow bands near the Fermi level can be engineered. This can give rise to new analogues of correlated
physics found in other electronic materials where multiple orbitals in d-band and f-band electrons give rise
a rich variety of phenomena.
There are other researchers at the Thomas Young Centre at Imperial interested in the electronic structure
of graphene and related systems. Our proposals can be confirmed with more sophisticated electronic
structure 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, strong
spin-orbit coupling, which is so small that it is undetectable in graphene, can be simulated in these systems
that 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 there
will be intense experimental attention in these systems in the next few years and plenty of challenges for
theorists to address.
Student Background. Mathieu dos Santos has a background in theoretical physics but has not
specialised in condensed matter physics. This project is designed to provide a gentle introduction to the
field with a route that could lead to interesting physics without initially too much technical knowledge in
the area.

Publications

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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509486/1 01/10/2016 31/03/2022
2034024 Studentship EP/N509486/1 01/10/2016 30/06/2022 Mathieu Dos Santos