Thesis presented December 21, 2022

Abstract:
Stacking two layers of graphene on top of each other with a twist gives rise to a moiré pattern. This moiré does not affect the linear dispersion of the charge carrier, but renormalises their Fermi velocity. The latter even cancels for an so called magic angle, triggering a new type of electron localisation which is induced by the moiré. This localisation gives rise to strongly correlated phases, such as the recently discovered superconducting phase that created intense interest in the condensed matter community.
In this thesis, we investigate the effect of the relative stacking between the layers on the electronic properties of the system. By using Scanning Tunneling Microscopy and Spectroscopy data from the literature we show that the relative strain between the layers, so called heterostrain, controls the physics of twisted bilayers of graphene near the superconducting twist angle regime. The exact stacking arrangement including heterostrain is enough to explain the sample to sample variability that has been observed in recent experiments.
At lower angles, in addition to the exact stacking arrangement, local deformations related to relaxation processes of the system on the atomic scale must be taken into account as well. We investigate a new type of moiré induced by biaxial heterodeformations, in which occurs a peculiar relaxation mode that we call a swirl relaxation pattern.
Last, aiming at using strain as a tool, we show the building and testing of a strain cell compatible with an Scanning Tunnaling Microscope that operates at room and cryogenic temperatures. Such a device can be used on a variety of materials in addition to twisted graphene layers.

Keywords:
Graphene Bilayers, moiré, magic angle, heterostrain, Scanning Tunneling Microscopy

On-line thesis. ​