Modelling, Fabrication and Characterisation of Twisted Bilayer Graphene Devices

Abstract

Recent research has revealed an exciting discovery - two sheets of graphene, layers of one-atom thick carbon, stacked at speci c relative twist angles ('magic angles') exhibit a diverse range of behaviour. Monolayer graphene, although an excellent conductor, does not display superconductivity on its own; twisted bilayer graphene (TwBLG) system does near 0K. Moreover, while the system is an insulator at charge neutrality when the bands are lled, it also exhibits insulating phases at half- lling, with superconducting phases at llings lower or higher than half- lling. Since, at half- lling, the Fermi level of the electrons should lie in the middle of the bands, one possible explanation for such insulating phases could be the creation of a Mott insulator at half- lling, or at least other strongly-correlated behaviour. In order to better understand this behaviour, Scanning Tunneling Microscopy (STM) is required to probe local electronic properties. This thesis introduces the basic tools of Solid State Physics and applies them to exact derivations of the band structures of monolayer graphene and rotated bilayer graphene in two limits (AA- and AB-stacking), before discussing the geometry and the rst model of TwBLG, the continuum model. An approximate result is derived that qualitatively captures the at band behaviour. A second, more recent model, the so-called 'ten-band' model, is introduced, and a development of it, using Mean-Field theory, treated in detail. Results of simulations indicate that this mean- eld treatment exhibits contrasting behaviour depending on the convergence threshold used for the iterative solving step characteristic of Hartree-Fock methods ('Modelling'). Furthermore, the steps involved in the fabrication of TwBLG devices for STM are reviewed, including some optimisations of an established routine which were carried out by the author ('Fabrication'). Finally, in order to carry observe the interesting correlated behaviour, the devices must exhibit 'magic angle' stacking regions. Since STM is a time-consuming technique, a quick, easy characterisation method using Conductive Atomic Force Microscopy (C-AFM) is described and developed. Some preliminary STM measurements and basic theory are also summarised ('Characterisation').