Theory and simulation of moiré graphene multilayers
File(s)
Author(s)
Goodwin, Zachary A H
Type
Thesis
Abstract
Graphene has been hailed as a material which is going to revolutionise myriad technologies due to its extraordinary stability, mechanical strength yet flexibility, and remarkable transport properties. Furthermore, it was recently discovered that if two graphene layers are stacked and twisted relative to one another, referred to as twisted bilayer graphene (tBLG), correlated insulating states and superconductivity are observed, even though graphene does not intrinsically exhibit these properties. These phases only emerge at twist angles close to the "magic angle" of 1.1 degrees, and by tuning the temperature and doping level, the system can undergo electronic phase transitions between these states.
I studied electron interactions and electronic screening in tBLG and other moiré graphene multilayers. In the absence of external and internal electronic screening, I found the on-site Hubbard parameter of the flat bands of tBLG scales linearly with twist angle. Upon considering internal screening, this linear scaling breaks down, where the Hubbard interaction energy decreases more rapidly towards the magic angle owing to increased screening. Moreover, external screening, from proximity to metallic gates which dope tBLG, was found to substantially affect these Hubbard interactions, owing to the moiré length scale of the magic-angle being comparable to the distance to these metallic gates. For a sufficiently small separation to these gates, I predicted that the correlated insulating states should be screened-out and the superconducting phase should be stabilised.
Long-ranged Hartree interactions were found to induced doping-dependent band-flattening in tBLG that I predicted to increase the magic-angle range of tBLG. For moiré graphene multilayers, the role of these Hartree interactions were found to sensitively depend on the stacking sequence of the structure: systems with alternating twist angles have similar interaction-driven band flattening, but systems where there are also adjacent layers that are aligned have no such interaction-driven band flattening.
I studied electron interactions and electronic screening in tBLG and other moiré graphene multilayers. In the absence of external and internal electronic screening, I found the on-site Hubbard parameter of the flat bands of tBLG scales linearly with twist angle. Upon considering internal screening, this linear scaling breaks down, where the Hubbard interaction energy decreases more rapidly towards the magic angle owing to increased screening. Moreover, external screening, from proximity to metallic gates which dope tBLG, was found to substantially affect these Hubbard interactions, owing to the moiré length scale of the magic-angle being comparable to the distance to these metallic gates. For a sufficiently small separation to these gates, I predicted that the correlated insulating states should be screened-out and the superconducting phase should be stabilised.
Long-ranged Hartree interactions were found to induced doping-dependent band-flattening in tBLG that I predicted to increase the magic-angle range of tBLG. For moiré graphene multilayers, the role of these Hartree interactions were found to sensitively depend on the stacking sequence of the structure: systems with alternating twist angles have similar interaction-driven band flattening, but systems where there are also adjacent layers that are aligned have no such interaction-driven band flattening.
Version
Open Access
Date Issued
2021-09
Date Awarded
2022-02
Copyright Statement
Creative Commons Attribution NonCommercial NoDerivatives Licence
License URL
Advisor
Lischner, Johannes
Mostofi, Arash
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/L015579/1
Publisher Department
Materials
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)