THESIS
2021
1 online resource (xi, 59 pages) : illustrations (some color)
Abstract
Fascinating physical phenomena emerges when stacking one single layer of graphene on
the other one with a small twist around 1.1
◦. Moiré potential induced by the small twsit
can result in flat bands. The electrons in the flat bands seem to be freezed and it causes
strong correlation effect in twist bilayer graphene system. This thesis can be mainly
separated into two parts. In the first part, I will review the classical method to cope
with the electronic spectrum in this kind of flat band system – continumm model(CM).
Based on the observations from CM, we proposed a tight binding planewave scheme to do
band structure calculation which can also provide us a flat band picture. Compared with
CM, our method has more details and is easy to reutilize for further calculation. In the
second pa...[
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Fascinating physical phenomena emerges when stacking one single layer of graphene on
the other one with a small twist around 1.1
◦. Moiré potential induced by the small twsit
can result in flat bands. The electrons in the flat bands seem to be freezed and it causes
strong correlation effect in twist bilayer graphene system. This thesis can be mainly
separated into two parts. In the first part, I will review the classical method to cope
with the electronic spectrum in this kind of flat band system – continumm model(CM).
Based on the observations from CM, we proposed a tight binding planewave scheme to do
band structure calculation which can also provide us a flat band picture. Compared with
CM, our method has more details and is easy to reutilize for further calculation. In the
second part, I will introduce two different techniques to help us navigate into the strong
correlation physics in TBG by taking advantage of tight binding planewave basis. The
first application is using constrained Random Phase Approximation to obtain effective
interaction in flat bands. The second one, I try to construct tight binding planewave
basis set under weak magnetic field in periodic Landau guage.
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