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Abstract
In AA-stacked twisted bilayer graphene, the lower energy bands become completely flat when the twist angle passes through certain specific values: the so-called “magic angles”. The Dirac peak appears at zero energy due to the flattening of these bands when the twist angle is sufficiently small [1-3]. When a constant perpendicular magnetic field is applied, Landau levels start appearing as expected [5]. We used the Kernel Polynomial Method (KPM) [6] as implemented in KITE [7] to study the optical and electronic properties of these systems. The aim of this work is to analyze how the features of these quantities change with the twist angle in the presence of an uniform magnetic field.
Highlights
The origin of the magic angles, which are characterized by the extreme flattening of the lowest energy bands, in twisted bilayer graphene (TBG) was unknown
0 p pσ where r is the 3D distance between the two atomic sites, c0 is the inter-layer distance, Vp0pσ is the hopping integral between two vertically-stacked atoms in untwisted bilayer graphene, and δ is a parameter that modulates the hopping cutoff at long distances
We will take a look at the DC conductivity in both the xx and the xy directions, which were obtained through KITE
Summary
The origin of the magic angles, which are characterized by the extreme flattening of the lowest energy bands, in twisted bilayer graphene (TBG) was unknown. Peres et al published two articles [1, 2] where they developed a continuum model for this material With this work, they were able to find a simple relation between supperlattice vectors with which they could explain the physics of all types of commensurate structures. Using KITE, which employs a Chebyshev polynomial-approach to approximate Green’s functions, it is possible to calculate the density of states for a multitude of 2D and 3D structures. This allows us to calculate the density of states for several commensurable angles, as well as the optical conductivity and the local density of states [7]
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