Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Optical properties of the Hofstadter butterfly in the Moir\'{e}
  superlattice   We investigate the optical absorption spectrum and the selection rule for the
Hofstadter butterfly in twisted bilayer graphene under magnetic fields. We
demonstrate that the absorption spectrum exhibits a self-similar recursive
pattern reflecting the fractal nature of the energy spectrum. We find that the
optical selection rule has a nested self-similar structure as well, and it is
governed by the conservation of the total angular momentum summed over
different hierarchies.

1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ