Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topology in the Sierpi\'nski-Hofstadter problem   Using the Sierpi\'nski carpet and gasket, we investigate whether fractal
lattices embedded in two-dimensional space can support topological phases when
subjected to a homogeneous external magnetic field. To this end, we study the
localization property of eigenstates, the Chern number, and the evolution of
energy level statistics when disorder is introduced. Combining these
theoretical tools, we identify regions in the phase diagram of both the carpet
and the gasket, for which the systems exhibit properties normally associated to
gapless topological phases with a mobility edge.

2
The categories of this paper are: math
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs