Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Higher-order topological states mediated by long-range coupling in
  $D_4$-symmetric lattices   Topological physics opens a door towards flexible routing and resilient
localization of waves of various nature. Recently proposed higher-order
topological insulators provide advanced control over wave localization in the
structures of different dimensionality. In many cases, the formation of such
higher-order topological phases is governed by the lattice symmetries, with
kagome and breathing honeycomb lattices being prominent examples. Here, we
design and experimentally realize the resonant electric circuit with $D_4$
symmetry and additional next-nearest-neighbor couplings. As we prove, a
coupling of the distant neighbors gives rise to an in-gap corner state.
Retrieving the associated invariant directly from the experiment, we
demonstrate the topological nature of the designed system, revealing the role
of long-range interactions in the formation of topological phases. Our results
thus highlight the distinctions between tight-binding systems and their
photonic counterparts with long-range couplings.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th