Abstract
Topological states are useful because they are robust against disorder and imperfection. In this study, we consider the effect of disorder and the breaking of parity symmetry on a topological network system in which the edge states are protected by Chern numbers. In the absence of periodicity, the local Chern number is adopted to characterize the topological features of the network. Our numerical results show that the local Chern number and the edge states are very robust against onsite disorder as long as the gap of the bulk state continuum remains open and survives even when the bulk band gap is closed. Breaking the parity symmetry can destroy the quantization of local Chern numbers, compromising the existence of edge modes. We observed non-integer local Chern number peaks that are non-zero inside the bulk bands but these non-zero non-integral local Chern numbers are not associated with the existence of robust edge states.
Highlights
The field of topological insulators has been extensively studied in the past decades
We studied the topological properties of transmission line networks under the influence of onsite disorder and parity symmetry breaking
From the local Chern number curves and field patterns, we found that some topological edge states still survive after the closure of the band gap
Summary
The field of topological insulators has been extensively studied in the past decades. We study the effects of disorder on topological transmission-line networks using local Chern numbers as a topological indicator. We will show that in a nonzero angular momentum subspace, the system can possess a nontrivial topological band gap, which behaves like the Haldane model. The chiral connectivity of the network induces non-zero Chern numbers in the bands within the subspaces with nonzero angular momentum. By calculating the local Chern numbers and field patterns, we verify the robustness of the topological states under onsite disorder. We found non-integer local Chern number peaks inside the bulk bands. These peaks are found to be topologically trivial (not related to edge modes) and can be removed by adding disorder
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