Disordered transmission-line networks with and without parity symmetry

TL;DR

This paper investigates how disorder and parity symmetry breaking affect topological edge states in transmission-line networks, revealing robustness against disorder but vulnerability to symmetry breaking, with implications for topological system design.

Contribution

It introduces the use of local Chern numbers to characterize topological features in disordered, non-periodic networks and analyzes their robustness and limitations.

Findings

Edge states are robust against onsite disorder if the bulk gap remains open.

Breaking parity symmetry destroys the quantization of local Chern numbers.

Non-integer local Chern numbers occur inside bulk bands but do not indicate robust edge states.

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.