# Degenerate Topological Edge States in Multimer Chains

## TL;DR

This paper introduces a new class of quasi-one-dimensional topological lattices with degenerate edge states and bound states in the continuum, experimentally realized using inductor-capacitor circuits, expanding understanding of topological phenomena.

## Contribution

It proposes and experimentally demonstrates degenerate topological edge states and bound states in the continuum in multimer chains with uniform hopping and inversion symmetry.

## Key findings

- Degenerate -1 energy edge states observed in multimer chains.
- Topological bound states in the continuum are embedded in continuous bands.
- Experimental realization using inductor-capacitor circuits confirms theoretical predictions.

## Abstract

We propose and experimentally realize a class of quasi-one-dimensional topological lattices whose unit cells are constructed by coupled multiple identical resonators, with uniform hopping and inversion symmetry. In the presence of path-induced effective zero hopping within the unit cells, the systems are characterized by complete multimerization with degenerate $-1$ energy edge states for open boundary condition. Su-Schrieffer-Heeger subspaces with fully dimerized limits corresponding to pairs of nontrivial flat bands are derived from the Hilbert spaces. In particular, topological bound states in the continuum (BICs) are inherently present in even multimer chains, manifested by embedding the topological bound states into a continuous band assured by bulk-boundary correspondence. Moreover, we experimentally demonstrate the degenerate topological edge states and topological BICs in inductor-capacitor circuits.