[Paper Review] Anomalous Floquet Topological Disclination States

Haoye Qin, Zhe Zhang+2 more|arXiv (Cornell University)|Apr 6, 2023

Topological Materials and Phenomena4 citations

TL;DR

This paper demonstrates the existence of anomalous Floquet topological disclination states in non-reciprocal scattering networks, where zero-dimensional topological states emerge at disclination defects due to a resonant rotation-symmetry condition. These states survive until bandgaps close and can form topological bound states in the continuum (BICs) with extreme field localization and infinite lifetime when coupled to chiral edge states, enabling robust, switchable lasing and anti-lasing behavior.

ABSTRACT

Recently, non-reciprocal two-dimensional unitary scattering networks have gained considerable interest due to the possibility of obtaining robust edge wave propagation in the anomalous Floquet phase. Conversely, zero-dimensional topological states in such networks have been left uncharted. Here, we demonstrate the existence of Floquet disclination states in non-reciprocal scattering networks. The disclination states, characterized by spectral charges, nucleate in the anomalous phase from a resonant rotation-symmetric phase matching condition, and survive until the bandgaps close. Once coupled to the radiation continuum feeding the anomalous chiral edge state, they can induce intriguing topological disclination bound states in the continuum (BICs), associated with an extreme confinement and lifetime. Altogether, anomalous Floquet disclination states and topological disclination BIC broaden the applications of disclination states to microwave, acoustic or optical scattering networks, with new possibilities in chiral topological lasing, robust energy squeezing from topological bound states, and switchable lasing and anti-lasing behavior induced via unidirectional topological coupling.

Motivation & Objective

• To explore the existence of 0D topological disclination states in non-reciprocal unitary scattering networks, which remain uncharted despite advances in anomalous Floquet edge states.
• To understand the conditions under which these disclination states nucleate and persist, particularly in relation to spectral charges and phase-rotation symmetry.
• To investigate the formation of topological bound states in the continuum (BICs) from coupling disclination states to the chiral edge state continuum.
• To demonstrate the topological protection and enhanced field localization of these BICs, enabling applications in robust lasing and anti-lasing.

Proposed method

• The study uses a hexagonal network of non-reciprocal circulators connected via transmission lines with tunable phase delays, enabling unitary Floquet dynamics.
• A cut-and-glue procedure is applied to create disclinations with 1/3 and 1/6 rotational symmetry, generating localized 0D states at defect sites.
• Spectral charges are used to characterize the disclination states, with their existence linked to a round-trip resonance condition at rotation-symmetry points.
• The system is analyzed via the unitary Bloch eigenproblem, with band structure computed as a function of circulator parameters (R, T) and phase delay φ.
• Coupling to the edge state continuum is introduced via 2-port scatterers with tunable reflection coefficient R = sinθ, enabling transition from BIC to quasi-BIC.
• The topological protection of BICs is verified by introducing disorder in the phase delay φ, showing robustness against perturbations.

Figure 1: Anomalous disclination states in non-reciprocal scattering networks. (a) Initial hexagonal network of circulators connected through transmission lines (TLs) with a phase delay $\varphi$ , and cut-and-glue method for generating disclinations. (b, c) Disclination networks of 1/3-cut (b) and

Experimental results

Research questions

• RQ1 Can anomalous Floquet topological 0D disclination states exist in non-reciprocal scattering networks, and under what conditions do they nucleate?
• RQ2 How do disclination states survive until bandgaps close, and what role does spectral charge play in their stability?
• RQ3 Can disclination states couple to the chiral edge state continuum to form topological bound states in the continuum (BICs)?
• RQ4 What is the role of topological protection in maintaining BICs under disorder, and how does this affect field localization and lifetime?
• RQ5 Can coupled disclination BICs enable switchable lasing and anti-lasing behavior via gain and loss modulation?

Key findings

• Anomalous Floquet disclination states emerge at 1/3- and 1/6-cut disclinations due to a resonant rotation-symmetry condition, with distinct spectral charges and inverse participation ratio scaling laws different from 1D edge states.
• The disclination states persist until bandgaps close, indicating topological robustness even in the absence of nontrivial Chern numbers.
• When coupled to the chiral edge state continuum, the disclination states form topological BICs with infinite scattering condition number and extreme field enhancement, reaching a factor of 1250 at φ₁/₃ = 0.5π.
• The BICs are topologically protected, as confirmed by robustness under phase disorder (φ perturbations), with the condition number remaining infinite at θ = 0.
• Coupled BICs in a mirror-symmetric octagonal network exhibit a transition from isolated (charges 1 and 0) to merged (charges 0.5 and 0.5) states upon detuning from the perfect circulator condition.
• Switchable lasing and anti-lasing behavior is demonstrated: at g = 0, the system transitions between gain and loss regimes, with the merged BIC state enabling tunable, robust amplification at disclination sites.

Figure 2: Different scaling properties of the inverse participation ratios of edge and disclination states. (a) Disclination states with high IPRs can be obtained in an anomalous phase subject to a 1/3-cut. (b,c) Focusing on the anomalous case, we plot the spectral charge distribution for (b) edge (