Probing topology in nonlinear topological materials using numerical 
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-theory

Wong, Stephan; Loring, Terry A.; Cerjan, Alexander

doi:10.1103/physrevb.108.195142

Phys. Rev. B

2023

DOI: 10.1103/physrevb.108.195142

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Probing topology in nonlinear topological materials using numerical K -theory

Stephan Wong,

Terry A. Loring,

Alexander Cerjan

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2024

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Cited by 5 publications

References 57 publications

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Classifying topology in photonic crystal slabs with radiative environments

Wong,

Loring,

Cerjan

2024

npj Nanophoton.

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In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. However, the out-of-plane radiative losses in those photonic Chern slabs has been previously neglected, yielding limited accuracy for predictions of these systems’ topological protection. Here, we develop a general framework for measuring the topological protection in photonic systems, such as in photonic crystal slabs, while accounting for in-plane and out-of-plane radiative losses. Our approach relies on the spectral localizer that combines the position and Hamiltonian matrices of the system to draw a real-picture of the system’s topology. This operator-based approach to topology allows us to use an effective Hamiltonian directly derived from the full-wave Maxwell equations after discretization via finite-elements method (FEM), resulting in the full account of all the system’s physical processes. As the spectral FEM-localizer is constructed solely from FEM discretization of the system’s master equation, the proposed framework is applicable to any physical system and is compatible with commonly used FEM software. Moving forward, we anticipate the generality of the method to aid in the topological classification of a broad range of complex physical systems.

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Classifying topology in photonic crystal slabs with radiative environments

Wong,

Loring,

Cerjan

2024

npj Nanophoton.

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Topological boundary modes in nonlinear dynamics with chiral symmetry

Zhou

2024

New J. Phys.

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Particle-hole symmetry and chiral symmetry play a pivotal role in multiple areas of physics, yet they remain unstudied in systems with nonlinear interactions whose nonlinear normal modes do not exhibit U ( 1 ) -gauge symmetry. In this work, we establish particle-hole symmetry and chiral symmetry in such systems. Chiral symmetry ensures the quantization of the Berry phase of nonlinear normal modes and categorizes the topological phases of nonlinear dynamics. We show topologically protected static boundary modes in chiral-symmetric nonlinear systems. Furthermore, we demonstrate amplitude-induced nonlinear topological phase transition in chiral-symmetric nonlinear dynamics. Our theoretical framework extends particle-hole and chiral symmetries to nonlinear dynamics, whose nonlinear modes do not necessarily yield U ( 1 ) -gauge symmetry.

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Real-space topological invariant for time-quasiperiodic Majorana modes

Qi,

Na,

Refael

et al. 2024

Phys. Rev. B

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Probing topology in nonlinear topological materials using numerical K -theory

Cited by 5 publications

References 57 publications

Classifying topology in photonic crystal slabs with radiative environments

Classifying topology in photonic crystal slabs with radiative environments

Topological boundary modes in nonlinear dynamics with chiral symmetry

Real-space topological invariant for time-quasiperiodic Majorana modes

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