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We propose a nanophotonic platform for topological quantum optics. Our system is composed of a two-dimensional lattice of non-linear quantum emitters with optical transitions embedded in a photonic crystal slab. The emitters interact…

Topological insulators are transformative quantum solids with immune-to-disorder metallic surface states having Dirac band structure. Ubiquitous charged bulk defects, however, pull the Fermi energy into the bulk bands, denying access to…

This work extends the theory of topological protection to dispersive systems. This theory has emerged from the field of topological insulators and has been established for continuum models in both classical and quantum settings. It predicts…

Analysis of PDEs · Mathematics 2023-11-13 Konstantinos Alexopoulos , Bryn Davies

Topological phases have been explored in various fields in physics such as spintronics, photonics, liquid helium, correlated electron system and cold-atomic system. This leads to the recent foundation of emerging materials such as…

Mesoscale and Nanoscale Physics · Physics 2013-05-28 Ryuichi Shindou , Ryo Matsumoto , Shuichi Murakami , Jun-ichiro Ohe

Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on…

Quantized electric quadrupole insulators have recently been proposed as novel quantum states of matter in two spatial dimensions. Gapped otherwise, they can feature zero-dimensional topological corner mid-gap states protected by the bulk…

Many examples from quantum and classical physics are known where topological protection is responsible for the robustness of the dynamics. Less explored is the role of topological protection in the context of classical oscillatory systems.…

Adaptation and Self-Organizing Systems · Physics 2025-08-07 Sayantan Nag Chowdhury , Hildegard Meyer-Ortmanns

Topological protection in photonics offers new prospects for guiding and manipulating classical and quantum information. The mechanism of spin-orbit coupling promises the emergence of edge states that are helical; exhibiting unidirectional…

Optics · Physics 2018-11-28 Nikhil Parappurath , Filippo Alpeggiani , L. Kuipers , Ewold Verhagen

The possibility of attaining chiral edge modes under periodic driving has spurred tremendous attention, both theoretically and experimentally, especially in light of anomalous Floquet topological phases that feature vanishing Chern numbers…

Quantum Gases · Physics 2024-01-04 Miguel F. Martínez , F. Nur Ünal

The discovery of the quantised Hall effect, and its subsequent topological explanation, demonstrated the important role topology can play in determining the properties of quantum systems. This realisation led to the development of…

Unidirectional and backscattering-free propagation of sound waves is of fundamental interest in physics, and highly sought-after in engineering. Current strategies utilize topologically protected chiral edge modes in bandgaps, or complex…

Soft Condensed Matter · Physics 2023-06-14 Wenting Cheng , Kai Qian , Nan Cheng , Nicholas Boechler , Xiaoming Mao , Kai Sun

In topological physics, one of the most intriguing phenomena is the presence of topological boundary states, accurately predicted by the well-established bulk-edge correspondence. For example, in three-dimensional Weyl semimetals, Fermi…

Mesoscale and Nanoscale Physics · Physics 2025-06-13 Yingxin Qi , Hanyu Wang , Qinghua Guo , Zhihong Zhu , Biao Yang

Recently the possibility of achieving one-way backscatter immune transportation of light by mimicking the topological order present within certain solid state systems, such as topological insulators, has received much attention. Thus far…

Wave scattering structures with amplification and dissipation can be modelled by non-Hermitian systems, opening new ways to control waves at small length scales. In this work, we study the phenomenon of topologically protected edge states…

Analysis of PDEs · Mathematics 2020-06-11 Habib Ammari , Erik Orvehed Hiltunen

We propose a bulk topological invariant for one-dimensional Floquet systems with chiral symmetry which quantifies the particle transport on each sublattice during the evolution. This chiral flow is physically motivated, locally computable,…

Strongly Correlated Electrons · Physics 2018-10-17 Xu Liu , Fenner Harper , Rahul Roy

Topological insulators are insulators in the bulk but feature chiral energy propagation along the boundary. This property is topological in nature and therefore robust to disorder. Originally discovered in electronic materials,…

Recently, we witnessed a tremendous effort to conquer the realm of acoustics as a possible playground to test with sound waves topologically protected wave propagation. Acoustics differ substantially from photonic and electronic systems…

Mesoscale and Nanoscale Physics · Physics 2019-05-14 Xiujuan Zhang , Meng Xiao , Ying Cheng , Ming-Hui Lu , Johan Christensen

The low-energy band-structure of electrons propagating on a lateral surface of a heterostructure consisting of three dimensional topological insulator (TI) and magnetic insulator layers has been calculated. The energy spectrum is highly…

Mesoscale and Nanoscale Physics · Physics 2015-06-22 A. G. Mal'shukov

The existence of chiral edge states, corresponding to the nontrivial bulk-band topology characterized by a non-vanishing topological invariant, and the manipulation of topological transport via chiral edge states promise topological…

Mesoscale and Nanoscale Physics · Physics 2023-07-25 Muhammad Nadeem , Xiaolin Wang

Recent interest in optical analogues to the quantum spin Hall and quantum valley Hall effects is driven by the promise to establish topologically protected photonic edge modes at telecommunication and optical wavelengths on a simple…

Mesoscale and Nanoscale Physics · Physics 2020-03-04 Matthias Saba , Stephan Wong , Mathew Elman , Sang Soon Oh , Ortwin Hess