Related papers: Probing topology in nonlinear topological material…
Recently, the spectral localizer framework has emerged as an efficient approach to classifying topology in photonic systems featuring local nonlinearities and radiative environments. In nonlinear systems, this framework provides rigorous…
Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic…
The spectral localizer is a predictive framework for the computation of topological invariants of natural and artificial materials. Here, three crucial improvements on the criterion for the validity of the framework are reported: first,…
Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…
Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this…
Mechanical topological insulators are well understood for linear and weakly nonlinear systems, however traditional analysis methods break down for strongly nonlinear systems since linear methods can not be applied in that case. We study one…
Higher-order topology is prized for its ability to realize lower-dimensional boundary states which are stable beyond fine-tuning. However, disorder presents a failure mechanism that can destroy topological in-gap states. Here, we…
In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…
Over the last few years, crystalline topology has been used in photonic crystals to realize edge- and corner-localized states that enhance light-matter interactions for potential device applications. However, the band-theoretic approaches…
Topological insulators are described by topological invariants that can be computed by integrals over momentum space, but also as traces over local, real-space topological markers. These markers are useful to detect topological insulating…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
This contribution describes the mathematical theory of topological indices in solid state systems composed of non-interacting Fermions. In particular, this covers the spectral localizer and the bulk-boundary correspondence.
The standard understanding of topological protection from band theory is that a system's topology cannot change without first closing the bulk band gap. However, in Floquet systems, this typical definition of topological protection is one…
The hallmark feature of topological insulators renders edge transport virtually impervious to scattering at defects and lattice disorder. In our work, we experimentally demonstrate a topological system, using a photonic platform, in which…
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.…
Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, non-reciprocal chiral edge states and cavity-like confined states that have applications in both linear and…
Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…
Although the classification of crystalline materials can be generally handled by momentum-space-based approaches, topological classification of aperiodic materials remains an outstanding challenge, as the absence of translational symmetry…