Topological modes (TMs) are typically localized at boundaries, interfaces and dislocations,
and exponentially decay into the bulk of a large enough lattice. Recently, the non-Hermitian …

Topological phases of matter are ubiquitous in crystals, but less is known about their
existence in amorphous systems, that lack long-range order. We review the recent progress …

Although topological band theory has been used to discover and classify a wide array of
novel topological phases in insulating and semimetal systems, it is not well suited to …

When subjected to quasiperiodic driving protocols, superconducting systems have been
found to harbor robust time-quasiperiodic Majorana modes, extending the concept beyond …

Recently, the study of topological structures in photonics has garnered significant interest, as
these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined …

Topological metals are conducting materials with gapless band structures and nontrivial
edge-localized resonances. Their discovery has proven elusive because traditional …

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 …

Nonlinear topological insulators have garnered substantial recent attention as they have
both enabled the discovery of new physics due to interparticle interactions, and may have …

In chiral crystals crystalline symmetries can protect multifold fermions, pseudorelativistic
masless quasiparticles that have no high-energy counterparts. Their realization in transition …

Recently, the spectral localizer framework has emerged as an efficient approach to
classifying topology in photonic systems featuring local nonlinearities and radiative …