Higher-order topological phases in crystalline and non-crystalline systems: a review Page 1
Journal of Physics: Condensed Matter ACCEPTED MANUSCRIPT • OPEN ACCESS Higher-order …

Recently, the studies of topological corner states (TCSs) have been extended from crystals
to quasicrystals, which are referred to as higher‐order topological quasicrystalline insulators …

Three-dimensional higher-order topological semimetals in crystalline systems exhibit higher-
order Fermi arcs on one-dimensional hinges, challenging the conventional bulk-boundary …

For the study of topological phases in photonics, while quantum-Hall-type first-order chiral
edge states are routinely realized in magneto-optical photonic crystals, higher-order …

Electromagnetic topological edge states typically are created in photonic systems with
crystalline symmetry and these states emerge because of the topological feature of bulk …

While higher-order photonic topological corner states typically are created in systems with
nontrivial bulk dipole polarization, they could also be created in systems with vanishing …

In recent years, there has been a surge of interest in higher-order topological phases
(HOTPs) across various disciplines within the field of physics. These unique phases are …

Recently, higher-order topology has been expanded to encompass aperiodic quasicrystals,
including those with eightfold or twelvefold rotational symmetry. The underlying mechanism …

In this work, we study topological states in Ammann-Beenker-tiling photonic quasicrystals
made of magneto-optical materials. While conventional topological states in photonic …

The systems without symmetries, eg, the spatial and chiral symmetries, are generally
thought to be improper for topological study and no conventional integral topological …