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, a new family of symmetry-protected higher-order topological insulators has been
proposed and was shown to host lower-dimensional boundary states. However, with the …

We introduce novel higher-order topological phases of matter in chiral-symmetric systems
(class AIII of the tenfold classification), most of which would be misidentified as trivial by …

We investigate disorder-driven topological phase transitions in quantized electric
quadrupole insulators in two dimensions. We show that chiral symmetry can protect the …

With significant advances in classifying and cataloguing topological matter, the focus of
topological physics has shifted towards quantum control, particularly the creation and …

A hyperbolic lattice allows for any p-fold rotational symmetry, in stark contrast to a two-
dimensional crystalline material, where only 2-fold, 3-fold, 4-fold, or 6-fold rotational …

Higher-order topological insulators are established as topological crystalline insulators
protected by crystalline symmetries. One celebrated example is the second-order …

To explore the non-Euclidean generalization of higher-order topological phenomena, we
construct a higher-order topological insulator model in hyperbolic lattices by breaking the …

Motivated by the recent experimental realizations of hyperbolic lattices in circuit quantum
electrodynamics and the research interest in the non-Euclidean generalization of topological …

Photonic crystals (PhCs) have emerged as a popular platform for realizing various
topological phases due to their flexibility and potential for device applications. In this article …