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 …

With the rapid development of topological states in crystals, the study of topological states
has been extended to quasicrystals in recent years. In this review, we summarize the recent …

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

The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of
aperiodic tilings. However, the physics of particles propagating in such a setting remains …

We propose counterintuitive topological pumps induced by disorder in noninteracting and
interacting systems. We show an extrinsic topological pump driven by the on-site …

Disorder and localization have dramatic influence on the topological properties of a
quantum system. While strong disorder can close the band gap thus depriving topological …

Quadrupole topological insulators are a new class of topological insulators with quantized
quadrupole moments, which support protected gapless corner states. The experimental …

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

The interplay among topology, disorder, and non-Hermiticity can induce some exotic
topological and localization phenomena. Here we investigate this interplay in a two …

The topological phase in amorphous systems adds a new dimension to the topological
states of matter. Here, we present an interesting phenomenon dubbed the topological …