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 …

Electronic properties of crystals are inherently pertained to crystalline symmetry, so that
amorphization that lowers and breaks symmetry is detrimental. One important crystalline …

Local topological markers, topological invariants evaluated by local expectation values, are
valuable for characterizing topological phases in materials lacking translation invariance …

Topological insulator phases of non-interacting particles have been generalized from
periodic crystals to amorphous lattices, which raises the question whether topologically …

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 …

We show that a chiral spin liquid spontaneously emerges in partially amorphous,
polycrystalline, or ion-irradiated Kitaev materials. In these systems, time-reversal symmetry …

While topological phases have been extensively studied in amorphous systems in recent
years, it remains unclear whether the random nature of amorphous materials can give rise to …

Band topology is traditionally analyzed in terms of gauge-invariant observables associated
with crystalline Bloch wave functions. Recent work has demonstrated that many of the free …

Crystalline symmetries have played a central role in the identification and understanding of
quantum materials. Here we investigate whether an amorphous analogue of a well known …

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 …