Two-dimensional (2D) materials including graphene, transition metal dichalcogenides, black
phosphorus, MXenes, and semimetals have attracted extensive and widespread interest …

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 …

We elaborate that for topological insulators and topological superconductors described by
Dirac models in any dimension and symmetry class, the topological order can be mapped to …

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 …

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

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 …

The search for novel topological quantum states has recently moved beyond naturally
occurring crystalline materials to complex and engineered systems. In this work we …

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 …

The conducting boundary states of topological insulators appear at an interface where the
characteristic invariant ℤ2 switches from 1 to 0. These states offer prospects for quantum …

We study phase transitions driven by structural disorder in noncrystalline topological
insulators. We introduce a procedural generation algorithm, the Perlin noise, typically used …