This paper provides a pedagogical introduction to recent developments in geometrical and
topological band theory following the discovery of graphene and topological insulators …

Stacking orders in 2D van der Waals (vdW) materials dictate the relative sliding (lateral
displacement) and twisting (rotation) between atomically thin layers. By altering the stacking …

Electronic states in quasicrystals generally preclude a Bloch description, rendering them
fascinating and enigmatic. Owing to their complexity and scarcity, quasicrystals are …

The discovery of topological phases in non-Hermitian open classical and quantum systems
challenges our current understanding of topological order. Non-Hermitian systems exhibit …

Topology and disorder have a rich combined influence on quantum transport. To probe their
interplay, we synthesized one-dimensional chiral symmetric wires with controllable disorder …

Topological quantum matter can be realized by subjecting engineered systems to time-
periodic modulations. In analogy with static systems, periodically driven quantum matter can …

Current understanding of higher-order topological insulators (HOTIs) is based primarily on
crystalline materials. Here, we propose that HOTIs can be realized in quasicrystals …

We show that it is possible to have a topological phase in two-dimensional quasicrystals
without any magnetic field applied, but instead introducing an artificial gauge field via …

Theoretical and experimental studies suggest that both Hermitian and non-Hermitian
quasicrystals show localization due to the fractal spectrum and to the transition to diffusive …

Motivated by recent realizations of hyperbolic lattices in superconducting waveguides and
electric circuits, we compute the Hofstadter butterfly on regular hyperbolic tilings. Utilizing …