Topology in quasicrystals

Abstract

Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result, they exhibit quantized bulk and boundary observable phenomena, motivating various applications that are robust to perturbations. In this review, we explore such a topological classification for quasiperiodic systems, and detail recent experimental activity in the field.

14 pages, 6 figures, contribution to feature issue "Photonic Topological Materials" in Optical Materials Express, comments are welcome

References in corpus (8)

• Topological Crystalline Insulators
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Topological Pumping over a Photonic Fibonacci Quasicrystal
• Virtual Topological Insulators with Real Quantized Physics
• The Colored Hofstadter Butterfly for the Honeycomb Lattice
• Determining topological order from a local ground state correlation function