Topological invariants in two-dimensional quasicrystals
Mikito Koshino, Hiroki Oka
Abstract
We provide a topological concept to characterize energy gaps in general two-dimensional quasiperiodic systems. We show that every single gap is uniquely characterized by a set of integers, which quantize the area of the momentum space in units of multiple Brillouin zones. These integers are found to be equivalent to the second Chern numbers by considering a formal relationship between an adiabatic charge pumping under a potential sliding and the four-dimensional quantum Hall effect. The integers are independent of commensurability, and invariant under an arbitrary continuous deformation, such as a relative rotation of a twisted bilayer system.
Topics & Concepts
Quasiperiodic functionInvariant (physics)Brillouin zoneCommensurability (mathematics)Topology (electrical circuits)Chern classMathematicsTopological quantum numberPhysicsQuantum Hall effectQuasicrystalAngular momentumPure mathematicsQuantum mechanicsMathematical analysisGeometryCombinatoricsElectronTopological Materials and PhenomenaQuasicrystal Structures and PropertiesQuantum many-body systems