Topological invariants in two-dimensional quasicrystals

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...

Full description

Bibliographic Details
Main Authors: Mikito Koshino, Hiroki Oka
Format: Article
Language:English
Published: American Physical Society 2022-01-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/PhysRevResearch.4.013028
_version_ 1827285609436151808
author Mikito Koshino
Hiroki Oka
author_facet Mikito Koshino
Hiroki Oka
author_sort Mikito Koshino
collection DOAJ
description 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.
first_indexed 2024-04-24T10:17:40Z
format Article
id doaj.art-c0998b48587b4dc58fc001e416ea7e48
institution Directory Open Access Journal
issn 2643-1564
language English
last_indexed 2024-04-24T10:17:40Z
publishDate 2022-01-01
publisher American Physical Society
record_format Article
series Physical Review Research
spelling doaj.art-c0998b48587b4dc58fc001e416ea7e482024-04-12T17:17:07ZengAmerican Physical SocietyPhysical Review Research2643-15642022-01-014101302810.1103/PhysRevResearch.4.013028Topological invariants in two-dimensional quasicrystalsMikito KoshinoHiroki OkaWe 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.http://doi.org/10.1103/PhysRevResearch.4.013028
spellingShingle Mikito Koshino
Hiroki Oka
Topological invariants in two-dimensional quasicrystals
Physical Review Research
title Topological invariants in two-dimensional quasicrystals
title_full Topological invariants in two-dimensional quasicrystals
title_fullStr Topological invariants in two-dimensional quasicrystals
title_full_unstemmed Topological invariants in two-dimensional quasicrystals
title_short Topological invariants in two-dimensional quasicrystals
title_sort topological invariants in two dimensional quasicrystals
url http://doi.org/10.1103/PhysRevResearch.4.013028
work_keys_str_mv AT mikitokoshino topologicalinvariantsintwodimensionalquasicrystals
AT hirokioka topologicalinvariantsintwodimensionalquasicrystals