Bulletin of the American Physical Society
2023 APS March Meeting
Volume 68, Number 3
Las Vegas, Nevada (March 5-10)
Virtual (March 20-22); Time Zone: Pacific Time
Session T25: Theory of Topological Insulators and Topological Band Structures
11:30 AM–2:30 PM,
Thursday, March 9, 2023
Room: Room 217/218
Sponsoring
Unit:
DCMP
Chair: Kai-Jie Yang, Pennsylvania State University
Abstract: T25.00010 : Topological gap labeling with third Chern numbers in three-dimensional quasicrystals
1:18 PM–1:30 PM
Presenter:
Kazuki Yamamoto
(Osaka university)
Authors:
Kazuki Yamamoto
(Osaka university)
Mikito Koshino
(Osaka Univ)
Quasicrystals are non-periodic but long-range ordered crystals found in a wide variety of physical systems including metallic alloys, photonic systems and twisted two-dimensional materials. Despite the increasing importance of quasicrystalline systems, the theoretical description of their physical properties is limited by the lack of Bloch theorem. In periodic crystals, each energy gap is characterized by an integer, which is the number of Bloch bands below the gap. In contrast, it is supposed that quasicrystals do not have any quantum units to count the number of states below the gap.
In this work, we show that a quasiperiodic structure has multiple Brillouin zones defined by redundant wave vectors, and the number of states below a gap is quantized as an integer linear combination of volumes of these Brillouin zones. The associated quantum numbers to characterize energy gaps can be expressed as third Chern numbers by considering a formal relationship between an adiabatic charge pumping under cyclic deformation of the quasiperiodic potential and a topological nonlinear electromagnetic response in 6D band insulators. This result is analogous to the gap labeling of 1D quasicrystals using first Chern numbers and 2D quasicrystals using second Chern numbers .
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