Help Privacy Policy Disclaimer
  Advanced SearchBrowse




Journal Article

Topological models in rotationally symmetric quasicrystals


Duncan,  Callum W.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;


Manna,  Sourav
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;


Nielsen,  Anne E. B.
Max Planck Institute for the Physics of Complex Systems, Max Planck Society;

External Resource
No external resources are shared
Fulltext (restricted access)
There are currently no full texts shared for your IP range.
Fulltext (public)

(Preprint), 6MB

Supplementary Material (public)
There is no public supplementary material available

Duncan, C. W., Manna, S., & Nielsen, A. E. B. (2020). Topological models in rotationally symmetric quasicrystals. Physical Review B, 101(11): 115413. doi:10.1103/PhysRevB.101.115413.

Cite as: https://hdl.handle.net/21.11116/0000-0008-AC45-9
We investigate the physics of quasicrystalline models in the presence of a uniform magnetic field, focusing on the presence and construction of topological states. This is done by using the Hofstadter model but with the sites and couplings denoted by the vertex model of the quasicrystal, giving the Hofstadter vertex model. We specifically consider two-dimensional quasicrystals made from tilings of two tiles with incommensurate areas, focusing on the fivefold Penrose and the eightfold Ammann-Beenker tilings. This introduces two competing scales: the uniform magnetic field and the incommensurate scale of the cells of the tiling. Due to these competing scales, the periodicity of the Hofstadter butterfly is destroyed. We observe the presence of topological edge states on the boundary of the system via the Bott index that exhibit two-way transport along the edge. For the eightfold tiling, we also observe internal edgelike states with nonzero Bott index, which exhibit two-way transport along this internal edge. The presence of these internal edge states is a characteristic of quasicrystalline models which leads to open questions on their properties and future applications. We then move on to considering interacting systems. This is challenging, in part because exact diagonalization on a few tens of sites is not expected to be enough to accurately capture the physics of the quasicrystalline system and in part because it is not clear how to construct topological flatbands having a large number of states. We show that these problems can be circumvented by building the models analytically, and in this way we construct models with Laughlin-type fractional quantum Hall ground states.