Comparison of quantum spin Hall states in quasicrystals and crystals
Abstract
We theoretically review the quantum spin Hall states in an Ammann-Beenker-type octagonal quasicrystal and a periodic snub-square crystal, both sharing the same basic building blocks. While the bulk states show significant differences in localization and transport properties, the topological phases manifest similarly in the two systems. This suggests the robustness of the topological properties regardless of symmetry and periodicity. We characterize the topological nature of the two systems with a nonzero topological invariant (spin Bott index Bs and Z2 invariant), robust metallic edge states, and quantized conductance. In spite of some quantitative differences, the topological phase diagram of the two systems also exhibits similar behaviors, indicating that the topological phase transition is mainly determined by similar interactions in the two systems regardless of their structural difference. This is also reflected by the observation that the transition point between the normal insulator and the quantum spin Hall state in both systems follows a universal linear scaling relation for topological phase transitions.
- Authors:
-
[1];
- Univ. of Utah, Salt Lake City, UT (United States)
- Univ. of Utah, Salt Lake City, UT (United States); Collaborative Innovation Center of Quantum Matter, Beijing (China)
- Publication Date:
- Research Org.:
- Univ. of Utah, Salt Lake City, UT (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22). Materials Sciences & Engineering Division
- OSTI Identifier:
- 1548255
- Alternate Identifier(s):
- OSTI ID: 1550595
- Grant/Contract Number:
- FG02-04ER46148
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 100; Journal Issue: 8; Related Information: https://journals.aps.org/prb/supplemental/10.1103/PhysRevB.100.085119/sup_mat_qshAB_0411.pdf; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE; 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; Quantum spin Hall effect; Quasicrystal
Citation Formats
Huang, Huaqing, and Liu, Feng. Comparison of quantum spin Hall states in quasicrystals and crystals. United States: N. p., 2019.
Web. doi:10.1103/PhysRevB.100.085119.
Huang, Huaqing, & Liu, Feng. Comparison of quantum spin Hall states in quasicrystals and crystals. United States. https://doi.org/10.1103/PhysRevB.100.085119
Huang, Huaqing, and Liu, Feng. Thu .
"Comparison of quantum spin Hall states in quasicrystals and crystals". United States. https://doi.org/10.1103/PhysRevB.100.085119. https://www.osti.gov/servlets/purl/1548255.
@article{osti_1548255,
title = {Comparison of quantum spin Hall states in quasicrystals and crystals},
author = {Huang, Huaqing and Liu, Feng},
abstractNote = {We theoretically review the quantum spin Hall states in an Ammann-Beenker-type octagonal quasicrystal and a periodic snub-square crystal, both sharing the same basic building blocks. While the bulk states show significant differences in localization and transport properties, the topological phases manifest similarly in the two systems. This suggests the robustness of the topological properties regardless of symmetry and periodicity. We characterize the topological nature of the two systems with a nonzero topological invariant (spin Bott index Bs and Z2 invariant), robust metallic edge states, and quantized conductance. In spite of some quantitative differences, the topological phase diagram of the two systems also exhibits similar behaviors, indicating that the topological phase transition is mainly determined by similar interactions in the two systems regardless of their structural difference. This is also reflected by the observation that the transition point between the normal insulator and the quantum spin Hall state in both systems follows a universal linear scaling relation for topological phase transitions.},
doi = {10.1103/PhysRevB.100.085119},
journal = {Physical Review B},
number = 8,
volume = 100,
place = {United States},
year = {Thu Aug 08 00:00:00 EDT 2019},
month = {Thu Aug 08 00:00:00 EDT 2019}
}
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Cited by: 22 works
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Figures / Tables:
FIG. 1: (a) A periodic approximant of the octagonal quasicrystal lattice obtained from the Ammann-Beenker tiling. (b) A snub-square crystalline lattice based on the semiregular Archimedean tiling. The rotational angle is α = 22.5°. The red square and yellow rhombus represent the basic building blocks for both lattices.
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