Self-consistent Study of Non-Abelian Topological Superconductivity in Quasicrystals

JPS Conf. Proc. 38, 011065 (2023) [6 pages]

Proceedings of the 29th International Conference on Low Temperature Physics (LT29)

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Masahiro Hori¹^,², Rasoul Ghadimi²^,³, Takanori Sugimoto²^,⁴, Takami Tohyama², and K. Tanaka¹^,*

¹Department of Physics and Engineering Physics, and Centre for Quantum Topology and Its Applications (quanTA), University of Saskatchewan, SK, Canada S7N 5E2

²Department of Applied Physics, Tokyo University of Science, Katsushika, Tokyo 125-8585, Japan

³Center for Correlated Electron Systems, Institute for Basic Science (IBS), Seoul 08826, Korea

⁴Center for Quantum Information and Quantum Biology, Osaka University, Toyonaka, Osaka 560-0043, Japan

Received July 30, 2022

Quasicrystals are emerging topological materials which defy all the laws of crystallography, with aperiodic long-range order and higher-dimensional symmetry. We study topological superconductivity (TSC) with broken time-reversal symmetry in prototypal two-dimensional quasicrystals, Penrose and Ammann–Beenker quasicrystals. By solving the Bogoliubov–de Gennes equations self-consistently for the mean fields, we show the stable occurrence of TSC in both Penrose and Ammann–Beenker quasicrystals. The topological nature of TSC in a quasicrystal is signified by the Bott index. We confirm the appearance of zero-energy Majorana fermions at surface boundaries when the Bott index is unity, in accordance with the bulk-boundary correspondence and the non-Abelian character of the system.

The Author(s)

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https://doi.org/10.7566/JPSCP.38.011065

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