Weyl superconductivity (WSC) is a three-dimensional (3D) topological superconducting phase that possesses point nodes with a linear dispersion in 3D momentum space [1]. The point nodes are named Weyl nodes because their dispersion is effectively described by the Weyl equation. Weyl nodes are stable due to topological protection by translational symmetry. The nontrivial topology also leads to surface Majorana arc states. Meanwhile, quasicrystals are materials without translational symmetry. Since 3D quasicrystals do not have 3D momentum space, a theory for WSC in quasicrystals is yet to be established.
In this presentation, we discuss the possibility of quasicrystalline WSC as a topological superconducting phase in layered quasicrystals [2], which are periodic only in the stacking direction. The band structure of quasicrystalline WSC has gapless nodes protected topologically, which we call quasicrystalline Weyl nodes. In a similar way to the characterization of conventional WSC, quasicrystalline Weyl nodes are defined by a change in a real-space topological invariant in one-dimensional momentum space [3]. We demonstrate that quasicrystalline WSC can be realized by using layered quasicrystalline topological superconductors. Furthermore, we show that quasicrystalline Weyl superconductors exhibit Majorana arcs on their surfaces.
[1] T. Meng and L. Balents, Phys. Rev. B 86, 054504 (2012).
[2] M. Hori, R. Okugawa, K. Tanaka, and T. Tohyama, Phys. Rev. Resarch 6, 033088 (2024).
[3] A. G. e Fonseca, T. Christensen, J. D. Joannopoulos, and M. Soljacic, Phys. Rev. B 108, L121109 (2023).
Keywords: Topological superconductivity, Quasicrystal, Weyl nodes, Majorana modes