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Abstract

Quasicrystals (QCs) are aperiodic materials with long-range order. Because translational symmetry is absent, a momentum-space framework cannot be directly used to study superconductivity in QCs. Nonetheless, various topological superconducting phases in QCs have been theoretically proposed beyond the conventional framework of topological band theory [1,2]. Some quasicrystalline systems, including Ammann-Beenker QCs, exhibit flat-band-like states despite the lack of periodicity. This feature distinguishes QCs from both periodic crystals and disordered systems, making them a unique platform for exploring nontrivial superconductivity.

In this talk, we discuss superconductivity with on-site pairing in two-dimensional Ammann-Beenker quasicrystals under magnetic field. We show that gapless superconductivity can emerge under a strong magnetic field, and that the gapless spectrum is supported by broken translational symmetry and flat-band states [3]. Furthermore, we demonstrate that the gapless superconducting phase can become topologically nontrivial in the presence of Rashba spin-orbit coupling. This gapless topological superconducting phase exhibits topological edge modes buried in the bulk spectrum.

Reference:
[1] I. C. Fulga, D. I. Pikulin, and T. A. Loring, Phys. Rev. Lett. 116, 257002 (2016).
[2] M. Hori, R. Okugawa, K. Tanaka, and T. Tohyama, Phys. Rev. Res. 6 033088 (2024).
[3] K. Saito, M. Hori, R. Okugawa, K. Tanaka, and T. Tohyama, arXiv:2410.01236 (to appear in Phys. Rev. Res.)