Abstract Body

Quasicrystals are materials with aperiodicity and long-range order. Due to the lack of periodicity, the conventional picture of Cooper pairs near the Fermi surface is not available. Nevertheless, some BCS-like superconducting quasicrystals have been experimentally discovered [1, 2]. In these superconductors, superconducting order parameters are non-uniformly distributed. In addition, quasicrystals have so-called confined states that are electronic states strictly localized at the certain sites. They are macroscopically degenerate and bring sharp peaks to the density of states.

We show that the non-uniformity and confined states can stabilize the gapless superconducting phase where the bulk quasiparticle excitation gap becomes infinitesimal in Ammann-Beenker quasicrystals under a magnetic field at half filling, unlike at low filling [3]. When the Rashba spin-orbit coupling is present, the quasicrystalline gapless superconductor can be topologically nontrivial with Majorana zero-energy edge modes, which is characterized by a nonzero pseudospectrum index given by the spectral localizer [4].

References

[1] K. Kamiya et al., Nat. Commun. 9, 154 (2018).

[2] Y. Tokumoto et al., Nat. Commun. 15, 1529 (2024).

[3] M. Hori, T. Sugimoto, T. Tohyama, and K. Tanaka, arXiv:2401.06355.

[4] A. Cerjan and T. A. Loring, Phys. Rev. B 106, 064109 (2022).

Acknowledgment

This work is supported by JST SPRING, Grant Number JPMJSP2151 and JSPS KAKENHI (Grant No. JP23K13033 and No. JP24K00586).

Figure 1. Probability amplitude of near-zero-energy modes in topologically (a) trivial, and (b) nontrivial phase.

Keywords: Gapless superconductivity, Topological superconductivity, Quasicrystals, Ammann-Beenker tiling