N.TAKEMORI: Superconducting properties of quasicrystals

	Superconductivity has been observed in systems lacking translational symmetry, such as amorphous metals Sn0.9Cu0.1 and Pb0.75Bi0.25, which exhibit a strong electron-phonon interaction. However, weak-coupling superconductivity with spatially extended Cooper pairs in aperiodic systems is a highly nontrivial issue. In 2018, a breakthrough occurred when bulk superconductivity was discovered in Al-Mg-Zn quasicrystals and 1/1 approximants [1]. 

We will present results of a theoretical analysis of the attractive Hubbard model [2,3] using Bogoliubov-de Gennes mean-field theory. Our findings reveal that quasicrystals exhibit a superconducting state in the quasiperiodic lattice, featuring non-BCS-type superconductivity with Cooper pairs possessing finite center-of-mass momentum (Figure 1) [2]. As a consequence, it is clarified that the paramagnetic currents can also flow in a direction perpendicular to the applied vector potential and are finite even at zero temperature [4]. We note that such phenomenon can be expected also in the Fulde-Ferrell-Larkin-Ovchinnikov state [5]. 

[1] K. Kamiya, et. al., Nat. Comm. 9, 154 (2018).
[2] S. Sakai, et. al., Phys. Rev. B 95, 024509 (2017); N. Takemori, et. al., Phys. Rev. B 102, 115108 (2020).
[3] F. P. M. Beenker, Tech. Rep. 82-WSK04 (Eindhoven University of Technology, 1982). 
[4] T. Fukushima, N. Takemori, S. Sakai, M. Ichioka, A. Jagannathan, J. Phys.: Conf. Ser. 2461 012014 (2023); T. Fukushima, N. Takemori, S. Sakai, M. Ichioka, A. Jagannathan, arXiv:2310.03484.
[5] P. Fulde and R. A. Ferrell, Phys. Rev. 135, A550 (1964); A. Larkin and Y. N. Ovchinnikov, Sov. Phys. JETP 20, 762, (1965).

Figure 1: Cooper pairs with finite center-of-mass momentum in Penrose tiling.