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Superconductivity on quasiperiodic lattice

Shiro Sakai

LPS, Bât. 510, Orsay, Parc Club bât 23-25, salle 215 1er étage

Motivated by a recent experimental search for superconducting quasicrystals [1], we theoretically study a possible superconductivity on a quasiperiodic lattice. The fundamental questions include whether the superconductivity can exist in a system without translational symmetry, and if it exists, what property differs from superconductors in periodic crystals. We portray the issue within an attractive Hubbard model on a two dimensional Penrose lattice. Applying a real-space dynamical mean-field theory to the model consisting of 4181 sites, we indeed find a superconducting phase at low temperatures. Reflecting the nonperiodicity of the Penrose lattice, the superconducting state exhibits a spatial inhomogeneity. According to the type of the inhomogeneity, the superconducting phase is categorized into three different states which cross over each other. Among them, the superconductivity appearing in a weak-coupling region exhibits the most nontrivial property -it shows spatially extended Cooper pairs, which are nevertheless distinct from the conventional BCS-type pairing of two electrons with opposite momenta [2].
[1] K.Deguchi et al., J. Phys. Soc. Jpn. 84, 023705 (2015). [2] S. Sakai, N. Takemori, A. Koga, and R. Arita, Phys. Rev. B 95, 024509 (2017).

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