Spin susceptibility in quasicrystal superconductor with spin-orbit interactions

We study impacts of spin-orbit interactions on the spin susceptibility in quasicrystal superconductors, motivated by the anomolous superconducting properties in the van der Waals quasicrystal Ta$_{1.6}$Te under magnetic fields. We consider the Penrose tiling model with $s$-wave pairing as a representative system and include anisotropic spin-orbit interactions allowed for the quasicrystal structure. It is shown that the spin-momentum locking locally takes place in the quasicrystal, and electron motion and spin directions are tightly connected at each spatial position in the real space. As a result, the spin susceptibility is enhanced for both in-plane and out-of-plane magnetic fields in the presence of a Rashba-type spin-orbit interaction. For an Ising-type spin-orbit interaction, the spin susceptibility only for in-plane magnetic fields is increased, while the out-of-plane spin susceptibility is almost unchanged. When there are both kinds of the spin-orbit interactions, temperature dependence of the spin susceptibility for any field directions is suppressed.