Spin susceptibility in quasicrystal superconductor with spin-orbit interactions

Abstract

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.

Figures (9)

• Figure 1: The edges of the rhombuses and the normal vector $\vec{n}_{ij}$ for the bonds (red) shared by both large and small rhombuses. $\vec{n}_{ij}=0$ for the bonds (navy) which are not shared by large and small rhombuses. The system size $N=96$ in this figure is chosen for clear visibility. For a large system, the ratio (the number of the red bonds)/(the total number of all the bonds) is $\simeq 0.6$. The $(x,y)$ coordinate is also shown.
• Figure 2: The inter-site spin correlation $\vec{s}_{ij}^{\perp}=(s_{ij}^x,s_{ij}^y)$ in the Rashba spin-orbit coupled system ($\alpha_{\perp}=0.2, \alpha_{\parallel}=0$), characterizing the local spin-momentum locking.
• Figure 3: The inter-site spin correlation $s_{ij}^z$ (normalized by ${\rm max}_{ij}|\vec{s}_{ij}|$) in the Ising spin-orbit coupled system ($\alpha_{\perp}=0, \alpha_{\parallel}=0.2$), characterizing the local spin-momentum locking.
• Figure 4: Spin susceptibility $\chi^{xx}$ for several values of the Rashba spin-orbit coupling $\alpha_{\perp}$ The Ising spin-orbit coupling is $\alpha_{\parallel}=0$ and the transition temperature is $T_c=0.1$.
• Figure 5: Spin susceptibility $\chi^{zz}$ for several values of the Rashba spin-orbit coupling $\alpha_{\perp}$. The Ising spin-orbit coupling is $\alpha_{\parallel}=0$ and the transition temperature is $T_c=0.1$.