Superconductivity in UTe$_2$ from local noncentrosymmetricity

Abstract

Superconductivity in UTe$_{2}$ has garnered significant attention, as it is widely recognized as a promising candidate for a spin-triplet superconductor. However, the symmetry of superconductivity and the microscopic origin of spin-triplet pairing remain subjects of debate. Nevertheless, various experiments imply an intimate coupling between magnetism and superconductivity. In this paper, we analyze a multi-sublattice periodic Anderson model that incorporates a spin-orbit coupling allowed in locally noncentrosymmetric crystals to discuss magnetic fluctuations and superconductivity in UTe$_2$. Due to the sublattice-dependent spin-orbit coupling, magnetic fluctuations become anisotropic, and the spin degeneracy of superconducting states is lifted. Our calculations reveal anisotropic antiferromagnetic fluctuations along the $b$- and $c$-axes, anisotropic ferromagnetic fluctuations along the $a$-axis, and their coexistence. These can be tuned by the $f$-electron's level. Superconductivity in the $A_u$ representation is predominant for a wide range of parameters, whereas the $B_{2u}$ representation is almost degenerate and can be stabilized. The direction of the $d$-vector changes as we increase the spin-orbit coupling. We discuss the consistency between our results and several experiments.

Figures (7)

• Figure 1: Momentum dependence of intra-sublattice spin susceptibility $\chi_\mathrm{AA}({\bm q}) = \chi_\mathrm{BB}({\bm q})$ on the $q_z=0$ plane without the SOC, $\alpha_1=\alpha_2=0$. The $f$-electron level $\Delta_f$ is shown on top of each figure. The antiferromagnetic fluctuation changes to the ferromagnetic one as increasing $\Delta_f$.
• Figure 2: Spin susceptibility $\chi^{\mu\mu}_\mathrm{AA}({\bm q})$ along each crystalline axis $\mu=x,y,z$ with the SOC. We assume $\alpha_1 = \alpha_2$ and show their magnitude on top of each figure. We set $\Delta_f=0.35$ and present the momentum dependence on the $q_z=0$ plane.
• Figure 3: Spin susceptibility $\chi^{\mu\mu}_\mathrm{AA}({\bm q})$ with the SOC for $\Delta_f=0.32$. We assume $\alpha_2 = 4\alpha_1$ and show their magnitudes on top of each figure. The momentum dependence on the $q_z=0$ plane is plotted.
• Figure 4: The $\Delta_f$ dependence of the superconducting eigenvalues for each IR in the absence of the SOC.
• Figure 5: The SOC dependence of superconducting eigenvalues for each IR. We assume $\alpha_1 = \alpha_2$ and set $\Delta_f=0.35$.