Spin-lattice relaxation for point-node-like s-wave superconductivity in f-electron systems

In this study, we examined the temperature dependence of the spin-lattice relaxation using an f-d-p model, which is an effective model of UTe2. Solving the linearized Eliashberg equation in the f-d-p model based on third-order perturbation theory, we obtain a point-node-like s-wave pairing state. Our result shows that the Hebel-Slichter peak in the point-node-like s-wave pairing state is smaller than that in the isotropic s-wave pairing state. However, the Hebel-Slichter peak remains robust even in the point-node-like s-wave pairing state, and the point-node-like s-wave state is inconsistent with the results of nuclear magnetic resonance measurements.

💡 Research Summary

In this work the authors address the long‑standing puzzle of the superconducting gap symmetry in the heavy‑fermion compound UTe₂ by employing a six‑orbital f‑d‑p tight‑binding model that reproduces the quasi‑two‑dimensional Fermi surfaces (α‑hole and β‑electron sheets) and the antiferromagnetic fluctuation peak at Q≈(0,π,0). Using third‑order perturbation theory (TOPT) they solve the linearized Eliashberg equation and find that the leading instability is an s‑wave state with accidental point nodes located at the corners of the α‑sheet in the k_z=0 plane. Although the overall symmetry is s‑wave, the nodes are not protected by any irreducible representation, giving rise to low‑energy quasiparticles and a T³ contribution to the specific heat, in agreement with experiments that suggest nodal behavior.

To test whether this point‑node‑like s‑wave state can explain the absence of a Hebel‑Slichter coherence peak in nuclear magnetic resonance (NMR) measurements, the authors compute the spin‑lattice relaxation rate 1/T₁. Starting from the transverse spin susceptibility χ⁺⁻(Q,Ω), they express it in terms of normal (G) and anomalous (F) Green’s functions, project onto the p‑ and p′‑orbitals (the light elements typically probed in f‑electron NMR), and derive a compact formula

 1/T₁ ∝ ∫ dε