Unconventional $s$-Wave Pairing with Point-Node-Like Gap Structure in UTe$_2$

We explore the pairing state and gap structure of UTe$_2$ using a six-orbital model which we call the $f$-$d$-$p$ model. Our model accurately reproduces the quasi-two-dimensional Fermi surfaces consistent with recent de Haas-van Alphen oscillation measurements and the $(0, \pm π, 0)$ antiferromagnetic spin fluctuations observed by neutron scattering. We incorporate on-site Coulomb repulsion for $f$ electrons and solve the linearized Eliashberg equation within the third-order perturbation theory to investigate the superconducting symmetry in UTe$_2$. The most likely state is found to be an $s$-wave state with a highly anisotropic superconducting gap structure that exhibits a point-node-like behavior of the specific heat at low temperatures.

💡 Research Summary

This theoretical study investigates the superconducting pairing state and gap structure of the heavy-fermion superconductor UTe2, challenging the prevailing spin-triplet paradigm. The authors construct a novel six-orbital “f-d-p” tight-binding model that accurately reproduces key experimental features: the quasi-two-dimensional Fermi surfaces observed in de Haas–van Alphen experiments (specifically the absence of a pocket near the X point) and the (0, ±π, 0) antiferromagnetic spin fluctuations detected by neutron scattering.

To probe superconductivity, they solve the linearized Eliashberg equation using the third-order perturbation theory (TOPT) for the on-site Coulomb repulsion among f-electrons. Crucially, TOPT includes third-order “vertex correction” diagrams that are absent in the commonly used random phase approximation (RPA). While RPA-based studies, focusing on magnetic fluctuation-mediated pairing, often predict spin-triplet states, the TOPT calculation yields a spin-singlet state as the most probable pairing channel for reasonable interaction strengths (U=1.50, 1.75 eV). This result aligns with recent high-quality NMR measurements showing a Knight shift decrease across all crystalline axes.

The dominant pairing symmetry is an unconventional, highly anisotropic s-wave state. Although the order parameter does not change sign across the Fermi surfaces (consistent with s-wave symmetry), its magnitude is highly anisotropic. It exhibits a point-node-like structure, where the gap becomes very small on the edges of the α Fermi surface at k_z=0. Calculations of the specific heat within the BCS approximation show a T^3 dependence over a wide low-temperature range, qualitatively matching experimental reports and stemming from low-energy excitations near these nodal regions.

The paper delves into the origin of this state. Analysis of the effective pairing interaction reveals that while it is strongly repulsive for scattering processes with k ≈ k’, it becomes attractive for k ≈ -k’. This attractive component, essential for forming the s-wave state without sign change, is shown to originate precisely from the third-order vertex corrections neglected in RPA. Furthermore, the authors demonstrate that in the regions of maximum gap, the inter-site f-orbital pairing amplitude is dominant over the intra-site one, providing a mechanism to mitigate the strong on-site Coulomb repulsion and allowing s-wave pairing to emerge.

In summary, this work proposes a spin-singlet, highly anisotropic s-wave state with a point-node-like gap structure as a strong candidate for the superconducting order in UTe2 at zero field. It highlights the potential importance of pairing interactions beyond magnetic fluctuation exchange (specifically those arising from higher-order vertex corrections) and offers a theoretical framework consistent with recent Knight shift and specific heat experiments. The findings suggest that the spin-singlet scenario should not be dismissed and call for further investigation into the complex pairing mechanism in UTe2.