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We explore the pairing state and gap structure of UTe$_2$ using a six-orbitalmodel which we call the $f$-$d$-$p$ model. Our model accurately reproduces thequasi-two-dimensional Fermi surfaces consistent with recent de Haas-van Alphenoscillation measurements and the $(0, \pm \pi, 0)$ antiferromagnetic spinfluctuations observed by neutron scattering. We incorporate on-site Coulombrepulsion for $f$ electrons and solve the linearized Eliashberg equation withinthe third-order perturbation theory to investigate the superconducting symmetryin UTe$_2$. The most likely state is found to be an $s$-wave state with ahighly anisotropic superconducting gap structure that exhibits apoint-node-like behavior of the specific heat at low temperatures.

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