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 $(0, \pm \pi, 0)$ 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.