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

Abstract

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.

Figures (13)

• Figure 1: (a) Crystal structure (Space group: $Immm$) and $t_{1,2,3}$, $t_4$, and $t_5$ correspond to U-U, U-Te2, and Te2-Te2 hoppings, respectively. (b) Model band structure. The line width indicates the weight of $f$ electrons. The light grey lines display the band structure given by GGA+U ($U$ = 2.0 eV). (c) Fermi surfaces Kawamura1. The weight of $f$ electrons is illustrated in color. (d) Bare static spin susceptibility $\chi^{(0)}(\bm{Q}) = \chi^{(0)}(\bm{Q}, i\Omega_n = 0)$ on the $Q_z = 0$ plane. $\chi^{(0)}(\bm{Q})$ has peaks at $\bm{Q} \approx (0, \pm \pi, 0)$.
• Figure 2: Feynman diagrams for the effective pairing interaction in TOPT. (a) -- (c) Diagrams are incorporated also in RPA. (d) -- (g) Diagrams representing vertex correction terms are not included in RPA. The empty square symbols represent the anti-symmetrized bare Coulomb interaction.
• Figure 3: (a) Eigenvalues of spin-singlet (circles) and triplet (triangles) states. The empty and filled symbols denote the results for $U=1.50$ and 1.75 eV, respectively. (b, c) Magnitude of the anomalous self-energy on the $\alpha$ and $\beta$ Fermi surfaces, expressed in color.
• Figure 3: (b, c) Magnitude of the anomalous self-energy $\Delta_a(\bm{k}, i \pi T)$ on the $\alpha$ and $\beta$ Fermi surfaces, expressed in color. Although point-node-like structures appeared at the corner of the $\alpha$-surface in the original text, correct point-node-like structures appear on the $\beta$-surface near the zone boundary of $k_z=2\pi/c$.
• Figure 4: Calculated specific heat as a function of $(T/T_c)^2$. The linear behavior is qualitatively consistent with experiments. The vertical axis is normalized by the normal state value at $T_c$. The $T^3$ dependence of $C$ (red line) indicates the existence of a point-node structure. The inset shows an enlarged view of the low-temperature behavior.