Theory of Magnetic Excitations in the Heavy-Fermion Spin-Triplet Superconductor UTe$_2$

Abstract

We study the dynamical spin response of UTe$_2$ by using a mixed-dimensional periodic Anderson model. Within the BCS-RPA formalism, we examine how the $f$-orbital character of the quasiparticles affects magnetic excitations in both the normal and superconducting (SC) states. In the normal state, finite mixing between localized $f$ electrons and conduction electrons produces a hybridization gap and enhances the spin response at $\mathbf{Q}_{\mathrm{Y}} = (0,\pi,0)$, indicating that the magnetic excitation originates from particle--hole scattering across the hybridization gap. In the SC state, we compare four odd-parity irreducible representations, $A_u$, $B_{1u}$, $B_{2u}$, and $B_{3u}$, for the spin-triplet order parameter. We find that, for the component of the spin susceptibility parallel to the $\mathbf{d}$ vector, a pronounced superconductivity-induced spin resonance appears at $\mathbf{Q}_{\mathrm{Y}}$ only in the $B_{2u}$ state. This behavior arises because the $B_{2u}$ order parameter remains finite and changes its sign between the relevant $f$-electron-dominated Fermi-surface regions connected by $\mathbf{Q}_\mathrm{Y}$ near $k_z=\pi$. The sign-change criterion is applicable to multiband superconductors in three-dimensional heavy-fermion systems, in the presence of (i) low-dimensional portions of the Fermi surface connected by a nesting vector, (ii) the dominance of the $f$-electron character, and (iii) the finite amplitude of SC gap on the portions.