Revealing isotropic abundant low-energy excitations in UTe$_2$ through complex microwave surface impedance

The complex surface impedance is a well-established tool to study the super- and normal-fluid responses of superconductors. Fundamental properties of the superconductor, such as the pairing mechanism, Fermi surface, and topological properties, also influence the surface impedance. We explore the microwave surface impedance of spin-triplet UTe$_2$ single crystals as a function of temperature using resonant cavity perturbation measurements employing a novel multi-modal analysis to gain insight into these properties. We determine a composite surface impedance of the crystal for each mode using resonance data combined with the independently measured normal state dc resistivity tensor. The normal state surface impedance reveals the weighting of current flow directions in the crystal of each resonant mode. For UTe$_2$, we find an isotropic $\Delta \lambda(T) \sim T^\alpha$ power-law temperature dependence for the magnetic penetration depth for $T\le T_c/3$ with $\alpha < 2$, which is inconsistent with a single pair of point nodes on the Fermi surface under weak scattering. We also find a similar power-law temperature dependence for the low-temperature surface resistance $R_s(T) \sim T^{\alpha_R}$ with $\alpha_R < 2$. We observe a strong anisotropy of the residual microwave loss across these modes, with some modes showing loss below the universal line-nodal value, to those showing substantially more. We compare to predictions for topological Weyl superconductivity in the context of the observed isotropic power-laws, and anisotropy of the residual loss.