Negatively enhanced thermopower near a Van Hove singularity in electron-doped Sr$_2$RuO$_4$

The layered perovskite Sr$_2$RuO$_4$ serves as a model material of the two-dimensional (2D) Fermi liquid but also exhibits various emergent phenomena including the non-Fermi-liquid (NFL) behavior under external perturbations such as uniaxial pressure and chemical substitutions. Here we present the thermoelectric transport of electron-doped system Sr$_{2-y}$La$_{y}$RuO$_4$, in which a filling-induced Lifshitz transition occurs at the Van Hove singularity (VHS) point of $y\approx 0.2$. We find that the sign of the low-temperature thermopower becomes negative only near the VHS point, where the NFL behavior has been observed in the earlier work. This observation is incompatible with either a numerical calculation within a constant relaxation-time approximation or a toy-model calculation for the 2D Lifshitz transition adopting an elastic carrier scattering. As a promising origin of the observed negatively enhanced thermopower, we propose a skewed NFL state, in which an inelastic scattering with a considerable odd-frequency term plays a crucial role to negatively enhance the thermopower.