Over the past decade, strain tuning of the unconventional superconductor Sr$_2$RuO$_$ has attracted considerable interest. ARPES measurements (Sunko et al.) have shown that Sr$_2$RuO$_4$ undergoes a Lifshitz transition under uniaxial strain, bringing a van Hove singularity (vHS) to the Fermi level at optimal compression. This transition strongly impacts physical properties, most notably enhancing the superconducting transition temperature $T_c$ from 1.5 K to 3.5 K. While often regarded as a purely electronic effect, it is also strongly coupled to the lattice, as evidenced by the pronounced softening of Young’s modulus at low temperatures (Noad et al.).

To probe the electron–phonon coupling (EPC) in a momentum-resolved manner, we performed inelastic x-ray scattering (IXS) on strained Sr$_2$RuO$_$. We observe a substantial softening of an acoustic phonon and uncover a pronounced $q$-dependence, indicating anisotropic EPC tuning by strain.

Complementary strain-dependent micro-Raman measurements provide access to symmetry-resolved electronic scattering rates. In XX and YY polarization configurations—equivalent in the unstrained tetragonal phase—we observe a clear dichotomy across the Lifshitz transition, with signatures of the two vHS points appearing selectively in only one configuration.

We further develop a focused ion beam (FIB) microstructuring approach to induce strain via controlled bending, generating a static strain gradient spanning compressive and tensile regimes. Exploiting the micron-sized spatial resolution of micro-Raman spectroscopy, we map the strain dependence within a single sample and identify clear signatures of the Lifshitz transition under tensile strain.