Raman study of electron-phonon coupling in thin films of LiTi$_2$O$_4$ spinel oxide superconductor

We performed a Raman scattering study of thin films of LiTi$_2$O$_4$ spinel oxide superconductor. We detected four out of five Raman active modes, with frequencies in good accordance with our first-principles calculations. Three T$_{2g}$ modes show a Fano lineshape from 5 K to 295 K, which suggests an electron-phonon coupling in LiTi$_2$O$_4$. Interestingly, the electron-phonon coupling shows an anomaly across the negative to positive magnetoresistance transition at 50 K, which may be due to the unset of other competing orders. The strength of the electron-phonon interaction estimated from the Allens formula and the observed lineshape parameters suggests that the three T$_{2g}$ modes contribute little to superconductivity.