Coherent A$_{\mathrm{1g}}$ Phonon in thin Film Superconductor FeSe$_{0.5}$Te$_{0.5}$: $\pi $/2 Phase Difference over Superconducting Phase Transition

Coherent $A_{1g}$ phonon mode in a thin film superconductor FeSe$_{0.5}$Te$_{0.5}$ was generated and detected using ultrafast laser pulses. At below and above the transition temperature $T_{\mathrm{c}}$, the coherent lattice oscillation we observed exhibited a $\pi $/2 phase difference, manifesting a ``displacive limit $\sim$ impulsive limit'' transition upon crossing a phase transition within the same sample. We ascribe this $\pi $/2 phase difference to the different lifetimes ($\tau_{\mathrm{c}})$ of excited charge density components that couples to the fully symmetric $A_{1g}$ phonon mode, i.e. the different strength of electron-phonon couplings. In the superconducting and paramagnetic metallic states the lifetimes of such carrier excitations are largely different. Our investigation reveals possible correlation of superconducting electrons with zone-center optical phonons. Our 170nm thin film sample contains tension stress, which leads to enhanced $T_{\mathrm{c}}$ and thus facilitated our measurements.