Interaction of in-plane Drude carrier with c-axis phonon in $\rm PdCoO_2$

We performed polarized reflection and transmission measurements on the layered conducting oxide $\rm PdCoO_2$ thin films. For the ab-plane, an optical peak near $\Omega$ $\approx$ 750 cm$^{-1}$ drives the scattering rate $\gamma^{*}(\omega)$ and effective mass $m^{*}(\omega)$ of the Drude carrier to increase and decrease respectively for $\omega$ $\geqq$ $\Omega$. For the c-axis, a longitudinal optical phonon (LO) is present at $\Omega$ as evidenced by a peak in the loss function Im[$-1/\varepsilon_{c}(\omega)$]. Further polarized measurements in different light propagation (q) and electric field (E) configurations indicate that the Peak at $\Omega$ results from an electron-phonon coupling of the ab-plane carrier with the c-LO phonon, which leads to the frequency-dependent $\gamma^{*}(\omega)$ and $m^{*}(\omega)$. This unusual interaction was previously reported in high-temperature superconductors (HTSC) between a non-Drude, mid-infrared band and a c-LO. On the contrary, it is the Drude carrier that couples in $\rm PdCoO_2$. The coupling between the ab-plane Drude carrier and c-LO suggests that the c-LO phonon may play a significant role in the characteristic ab-plane electronic properties of $\rm PdCoO_2$ including the ultra-high dc-conductivity, phonon-drag, and hydrodynamic electron transport.