Temperature dependence of the excitation spectrum in the charge-density-wave ErTe$_3$ and HoTe$_3$ systems

We provide optical reflectivity data collected over a broad spectral range and as a function of temperature on the ErTe$_3$ and HoTe$_3$ materials, which undergo two consecutive charge-density-wave (CDW) phase transitions at $T_{CDW1}$= 265 and 288 K and at $T_{CDW2}$= 157 and 110 K, respectively. We observe the temperature dependence of both the Drude component, due to the itinerant charge carriers, and the single-particle peak, ascribed to the charge-density-wave gap excitation. The CDW gap progressively opens while the metallic component gets narrow with decreasing temperature. An important fraction of the whole Fermi surface seems to be affected by the CDW phase transitions. It turns out that the temperature and the previously investigated pressure dependence of the most relevant CDW parameters share several common features and behaviors. Particularly, the order parameter of the CDW state is in general agreement with the predictions of the BCS theory.