Optical conductivity of single plane cuprate superconductor HgBa$_2$CuO$_4$

We investigated the ab-plane infrared and visible spectra of a HgBa$_2$CuO$_4$ single crystal close to optimal doping ($T_c = 90$~K) from 100 to 40000 cm$^{-1}$. Data as a function of temperature (down to 30 K) was limited to frequencies below 10000 cm$^{-1}$. The low frequency scattering rate has a linear frequency dependence. Under 120~K a supplementary small drop below 1000 cm$^{-1}$ suggests the presence of a pseudogap. This is the same frequency at which the optical conductivity shows a clear loss of spectral weight in the superconducting state. The low frequency effective mass is temperature dependent and increases from 1.5 at room temperature to 2.5 just above $T_c$. We will compare our results to other single plane cuprates.