Normal state electrodynamics of superconducting Cu$_x$Bi$_2$Se$_3$

Using infrared spectroscopy, we have studied the bulk electronic structure of superconducting Cu$_x$Bi$_2$Se$_3$ (x = 0.15, 0.2, 0.3, 0.4), a candidate topological superconductor. The screened plasma frequency is observed to red-shift monotonically with doping, ranging from 198 meV for x = 0.15 to 156 meV for x = 0.4. We have also investigated the effects of electron-boson coupling in this compound. An extended Drude analysis of the free carrier charge dynamics suggests a mass enhancement $m^*/m_b$ of roughly 1.2 for x = 0.2.