Electron-boson mode coupling and the pseudogap of Na$_x$CoO$_2$ by   infrared spectroscopy
  We report the in-plane optical measurements on Na$_x$CoO$_2$ with 0.18$\leq$x$\leq$0.92. The crystal growth and characterization were described in detail. The spectral weight increases monotonically with decreasing x. For sample with the lowest Na content x$\sim$0.18, the optical conductivity was strongly suppressed below 2200 $cm^{-1}$ at low temperature. The suppression becomes weaker with increasing Na content, and disappears in charge-ordered sample with x$\sim$0.5. At higher Na contents, similar suppression appears again but locates at higher energy scale near 3300 $cm^{-1}$. Our analysis indicates that those spectral features are dominated by a combination of electrons coupling to a bosonic mode and a pseudogap-like phenomenon. We suggest that the pseudogap-like phenomenon is purely a band structure effect. The infrared activated phonon modes were discussed in relation with the structural geometries. 
D. Wu, J. L. Luo, and N. L. Wang