The infrared conductivity of Na$_x$CoO$_2$: evidence of gapped states

Abstract

We present infrared ab-plane conductivity data for the layered cobaltate Na$_x$CoO$_2$ at three different doping levels ($x=0.25, 0.50$, and 0.75). The Drude weight increases monotonically with hole doping, $1-x$. At the lowest hole doping level $x$=0.75 the system resembles the normal state of underdoped cuprate superconductors with a scattering rate that varies linearly with frequency and temperature and there is an onset of scattering by a bosonic mode at 600 \cm. Two higher hole doped samples ($x=0.50$ and 0.25) show two different-size gaps (110 \cm and 200 \cm, respectively) in the optical conductivities at low temperatures and become insulators. The spectral weights lost in the gap region of 0.50 and 0.25 samples are shifted to prominent peaks at 200 \cm and 800 \cm, respectively. We propose that the two gapped states of the two higher hole doped samples ($x$=0.50 and 0.25) are pinned charge ordered states.