Optical conductivity of Yb1-xLuxB12 : Energy gap and mid-infrared peak in diluted Kondo semiconductors

We have measured the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ of ${\mathrm{Yb}}_{1\ensuremath{-}x}{\mathrm{Lu}}_{x}{\mathrm{B}}_{12}$ $(0l~xl~1),$ where the system evolves from a Kondo semiconductor at $x=0$ to a nonmagnetic metal at $x=1.$ For $x=0,$ $\ensuremath{\sigma}(\ensuremath{\omega})$ exhibits a clear energy gap with an onset at $\ensuremath{\sim}20 \mathrm{meV}$ and a shoulder at 38 meV. As x increases, the gap is rapidly filled in from the bottom, while the shoulder remains at $\ensuremath{\sim}40 \mathrm{meV}$ up to $x=\frac{1}{2}.$ These results suggest that Lu substitution into ${\mathrm{YbB}}_{12}$ produces an in-gap band, but the characteristic energy for the gap remains unchanged in a wide range of x. Spectral evolutions of a characteristic mid-infrared peak, which results from Yb $4f$-derived states near the Fermi level, suggest a strong coupling of Yb $4f$ electrons with conduction electrons.