Indirect and direct energy gaps in the Kondo semiconductor YbB12

Optical conductivity [$\sigma(\omega)$] of the Kondo semiconductor YbB$_{12}$ has been measured over wide ranges of temperature ($T$=8$-$690 K) and photon energy ($\hbar \omega \geq$ 1.3 meV). The $\sigma(\omega)$ data reveal the entire crossover of YbB$_{12}$ from a metallic electronic structure at high $T$ into a semiconducting one at low $T$. Associated with the gap development in $\sigma(\omega)$, a clear onset is newly found at $\hbar\omega$=15 meV for $T \leq$ 20 K. The onset energy is identified as the gap width of YbB$_{12}$ appearing in $\sigma(\omega)$. This gap in \sigma(\omega)$ is interpreted as the indirect gap, which has been predicted in the band model of Kondo semiconductor. On the other hand, the strong mid-infrared (mIR) peak observed in $\sigma(\omega)$ is interpreted as arising from the direct gap. The absorption coefficient around the onset and the mIR peak indeed show characteristic energy dependences expected for indirect and direct optical transitions in conventional semiconductors.