Formation Mechanism of Hybridization Gap in Kondo Insulators based on a Realistic Band Model and Application to YbB${}_{12}$

A new LDA+U band calculation is performed on the Kondo insulator material YbB${}_{12}$ and an energy gap of about 0.001Ryd is obtained. Based on this, a simple tight-binding model with 5d$ϵ$ and 4f ${\mathrm{\Gamma }}_8$ orbitals on Yb atoms and the nearest neighbor $\sigma$-bonds between them is constructed with a good agreement to the above the LDA+U calculation near the gap. The density of states is also calculated and the shape is found to be very asymmetric with respect to the gap. A formation mechanism of the gap is clarified for the first time in a realistic situation with the orbital degeneracies in both conduction bands and the f states. This model can be a useful starting point for incorporating the strong correlation effect, and for understanding all the thermal, thermoelectric, transport and magnetic properties of YbB${}_{12}$.