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

TL;DR

This paper develops a realistic band model for YbB$_{12}$ to elucidate the formation of the hybridization gap, providing insights into its electronic structure and properties.

Contribution

It introduces a new tight-binding model based on LDA+U calculations that explains the hybridization gap in YbB$_{12}$ considering orbital degeneracies.

Findings

Energy gap of about 0.001 Ryd obtained from LDA+U calculations.

The tight-binding model agrees well with LDA+U near the gap.

The density of states is highly asymmetric around the gap.

Abstract

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$\epsilon$ and 4f $\Gamma_8$ 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$_{12}$.