Supplyment to the article"Interband optical conductivities in two-dimensional tilted Dirac bands revisited within the tight-binding model"

We identified four characteristic critical frequencies in the interband LOCs of the TB model: the conventional critical frequencies, the partner frequencies, the sharp-peak frequency, and the cutoff frequency.

The latter three types are consistently absent in the corresponding linearized k⋅p model. Notably, the sharp-peak frequency and cutoff frequency remain robust against variations in band tilting and Dirac-point shifting. By employing analytical expressions derived via the Lagrange multiplier method, we elucidate the origins of the conventional critical frequencies and their partner counterparts.