Honestly, I don't think this extrapolation qualifies as evidence for a "negative band gap". That is defined as the result of a certain form of band intersection:

Article Negative-band-gap quantum dots: Gap collapse, intrinsic surf...

I don't think you can find or prove the existence of such a gap without ARPES.

When it comes to the determination of an absolute valence of the band gap, the usefulness of these Tauc plots is very limited. You can use it for a qualitative study, in your case maybe something like "X has a band gap lower than Y", but keep in mind that, depending in the quality of your data and also on what you know about your material, you may introduced an error of 200-300meV easily.

As Jürgen said, use other quantitative methods to substantiate your result. Spectroscopic ellipsometry and modelling is usually working well for me.

Hello Md. Saiduzzaman,

the properties of pyrochlore are unknown for me. Nevertheless, the expression "negative bandgap" even though unusual, seems me explainable:

I know a comparable case for the material Bi. This material is halfmetallic. Halfmetal means, that 2 bands overlap. Here, we have 2 bands with bandextrema at different points at the Brillouinzone. Therefore, 2 bands overlap at different points in momentum space (for Bi: k=0 and L-point). The fermilevel cuts both bands and you have equal concentrations for holes and electrons. Both bands contribute independently to conductivity. Therefore it is a half metal. If you apply strain, a gap opens and you have a semiconductor. In your case - if you add a carbonate group- the gap shifts and can be negatively.

If the bands overlap at the same k-value, you have a metal - semiconductor transition, if the k-values are different, you have a semiconductor - half metal transition.

I recommend to study the energy structure. This helps to explain your effect.

With regard

R. Mitdank