# How can there be negative energy gaps sandwiching a topological insulator?

At the 37:37 instant of the timeline in this youtube video Stanford University theoretical physicist Shoucheng Zhang presents a graph of "theoretical prediction of the first topological insulator".

In this graph, the vertical axis is 'energy gap (Eg)' and horizontal axis is 'lattice constant (a)', and various 'lattice matched' material combinations are plotted on this graph. Dr. Zhang mentioned the material combination HgTe located below the bottom 0 energy gap red line. He mentioned that this material combination would make possible a negative energy gap.

A google search revealed this article as the closest content to anything on this topic but negative energy gap is nowhere mentioned.

Being an electronics engineer, I understand band gaps and energy gaps in semiconductors. I just can't conceptually fathom what a negative energy gap is, and how is it theoretically possible? I can picture a zero energy gap as something we can get close to as with absolute zero. But a negative energy gap seems to imply in my mind some kind of stored energy as in a battery cell but there is no chemical reaction as in oxidation-reduction to cause the electrical potential difference.

Below the picture from the classical article by Volkov and Pankratov in 1985, where $x$ represents the parameter you vary to put the valence and conduction bands upside down, which I called pressure in my example above, whereas $E$ is the energy of the bands, which you can identify though only their quadratic bottom (for conduction) and upper (for valence) parts appear. The straight lines are guides for the eyes, they represent the displacements of the bottom and top of the bands under the $x$-variation.