This is indeed counterintuitive, I suggest you to carefully check the eigenvalue SC procedure. You can find here a tutorial on that:Applying G₀W₀ slightly increases the gap.
However, when I move toward self-consistency (scGW), the gap closes again, and the system becomes effectively metallic.
https://wiki.yambo-code.eu/wiki/index.p ... alues_only
Kind regards,
Daniele