Hydrogen: Whether it's a metal or non-metal

I know hydrogen is a non metal, but when I just study about some introductory elementary band theory I find the band structure of hydrogen has a half filled valence band just like alkali metals, and this should make it conductive. Is there some thing more complex about it or is my understanding is wrong? How can the non metallic nature of hydrogen be explained using band theory?

Solid hydrogen is not made up from hydrogen atoms. It contains hydrogen molecules held together by relatively weak Van der Waals forces. In the hydrogen molecule the two $$1s$$ levels of the atoms form a bonding $$\sigma$$ molecular orbital that is full and an antibonding $$\sigma^*$$ orbital that is empty:
In the solid the $$\sigma$$ level broadens to form a full valence band and the $$\sigma^*$$ level broadens to form an empty conduction band, with a gap of around 15eV between the two bands. That is why solid hydrogen is an insulator.
• They have compressed it (in the form of $H_2 S$) enough to turn it into a BCS superconductor arxiv.org/abs/1506.08190 – tbt May 21 at 18:58