Energy Gap Closure of Crystalline Molecular Hydrogen with Pressure

We study the gap closure with pressure of crystalline molecular hydrogen. The gaps are obtained from grand-canonical quantum Monte Carlo methods properly extended to quantum and thermal crystals, simulated by coupled electron ion Monte Carlo methods. Nuclear zero point effects cause a large reduction in the gap (∼2  eV). Depending on the structure, the fundamental indirect gap closes between 380 and 530 GPa for ideal crystals and 330-380 GPa for quantum crystals. Beyond this pressure the system enters into a bad metal phase where the density of states at the Fermi level increases with pressure up to ∼450-500  GPa when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen.