Energy Gap Closure of Crystalline Molecular Hydrogen with Pressure*

We study the gap closure with pressure in Phases III and IV of molecular crystalline hydrogen by Quantum Monte Carlo methods [1]. Nuclear quantum and thermal effects are considered from first principles with Coupled Electron Ion Monte Carlo. The fundamental electronic gaps are obtained from grand-canonical Quantum Monte Carlo methods [2] properly extended to quantum crystals. Nuclear zero point effects cause a large reduction in the gap (~2eV ). As a consequence the fundamental gap closes at 530GPa for ideal crystals while at 360GPa for quantum crystals. Since the direct gap remains open until ~450GPa, the emerging scenario is that upon increasing pressure in phase III (C2/c-24 crystal symmetry) the fundamental (indirect)gap closes and the system enters into a bad metal phase where the density of states at the Fermi level increases with pressure up to ~450GPa when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen.
[1] Phys. Rev. Letts.1 24, 116401 (2020)
[2] Phys. Rev. B 101, 085115 (2020)