Title : Energy gap closure of crystalline molecular hydrogen with pressure
Abstract : We study the gap closure with pressure of crystalline molecular hydrogen. The gaps are obtained by a novel grand-canonical Quantum Monte Carlo method with twisted boundary conditions properly extended to quantum and thermal crystals, simulated by Coupled Electron Ion Monte Carlo. Nuclear zero point effects cause a large reduction in the gap ($\sim 2eV$). Depending on the structure, the fundamental indirect gap closes between 380GPa and 530GPa for ideal crystals and 330-380GPa 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 $\sim$450-500 GPa when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen.