Nature of the metallization transition in solid hydrogen

We present an accurate study of the static-nucleus electronic energy band gap of solid molecular hydrogen at high pressure. The excitonic and quasiparticle gaps of the $C2/c, Pc, Pbcn$, and $P{6}_3/m$ structures at pressures of 250, 300, and 350 GPa are calculated using the fixed-node diffusion quantum Monte Carlo (DMC) method. The difference between the mean-field and many-body band gaps at the same density is found to be almost independent of system size and can therefore be applied as a scissor correction to the mean-field gap of an infinite system to obtain an estimate of the many-body gap in the thermodynamic limit. By comparing our static-nucleus DMC energy gaps with available experimental results, we demonstrate the important role played by nuclear quantum effects in the electronic structure of solid hydrogen.

Figure 1

Top panel: VMC and DMC energies of the $C2/c$ structure at 250 GPa. Various wave functions were used as explained in the text. Total energies were calculated at the $\mathrm{\Gamma }$ point of a simulation cell containing 288 atoms. Bottom panel: VMC and DMC energies relative to their values calculated using a SJ($1b+2b$) wave function. The incorporation of BF significantly improves the DMC total energy.

Figure 2

DMC scissor-corrected DFT-BLYP band structures of the $C2/c$ phase at pressures $P=250$, 300, and 350 GPa. The dashed line shows the Fermi energy.

Figure 3

As Fig. 2, but for the $Pc$ phase at pressures $P=250$, 300, and 350 GPa.

Figure 4

As Fig. 2, but for the $Pbcn$ phase at pressures $P=250$, 300, and 350 GPa.

Figure 5

As Fig. 2, but for the $P{6}_3/m$ phase at pressures $P=250$, 300, and 350 GPa.

Figure 6

DFT energy gap as a function of molecular bond length for the $P{6}_3/m$ phase at fixed density. The results are calculated using the BLYP, PBE, and vdW-DF functionals.

Figure 7

Static-nucleus DMC energy gaps for the $C2/c, Pc, Pbcn$, and $P{6}_3/m$ structures against pressure $P$. References (a) [57], (b) [11], (c) [18], and (d) [7] are energy gaps at different $P$ ($\pm 3$ GPa) reported by experiments.