High-pressure melting line of helium from ab initio calculations

We applied two-phase simulations to directly calculate the high-pressure melting line of helium from 425 to 10 000 K and from 15 GPa to 35 TPa by using molecular dynamics based on density-functional theory. The implementation of the two-phase simulation method and the relaxation of the simulation to an equilibrium state was studied in detail, as well as its convergence with respect to particle number. We performed extensive two-phase simulations with the Perdew, Burke and Ernzerhof and the van der Waals density functional exchange-correlation functional and found almost identical results.

Figure 1

Pressure deviations between the PAW pseudopotentials and the Coulomb potential. The pressure that was obtained for the perfect hcp crystal with the full Coulomb potential is shown on the upper $x$ axis. The horizontal dotted line guides the eye.

Figure 2

Convergence of the melting temperature with respect to the number of atoms at a density of 1.6 and 17 g/${\mathrm{cm}}^3$. Shown are results for c-TPS (circles), cr-TPS (crosses), and e-TPS (diamonds). The lower panel demonstrates the necessity to change the k-point sampling at higher densities, see the discussion below.

Figure 3

Helium phase diagram with the TPS results (diamonds) that employed the PBE (blue) and vdW-DF1 (red) XC functional compared with experimental data (orange) [1, 2, 3, 4, 5, 6, 7]. Note that we plotted the data of Ref. [7] as corrected by Ref. [24]. The previous melting line predictions (blue line, black squares, and red circles) [24, 38], the coldest Jupiter adiabat of the preliminary Jupiter model of Hubbard and Militzer [64], the coldest possible adiabatic layer of helium around Saturn's core of Püstow et al. [65], and the coldest P-T profile of white dwarfs of Ref. [66] are displayed as well. The inset shows a magnification of the melting line between 400 and 1000 K. The fit function to our TPS results is depicted as a bold black line.