Prediction of a Supersolid Phase in High-Pressure Deuterium

Supersolid is a mysterious and puzzling state of matter whose possible existence has stirred a vigorous debate among physicists for over 60 years. Its elusive nature stems from the coexistence of two seemingly contradicting properties, long-range order and superfluidity. We report computational evidence of a supersolid phase of deuterium under high pressure ($p>800\mathrm{GPa}$) and low temperature ($T<1.0\mathrm{K}$). In our simulations, that are based on bosonic path integral molecular dynamics, we observe a highly concerted exchange of atoms while the system preserves its crystalline order. The exchange processes are favored by the soft core interactions between deuterium atoms that form a densely packed metallic solid. At the zero temperature limit, Bose-Einstein condensation is observed as the permutation probability of $N$ deuterium atoms approaches $1/N$ with a finite superfluid fraction. Our study provides concrete evidence for the existence of a supersolid phase in high-pressure deuterium and could provide insights on the future investigation of supersolid phases in real materials.

Figure 1

Atomic density of high-pressure deuterium solid with exchange. Two-dimensional (2D) cross sections of the atomic density $n(r)$ of high-pressure deuterium in path integral molecular dynamics (PIMD) (a)–(c) and bosonic path integral molecular dynamics (PIMDB) (d)–(f) simulations at $p=800\mathrm{GPa}$ and $T=0.5\mathrm{K}$. While the ring polymers of PIMD simulation are always closed form (a)–(c), the PIMDB simulations allow deuterium atoms to exchange (d)–(f).

Figure 2

Exchange effect on the geometry and electronic properties of high-pressure deuterium. (a) A snapshot taken from the ($N\times P$) trajectory of PIMDB simulations at $T=0.5\mathrm{K}$ and $p=800\mathrm{GPa}$. Each blue sphere represents a one bead of a ring polymer (in total $P=256$ beads and $N=128$). (b) Structure factors $S(q)$ of high-pressure deuterium from the MD (green line), PIMD (blue line), and PIMDB (red line) simulations. The amplitude of omitted $S(q)$ peak (*) of the MD simulation (green) is 14.9. (c) Radial distribution functions $g(r)$ of high-pressure deuterium from the MD (green line), PIMD (blue line), and PIMDB (red line) simulations. (d) The density of states (red points) and inverse participation ratio (green bars) of a supersolid phase. The Fermi level ($E_F$) is set to zero (cyan dashed line).

Figure 3

The superfluid fraction of high-pressure deuterium. The superfluid fraction (red points with error bar) at $p=800\mathrm{GPa}$ as the function of temperature with a guiding line (dotted gray line).