Exchange-driven self-diffusion of nanoscale crystalline parahydrogen clusters on graphite

TL;DR

This work investigates whether quantum exchanges can sustain mobility in nanoscale parahydrogen clusters adsorbed on a highly corrugated graphite surface. Using the canonical continuous-space Worm Algorithm to simulate clusters up to $N=16$ at temperatures down to $30$ mK, the study quantifies superfluid response and center-of-mass diffusion through the imaginary-time diffusion coefficient $D(\tau)$ and the plateau behavior of $\delta(\tau) = D_F(\tau)/D(\tau)$, alongside exchange probabilities $P_{ex}$. It finds that clusters with $8 \le N \le 12$ exhibit crystalline order coexisting with robust quantum exchanges (a nanoscale supersolid), and crucially, undergo self-diffusion across the substrate driven by coordinated exchanges; clusters with $N=7$ show suppressed exchanges and $N \ge 13$ have negligible exchanges. This exchange-driven mobility contrasts with behavior observed in bulk p-H$_2$ and with $^4$He clusters on graphite, and it suggests experimental signatures accessible via surface probes such as STM.

Abstract

Computer simulations yield evidence of superfluid behavior of nanoscale size clusters of parahydrogen adsorbed on a graphite substrate at low temperature ($T\lesssim 0.25 \text{ K}$). Clusters with a number of molecules between 7 and 12 display concurrent superfluidity and crystalline order, reflecting the corrugation of the substrate. Remarkably, it is found that specific clusters with a number of molecules ranging between 7 and 12 self-diffuse on the surface like free particles, despite the strong pinning effect of the substrate. This effect is underlain by coordinated quantum-mechanical exchanges of groups of identical molecules, i.e., it has no classical counterpart.

Figures (4)

• Figure 1: Molecular density maps (obtained from particle world lines) for representative configurations of a ($p$-H$_2$)$_N$ cluster adsorbed on graphite at a temperature $T=0.125$ K. Maps shown are for $N=6$ (top left), $N=6$without quantum exchanges (top right), $N=7$ (bottom left), and $N=13$ (bottom right). Dots arranged on a hexagonal lattice represent the top layer of carbon atoms on the graphite substrate (nearest-neighbor distance is 1.42 Å.)
• Figure 2: Radially averaged 2D particle density for the $N=6$ and $N=7$ clusters as a function of distance from the center of mass. For $N=6$, the consistent density of molecules throughout the cluster indicates a fluid-like lack of structure. For $N=7$, the high-peaked oscillations separated by a region of zero density indicate an orderly solid-like structure.
• Figure 3: Molecular density maps (obtained from particle world lines) for representative configurations of a ($p$-H$_2$)$_{12}$ cluster adsorbed on graphite at a temperature $T=0.0625$ K (top left), $T=0.125$ K (top right), $T=0.25$ K (bottom left), and $T=1$ K (bottom right). Dots arranged on a hexagonal lattice represent the top layer of carbon atoms on the graphite substrate (nearest-neighbor distance is 1.42 Å.)
• Figure 4: The quantity $\delta(\tau)$ defined in text for clusters of $N=6, 7, 12,$ and $13$$p$-H$_2$ molecules plotted against imaginary time at $T=0.125$ K.