Hexatic phase and cluster crystals of two-dimensional GEM4 spheres

TL;DR

This paper investigates the phase behavior of two-dimensional GEM4 spheres, revealing a sequence of melting from a crystal to a hexatic phase and then to a cluster phase, highlighting the effects of low dimensionality and potential softness.

Contribution

It introduces a combined density-functional and free-energy approach to study 2D GEM4 systems, identifying multiple cluster crystal phases and their melting behavior.

Findings

The 2D GEM4 system exhibits multiple cluster crystal phases.

Only the ordinary crystal transitions directly to a hexatic phase.

Cluster phases merge into a single phase at high temperature.

Abstract

Two-dimensional crystals of classical particles are very peculiar in that melting may occur in two steps, in a continuous fashion, via an intermediate hexatic fluid phase exhibiting quasi-long-range orientational order. On the other hand, three-dimensional spheres repelling each other through a fast-decaying bounded potential of generalized-exponential shape (GEM4 potential) can undergo freezing into cluster crystals, allowing for more that one particle per lattice site. We hereby study the combined effect of low spatial dimensionality and extreme potential softness, by investigating the phase behavior of the two-dimensional (2D) GEM4 system. Using a combination of density-functional theory and numerical free-energy calculations, we show that the 2D GEM4 system displays one ordinary and several cluster triangular-crystal phases, and that only the ordinary crystal first melts into a hexatic phase. Upon heating, the difference between the various cluster crystals fades away, eventually leaving a single undifferentiated cluster phase with a pressure-modulated site occupancy.