Freezing and reentrant melting of hard disks in a one-dimensional potential: Predictions based on a pressure-balance equation

Abstract

We investigate theoretically the freezing behavior of a two-dimensional system of hard disks on a one-dimensional external potential (typically called laser-induced freezing). As shown by earlier theoretical and numerical studies, one observes freezing of the modulated liquid upon increase of the substrate potential amplitude, and reentrant melting back into the modulated liquid when the substrate potential amplitude is increased even further. The purpose of our present work is to calculate the freezing and reentrant melting phase diagram based on information from the bulk system. To this end, we employ an integrated pressure-balance equation derived from density functional theory [Phys. Rev. E 101, 012609 (2020)2470-004510.1103/PhysRevE.101.012609]. Furthermore, we define a measure to quantify the influence of registration effects that qualitatively explain reentrant melting. Despite severe approximations, the calculated phase diagram shows good agreement with the known phase diagram obtained by Monte Carlo simulations.