Freezing transition in three and two dimensions by the generalized density functional theory

TL;DR

This paper extends density functional theory to two dimensions, enabling the description of the hexatic phase and two-stage melting, and applies it to various 2D systems to analyze phase transitions.

Contribution

The authors develop a generalized DFT capable of describing the hexatic phase and two-stage melting in 2D systems, which traditional DFT cannot handle.

Findings

Derived microscopic expressions for elastic moduli and Frank constant.

Calculated phase boundaries between isotropic liquid, hexatic, and solid phases.

Applied the theory to systems like hard disks and superconducting films.

Abstract

A brief introduction to conventional DFT of 3D freezing is given and some recent results are reviewed. The conventional DFT, however, can not be used in the 2D case, particularly, because it can not describe the hexatic phase -- intermediate phase of 2D melting. We generalize DFT to describe 2D systems and two-stage melting scenario including intermediate hexatic phase. Hexatic phase is characterized by the appearance of bond orientational ordering. Our approach describes this fact in terms of the appearance of nonisotropic part of the two-particle distribution function while one-particle density remains constant. Now we are dealing with the bifurcation of the solution of the equation for the binary distribution function. Microscopic expressions for elastic moduli and the Frank constant of hexatic phase are derived on the base of comparison of distribution functions asymptotic behavior with the results of phenomenological theories. We use our approach for the calculation of the phase boundary between usual isotropic liquid and hexatic phase and slightly modified traditional DFT for the phase boundary between hexatic phase and crystalline solid for a number of 2D systems (hard disks, classical electron crystal, thin superconducting films, Yukawa system etc.)