Manifestation of the Hexatic Phase in Confined Two-Dimensional Systems with Circular Symmetry

Quasi-two-dimensional systems play an important role in the manufacture of various devices for the needs of nanoelectronics. Obviously, the functional efficiency of such systems depends on their structure, which can change during phase transitions under the influence of external conditions (e.g., temperature). Until now, the main attention has been focused on the search for signals of phase transitions in continuous two-dimensional systems. One of the central issues is the analysis of conditions for the nucleation of the hexatic phase in such systems, which is accompanied by the appearance of defects in the Wigner crystalline phase at a certain temperature. However, both practical and fundamental questions arise about the critical number of electrons at which the symmetry of the crystal lattice in the system under consideration will begin to break and, consequently, the nucleation of defects will start. The dependences of the orientational order parameter and the correlation function, which characterize topological phase transitions, as functions of the number of particles at zero temperature have been studied. The calculation results allow us to establish the precursors of the phase transition from the hexagonal phase to the hexatic one for N = 92, 136, and 187 considered as an example.