Manifestation of the hexatic phase in confined two-dimensional systems with circular symmetry

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Abstract

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 (for example, 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 the 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 allows us to establish the precursors of the phase transition from the hexagonal phase to the hexatic one for N = 92, 136, 187, considered as an example.

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About the authors

E. G. Nikonov

Joint Institute for Nuclear Research; National Research University Higher School of Economics; Dubna State University

Author for correspondence.
Email: e.nikonov@jinr.ru
Russian Federation, 141980, Dubna; 119048, Moscow; 141980, Dubna

R. G. Nazmitdinov

Joint Institute for Nuclear Research; Dubna State University

Email: e.nikonov@jinr.ru
Russian Federation, 141980, Dubna; 141980, Dubna

P. I. Glukhovtsev

Joint Institute for Nuclear Research; Dubna State University

Email: e.nikonov@jinr.ru
Russian Federation, 141980, Dubna; 141980, Dubna

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Supplementary files

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2. Fig. 1. Distribution of defects with a nonzero orientation parameter of order for a system of point electrons in a circular region with an infinite rigid boundary. The dark dots represent electrons with a parameter of the order Ψ6(rk) = 0, the light ones represent electrons with a nonzero parameter of the order.

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3. Fig. 2. Distribution of the topological charge for the number of particles N: a – 92; b – 136; c – 187.

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4. Fig. 3. Distribution of the orientation order of the bond ψ6 (5) for the number of particles N: a – 92; b – 136; c – 187.

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5. Fig. 4. Orientation correlation function G6(r) (9) for the number of particles N: a – 92; b – 136; c – 187.

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