On the spatially periodic ordering in the system of electrons above the surface of liquid helium in an external electric field

TL;DR

This paper develops a quantum statistical theory to describe equilibrium states of electrons above liquid helium, revealing conditions for phase transitions to spatially periodic structures under external electric fields.

Contribution

It introduces a self-consistent theoretical framework combining quantum statistics and the Thomas-Fermi model for this electron-liquid helium system.

Findings

Identifies conditions for phase transition to periodic states.

Derives self-consistency equations linking system parameters.

Analyzes characteristics of the phase transition.

Abstract

A theory of equilibrium states of electrons above a liquid helium surface in the presence of an external clamping field is built based on the first principles of quantum statistics for the system of many identical Fermi-particles. The approach is based on the variation principle modified for the considered system and on Thomas-Fermi model. In terms of the developed theory we obtain the self-consistency equations that connect the parameters of the system description, i.e., the potential of a static electric field, the distribution function of electrons and the surface profile of a liquid dielectric. The equations are used to study the phase transition of the system to a spatially periodic state. To demonstrate the capabilities of the proposed method, the characteristics of the phase transition of the system to a spatially periodic state of a trough type are analyzed.