Open AccessA two–dimensional electron–hole system under the influence of the Chern–Simons gauge field created by quantum point vortices
Author(s) -
S. A. Moskalenko,
V. A. Moskalenko,
I. V. Podlesny,
Michael A. Liberman
Publication year - 2021
Publication title -
moldavian journal of the physical sciences
Language(s) - English
Resource type - Journals
eISSN - 2537-6365
pISSN - 1810-648X
DOI - 10.53081/mjps.2021.20-1.01
Subject(s) - physics , gauge theory , quantum mechanics , quantum electrodynamics , quantum hall effect , electron , condensed matter physics , mathematical physics
In the present work, the Chern–Simons (CS) gauge field theory developed by Jackiw and Pi [8] and widely used to interpret the fractional quantum Hall effects, is applied to describe a two-dimensional (2D) electron–hole (e–h) system in a strong perpendicular magnetic field and under the influence of quantum point vortices creating the CS gauge field. Composite particles formed by electrons and holes with equal integer positive numbers Ø of attached quantum point vortices are described by dressed field operators, which obey the Fermi or Bose statistics depending on even or odd numbers Ø . It is shown that the phase operators, as well as the vector and scalar potentials of the CS gauge field, depend on the difference between the electron and hole density operators. They vanish in the mean field approximation, when the average values of electron and hole densities coincide. Nevertheless, even in this case, the quantum fluctuations of the CS gauge field lead to new physics of the 2D e–h system.