Calculation of the Exchange Constant in 2D Wigner Liquid

Abstract

The recent observation of a two-dimensional (2D) metal–insulator transition in semiconductor devices and the strong influence of a magnetic field on the metallic phase has attracted a great deal of interest. This gives rise to the important theoretical question about the nature and the magnetic order of insulating and conducting phases. In the present paper we calculate (both analytically and numerically) the exchange constant for a two-dimensional Wigner liquid— the state with destroyed long-range order but preserved short-range order. It is demonstrated that there is an antiferromagnetic spin–spin interaction between nearest electrons. We also discuss a possible pairing of the electrons in a 2D Wigner crystal by the spin-Peierls mechanism.