The nambu-goldstone modes of bose-einstein condensed two-dimensional magnetoexcitons

Abstract

The collective elementary excitations of the two-dimensional (2D) electron-hole systems in a strong perpendicular magnetic field are discussed from the point of view of the Bogoliubov [1]and Goldstone [2] theorems concerning the many-body Hamiltonian with continuous symmetries,continuously degenerate ground states, forming a ring of minima on the energy scale in dependence on the phase of the field operator. This system due to the quantum fluctuations does select a concrete ground state with a fixed phase of the field operator forming a ground state with a spontaneously broken continuous symmetry [1-3]. The collective excitation of this new ground state related only with the changes of the field operator phase without changing its amplitude leads to the quantum transitions along the ring of the minima and does not need excitation energy in the long wavelength limit. This type of gapless excitations is referred to as Nambu-Goldstone modes [2-8]. They are equivalent to massless particles in the relativistic physics. The concrete realization of these theorems in the case of 2D magnetoexcitons with direct implications of the plasmon-type excitations side by side with the exciton ones is discussed below in terms of the Bogoliubov [1] theory of quasiaverages.