True, quasi and unstable Nambu Goldstone modes of the twodimensional Bose Einstein condensed magnetoexcitons

TL;DR

This paper investigates the collective excitations of two-dimensional magnetoexcitons in a Bose Einstein condensate, revealing a true Nambu Goldstone mode and several quasi modes with complex behaviors, using Bogoliubov theory.

Contribution

It introduces a detailed analysis of the elementary excitations in 2D magnetoexcitons BEC, highlighting the existence of a true NG mode and quasi NG modes influenced by virtual Landau level transitions.

Findings

One true gapless Nambu Goldstone mode identified.

Presence of two gapped exciton branches with roton segments.

An unstable acoustical plasmon mode at certain wavevectors.

Abstract

The collective elementary excitations of two dimensional magnetoexcitons in a Bose Einstein condensate with zero wavevector are investigated in the framework of the Bogoliubov theory of quasi averages. The Hamiltonian of the electrons and holes lying in the lowest Landau levels contains supplementary interactions due to virtual quantum transitions of the particles to the excited Landau levels and back. As a result, the interaction between the magnetoexcitons zero wavenumbers does not vanish and their BEC becomes stable. The energy spectrum contains only one gapless,true Nambu Goldstone mode of the second kind, proportional to the square of wavenumber at small values of wavenumber describing the optical plasmon type oscillations. There are two exciton type branches corresponding to normal and abnormal Green functions. Both modes are gapped with roton type segments at intermediary values of the wavevectors and can be named quasi NG modes. The fourth branch is the acoustical plasmon type mode with absolute instability in the region of small and intermediary values of the wavevectors. All branches have a saturation type dependencies at great values of the wave vectors. The number and the kind of the true NG modes are in accordance with the number of the broken symmetry operators.