The collectiveelementaryexcitationsoftwo-dimensionalmagnetoexcitonsinaBose–Einsteincon- densate(BEC)withwavevector k ! ¼ 0 wereinvestigatedintheframeworkoftheBogoliubovtheoryof quasi-averages.TheHamiltonianoftheelectronsandholeslyinginthelowestLandaulevels(LLLs) containssupplementaryinteractionsduetovirtualquantumtransitionsoftheparticlestotheexcited Landaulevels(ELLs)andback.Asaresult,theinteractionbetweenthemagnetoexcitonswith k ! ¼ 0 does notvanishandtheirBECbecomesstable.Theenergyspectrumcontainsonlyonegapless,true Nambu–Goldstone(NG)modeofthesecondkindwithdependence oðkÞ  k2 at smallvalues k describingtheoptical-plasmon-typeoscillations.Therearetwoexciton-typebranchescorresponding to normalandabnormalGreen’sfunctions.Bothmodesaregappedwithroton-typesegmentsat intermediaryvaluesofthewavevectorsandcanbenamedasquasi-NGmodes.Thefourthbranchisthe acousticalplasmon-typemodewithabsoluteinstabilityintheregionofsmallandintermediaryvalues of thewavevectors.Allbrancheshaveasaturation-typedependenciesatgreatvaluesofthewave vectors.ThenumberandthekindofthetrueNGmodesareinaccordancewiththenumberofthe brokensymmetryoperators.
Solid StateCommunications155(2013)57–61