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Theory of electronphonon interaction in the quantum Hall regimeThe quantum Hall effect (QHE) is the most fascinating physical phenomenon in lowdimensional systems, and its discovery resulted in the awarding of two Nobel Prizes. Despite extensive worldwide research in this field there are still many unanswered questions related to both fractional and integer quantum Hall effects. Being an essentially quantum phenomenon, the QHE is observed in twodimensional systems at extremely low temperatures and high magnetic fields. However, there are several unanswered questions relating to the disappearance of the QHE with increasing temperature, decreasing magnetic field, and increasing width of the quasi twodimensional electron layer. Under these conditions the interaction between electrons and crystal lattice vibrations (phonons), which is usually suppressed in the quantum Hall regime, becomes significant. This attracted our attention to the electronphonon interaction in the QHE regime and suggested a set of problems to be addressed.Firstly, we considered electronphonon interaction in twosubband quasitwodimensional systems in quantising magnetic fields. In such systems it is possible to tune the energy separation between Landau levels corresponding to different sizequantisation subbands. There is a strong enhancement of electronphonon interaction when the interlevel separation is close to the energy of the acoustic phonon with wavevector of the order of the inverse magnetic length. We carefully studied this resonance phenomenon and predicted Rabilike oscillations of electron populations in the presence of nonequilibrium phonons [21]. We have also shown the essence of manyelectron effects in the same system, and have created a theory of phonon magnetospectroscopy of manyelectron fewsubband systems at different filling factors. The opening of manybody gaps at odd filling factors [29] and the prospect of phonon spectroscopy of quantum Hall ferromagnets at even filling factors [24] were both considered. Another problem we considered was related to phononassisted recombination of both interband and intraband magnetoexcitons [26,32]. For interband excitons the photoluminescence has a single slightly asymmetric line with the width saturating with increasing temperature. This linewidth saturation results from the suppression of the absorption or emission of phonons with momenta exceeding the inverse magnetic length. For intraband excitons, we predicted a double peak of the emission line when the electron filling factor is odd, and greater than or equal to three. In the latter case the lowest magnetoexciton dispersion curve has a minimum at nonzero momentum. Then, the higherenergy peak results from the direct optical emission of zeromomentum excitons. The origin of the lowerenergy peak is the phononassisted transition from the nonzero momentum exciton states. With increasing temperature, the higherenergy peak becomes more pronounced and the lowerenergy peak vanishes. With increasing well width the separation between the lines becomes smaller, and the temperature at which the lowerenergy peak can be observed is decreased. Finally, we have predicted that direct cyclotron absorption in this system at very low temperature results in the generation of nonequilibrium phonons, which becomes suppressed with increasing temperature. Phonon absorption spectroscopy has recently been applied to probe magnetoroton dispersion in the fractional quantum Hall regime. Whilst the mechanism of magnetoroton creation by absorption of a nonequilibrium phonon was well understood, the mechanism of magnetoroton dissociation into unbound quasiparticles remained a mystery. A singlephonon process could not dissociate a magnetoroton due to restrictions imposed by the energy and momentum conservation laws. However, dissociation is necessary to produce a signal in the dissipative conductivity, which is measured in phonon absorption spectroscopy experiments. We have resolved this puzzle and calculated the rate of magnetoroton dissociation for different fractional filling factors [27,32]. We have shown that the phononpulseinduced dissociation of the magnetoroton occurs as a secondorder process in the electronphonon interaction. Depending on the temperature of the twodimensional electron gas, the magnetoroton decay can be considered either as a direct twophonon dissociation or as the result of the twophonon diffusion of a quasiexciton in momentum space. This part of our research provides the basis for our planned future work on magnetorotonassisted recombination of fewparticle anyon excitons in the fractional quantum Hall regime. Our work on electronphonon interaction in the quantum Hall regime was supported by a twoyear EPSRC research grant, which resulted in eight journal publications and several conference presentations. A number of other papers are currently in preparation. The projects final report received an excellent response from both referees and the panel. One of the objectives of this project was to explain puzzling temperature dependence of the highcurrent breakdown of the quantum Hall effect observed at Exeter University by the experimental team of Dr Alan Usher. We found out that this dependence resulted from a nonuniform distribution of induced charges [36,41,43] and had nothing to do with electronphonon interaction. This work led to a very close and fruitful ongoing collaboration between our theoretical team and one of the School's most successful experimental groups. 