Physica E 13 (2002) 155–160 www.elsevier.com/locate/physe Polaron states in InAs= GaAs quantum dots: strong electron–phonon coupling regime E.Deleporte a ; * ,S.Hameau a ,J.N.Isaia a ,Y.Guldner a ,O.Verzelen a ,R.Ferreira a , G.Bastard a ,J.Zeman b ,J.M.G erard c a Laboratoire de Physique de la Mati ere Condens ee de l’Ecole Normale Sup erieure, 24 rue Lhomond, 75231 Paris, Cedex 05, France b High Magnetic Field Laboratory, CNRS=MPI, 25 av. des Martyrs, 38042 Grenoble, Cedex 9, France c CNRS-Laboratoire de Photonique et Nanostructures, BP 29, 92225 Bagneux, Cedex, France Abstract We report on the magneto-optical evidence and theoretical modelling of polaron eects in self-assembled InAs= GaAs quantum dots. Using far-infrared magneto-transmission experiments performed up to 28 T at T =2KindopedQDssamples, we investigate the electronic transitions between the ground and rst excited states. We observe very large anticrossings in the B-dispersion of the magneto-optical transitions, whose existence cannot be explained by a purely electronic model. We thus calculate the coupling between the mixed electron-lattice states using the Fr ohlich Hamiltonian and determine the polaron states and the energies of the dipolar electric transitions. An excellent agreement between the calculations and the experimental data is obtained, demonstrating that the magneto-optical transitions occur between polaron states. The time dependence of the survival probability is calculated for the various non-interacting electron–phonon states. Such probabilities are found to oscillate and do not show an exponential decay as it would be the case for a weak coupling regime. This last argument conrms that the electrons and the LO-phonons experience a strong coupling regime in QDs. ? 2002 Elsevier Science B.V. All rights reserved. Keywords: InAs quantum dots; Electron–LO phonon interaction; Polaron eects; Far-infrared magneto-spectroscopy The investigations of the conned states in self-assembled semiconductor quantum dots (QDs) have attracted recently considerable attention. Semi- conductor QDs, like articial atoms, display discrete energy levels. For electrons (or holes) placed in ex- cited levels, the spontaneous emission of photons is inecient for the relaxation due to the characteris- tic energy splitting of the dot states (∼ 50 meV for the electron states in a ∼ 20 nm dot). The carriers ∗ Corresponding author. Tel.: +33-1-44-32-34-49; fax: +33- 1-44-32-38-40. E-mail address: emmanuelle.deleporte@lpmc.ens.fr (E. Deleporte). bound to the QDs are, however, in interaction with phonons which display a continuum of nite width. The LA-phonons are inecient for the relaxation of the electron energy [1], the energy between elec- tron states being too large. The longitudinal optical (LO) phonons play a decisive part in semiconductor physics. In bulk (3D), quantum well (2D) or quan- tum wire (1D) structures, the irreversible emission of LO-phonons is the most ecient process for the relaxation of electrons placed in excited levels as the electron–LO-phonon interaction corresponds to a weak coupling regime. On contrary in QDs, because the LO-phonons have a very little energy disper- sion, it has been suggested both theoretically [2] and 1386-9477/02/$-see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII:S1386-9477(01)00509-4