Physica E 13 (2002) 309–312 www.elsevier.com/locate/physe Polaron couplings in quantum dot molecules O. Verzelen * , R. Ferreira, G. Bastard LPMC ENS, 24 rue Lhomond F75005 Paris, France Abstract We report on the calculation of polaron energies in InAs quantum dot molecules. Polaron eects are larger in vertical than in lateral molecules. The far-infrared absorption associated with molecular polaron transitions is calculated. It may show prominent lines associated with inter-dot polaron transitions. We have also calculated the polaron relaxation time to thermodynamical equilibrium when its lifetime is limited by the decay of its phonon component due to crystal anharmonicity. ? 2002 Elsevier Science B.V. All rights reserved. PACS: 71.38.+i; 73.61.+r Keywords: Polaron; Quantum dot; Relaxation; Electron–phonon interaction 1. Introduction Both experimental and theoretical ndings [1–3] have recently pointed out that electrons and longitu- dinal optical (LO) phonons enter a strong coupling regime in semiconductor quantum dots. This means that the most accurate description of the interacting electrons and LO phonons is not in terms of slightly damped products of electrons and LO phonons states but of coherent admixtures of electron and phonon states: the polarons. Attention was so far focussed on intra-dot eects where the electron–phonon coupling aects only electron states which belong to a given dot. In this paper, we report on the evaluation of the polaron couplings between the electron states which belong to a dot molecule formed by two dierent, vertically displaced, dots. * Corresponding author. Fax: +33-(0)-1-44-32-38-40. E-mail address: olivier.verzelen@ens.fr (O. Verzelen). 2. Polaron eects in vertical dot molecules Let us consider two dots separated by a distance d along the growth (z) axis (see inset Fig. 1). The dot radii (heights) are R u and R ‘ (h u and h ‘ ), respectively. Each dot is modelled by a truncated cone oating on a one monolayer thick (0:333 nm) wetting layer, as ap- proximately realized in the InAs= GaAs self-assembled quantum dots structures. In the following, we shall assume that the dot molecules contain one electron. The conning poten- tial is -V e inthedotsandwettinglayer,andzerointhe GaAs barrier. The barrier edge is taken as the energy zero of the calculations and we take V e =0:4 eV and a carrier eective mass of 0:07m 0 in the following. The LO phonons will be taken bulk-like and dispersion- less: ˜! 0 = 36 meV. This approximation provides an excellent description of the single-dot polarons [1,2]. Fig. 1 shows the tunnel-coupled electron states with zero phonon (solid lines) and one LO phonon (dashed lines), respectively, but no electron–phonon coupling for two dots separated by d = 10 nm. The lower dot 1386-9477/02/$ - see front matter ? 2002 Elsevier Science B.V. All rights reserved. PII:S1386-9477(01)00545-8