Second-Order Resonant Polaron in a Self-Assembled Quantum Dot

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A compound system consisting of an electron in a quantum dot (QD) and longitudinal optical (LO) phonons has interesting features that cannot be observed in higher-dimensional semiconductor structures. Because of a relatively large size of the QD (compared to the lattice constant), only long wavelength phonon modes are coupled to the electron. Since the LO phonons are almost dispersionless in the vicinity of the Γ point, these effectively coupled modes can be represented as a system of discrete oscillators, rather than a continuum. As a result of the interaction between the confined electron and the set of LO phonon oscillators with a well-defined frequency, pronounced anticrossings are observed in the intraband absorption spectra of a single dot whenever the energy difference between electron levels matches a multiple of the LO phonon energy [1]. Such resonant polarons are an object of current interest, both from the point of view of their properties in various QD systems as well as of the formal methods that can be used to describe them [2–4]. The spectrum of a resonant polaron can easily be described for a single-phonon (first order) resonance [5]. However, in most self-assembled structures the energy spacing between the electron levels considerably exceeds the LO phonon energy. In fact, resonances observed in experiments performed at moderate magnetic fields occur at the crossing of the electron levels with twice the LO phonon energy. Contrary to the first-order resonance, modeling of two-phonon polaron states is less trivial, since the carrier–phonon interaction has no matrix elements directly coupling the anticrossing states. Thus, the effect