PHYSICAL REVIEW B 85, 205144 (2012) Treatment of carrier scattering in quantum dots beyond the Boltzmann equation Alexander Steinhoff, 1 Paul Gartner, 1,2 Matthias Florian, 1 and Frank Jahnke 1 1 Institute for Theoretical Physics, University of Bremen, 28334 Bremen, Germany ∗ 2 National Institute of Materials Physics, Bucharest-Magurele, Romania (Received 14 March 2012; published 29 May 2012) As quantum dots (QD) can confine a small number of carriers in localized states with discrete energies, it is questionable to neglect correlations between the carriers when describing their dynamics. We analyze the influence of carrier correlations in a single QD on Coulomb scattering processes, which are due to the contact with a quasicontinuum of wetting-layer (WL) states. Results obtained from a Boltzmann equation are compared with the fully correlated dynamics governed by a von Neumann–Lindblad equation. In a first step, we take into account correlations generated by the exact treatment of Pauli blocking due to the contributing QD carrier configurations. Subsequently, we include correlations generated by energy renormalizations due to Coulomb interaction between the QD carriers. It is shown that at low WL carrier densities, neither Pauli correlations nor Coulomb correlations can be safely neglected, if the dynamics of single-particle states in the QD are to be predicted qualitatively and quantitatively. In the high-density regime, both types of correlations play a lesser role and thus a description of carrier dynamics by a Boltzmann equation becomes reliable. Furthermore, the efficiency of WL-assisted scattering processes as well as scattering-induced dephasing rates depending on the WL carrier density are discussed. DOI: 10.1103/PhysRevB.85.205144 PACS number(s): 73.21.La, 78.67.Hc I. INTRODUCTION Self-assembled semiconductor quantum-dot (QD) structures 1 play an important role as active material in new light-emitting devices with improved emission properties. 2 In addition to their use in conventional laser diodes or microcavity lasers, 3–6 single QDs have established their role as efficient nonclassical light sources 7–10 with applications in quantum information. Common to QD devices is the excitation of electrons and holes into higher states, for self-assembled QD structures typically into delocalized states. Efficient light emission from the QD ground state requires fast carrier capture into the localized states and rapid carrier relaxation within the QD. The dephasing associated with the carrier scattering plays an important role in the homogeneous QD linewidth, 2 for the photon statistics of single-QD emitters, 11 and for the decoherence of quantum information stored in electronic QD excitations. Due to their direct relevance for various QD applications, in the past two decades carrier scattering processes in QD systems have been studied intensively both in experiment 12–19 and theory. 20–28 Detailed information about the carrier dynamics is experimentally accessible, for instance, via two-color pump- probe spectroscopy, allowing for time-resolved differential transmission, in combination with time-integrated photolu- minescence measurements. 17 While differential transmission is sensitive to the population of a confined QD shell with holes, electrons, or both simultaneously, photoluminescence can only account for the latter case, as recombination of an electron-hole pair is required. Furthermore, the effect of Coulomb interaction in multiexciton complexes becomes vis- ible by opening additional absorption and emission channels at renormalized energies, which are indicated by negative differential transmission signals and additional lines in the photoluminescence spectrum. 18 Thus, from the experimental side, it is possible to identify contributions of different excited QD configurations. This leads to the question as to what extent the QD carrier dynamics can be described in terms of one-particle occupation probabilities that are averaged over the QD ensemble and/or over repeated measurements, or whether the system needs to be described in terms of many-body configurations. Related to this is the importance of carrier correlations and their inclusion in the theoretical models. The usual understanding is that as long as the relevant electronic states reside in a large Hilbert space, such as a quasicontinuum of states, approximate treatments of carrier correlations are possible. On the other hand, when only a small number of discrete electronic states contribute, the full configuration interaction becomes important. Self-organized QDs form a hybrid system since a finite and usually small number of localized electronic states with discrete energies is interacting with a quasicontinuum of delocalized electronic states. The latter is due to the energetically nearby (two- dimensional) wetting-layer (WL) and (three-dimensional) bulk barrier states. For the characterization of the system, observables of central interest are single-particle expectation values, such as occupation probabilities of electrons and holes f e α = 〈e † α e α 〉 and f h α =〈h † α h α 〉, respectively, or transition amplitudes between single-particle states  α,β =〈e † α h β 〉, which have been formulated with creation and annihilation operators in the electron-hole picture. In the interacting system, the dynamics of f e,h α and  α,β generally depends on correlations between the carriers, as can be seen from solving the corresponding Heisen- berg equations of motion with the Coulomb Hamiltonian. 29 A whole class of approximations can be used to express the many-body interaction in terms of single-particle expectation values: Hartree-Fock (mean-field), screened Hartree-Fock, or second-order Born approximations. The latter leads to Boltzmann-type kinetic equations for the occupation dynamics if the quasiparticle and Markov approximation are applied. 30 205144-1 1098-0121/2012/85(20)/205144(15) ©2012 American Physical Society