Quantum-Kinetic Effects in the Linear Optical Response of GaAs Quantum Wells

Abstract

We investigate the influence of quantum-kinetic effects on the linear optical properties of GaAs quantum wells. We demonstrate that these effects arising from a non-Markovian treatment of the scattering terms in the semiconductor Bloch equations lead in the linear optical response to a dependence of many-body effects on the energy. A non-Markovian treatment of scattering terms corresponds to a quasi-particle approximation of many-body effects, where they are independent of the energy. We compare both treatments and show that the quasi-particle treatment (i) overestimates both energy shift and broadening of the exciton resonance and (ii) fails to give quantitative description of the excitonic Mott transition with increasing excitation.Introduction The dielectric response of semiconductors for frequencies close to the fundamental gap is dominated by electron-hole correlations. To lowest order in density, electrons and holes form excitonic pair states. With increasing excitation the dielectric polarization is influenced by many-body effects between excited carriers and the exciton resonance becomes more and more broadened. The Mott transition of excitons as a consequence of screening of the Coulomb interaction between carriers is well understood. The two basic effects of band gap shrinkage and weakening of the Coulomb interaction cancel nearly complete, leading to a widely unchanged exciton position, while the sharp line feature is broadened and disappears in the shrinking band edge. This was first shown by Zimmermann et al.[1] reducing the Bethe-Salpeter Equation (BSE) for an electron-hole pair in an equilibrium electron-hole plasma to an effective wave equation of the Wannier exciton, and verified in several experiments (see Ref. [2] for GaAs).The basic idea of [1] was developed further in a series of papers (for a review see [3]), directly solving the BSE for the optical polarization, and giving experimental evidence. Different models of screening were discussed in this context, in particular the effect of dynamical screening [4][5][6], which requires the use of the so-called Shindoapproximation in the BSE. The results turn out to be restricted to lower carrier densities, since divergencies appear if the sum of the carrier distribution functions of electrons and holes approaches unity. Another aspect is the use of the quasi-particle concept [7] for the one-particle Green's functions in order to reduce the numerical effort for the solution of the BSE.New insight into the role of many-body effects came into play with the development of the Semiconductor-Bloch Equations (SBE) [8], describing the time evolution of the

Ionization equilibrium in an excited semiconductor: Mott transition versus Bose-Einstein condensation

“…The experimental verification of this approach was given in several optical experiments, measuring the transmission/reflection of semiconductor heterostructures. In previous papers [35][36][37][38] we have demonstrated how the influence of many-body effects on the exciton line, e.g., carrier-induced line broadening, shift of the exciton resonance and band gap shrinkage show up in the phase and amplitude of transmitted/reflected light. The semiconductor Bloch equation approach sketched above describes systems with a band structure in an electromagnetic field.…”

“…33 If one considers the carriers to be in quasiequilibrium, the carrier distributions are Fermi functions with given chemical potential and temperature, which are not affected by the weak probe pulse, and only the kinetic equation for the polarization has to be solved. In this case, the equation for the polarization p͑k , ͒, generated by the probe pulse E͑͒ and coupled via the dipole matrix element d to the semiconductor, can be written in excitonic units as [34][35][36][37][38] ͕ − k 2 − ⌬ HF ͑k͒ − ⌺ r ͑k,͖͒p͑k,͒…”

Mott transition of excitons in GaAs-GaAlAs quantum wells

“…In [30], we have demonstrated for a bulk semiconductor (ZnSe) that there is a pronounced influence of manybody effects on the chemical potentials even at higher excitation around the Mott transition. In this paper, we extend the earlier treatments for quantum wells [28,50] and include the renormalized carrier energies in the distributions f a,0 (e a k ) → f a (ε a k ). The change of chemical potentials µ a has to be determined for a given density n * a and temperature T of carriers from…”

“…containing the eigenfunctions a (z a ) of carriers in the wells. A detailed description of the dynamically screened potentials V aa,≷ k−q (ω) is given in [50]. In that paper, the QP energies and damping have been determined with…”

Influence of carrier-carrier and carrier-phonon correlations on optical absorption and gain in quantum-dot systems

“…[10] the dephasing due to Coulomb interaction has been calculated using SBE with correlation contributions due to Auger-like WL-assisted capture processes (see below) where scattering integrals have been evaluated in terms of free-carrier energies. A more elab- * Electronic address: www.itp.uni-bremen.de/ag-jahnke/ orate analysis of dephasing due to Coulomb interaction in quantum wells (QWs), which included non-Markovian scattering integrals based on renormalized energies, revealed quantitative modifications of the results [11]. We show that for QD systems the situation is different due to the appearance of localized states with a discrete spectrum.…”