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A linear algebraic method named the shifted conjugate-orthogonal-conjugate-gradient method is introduced for large-scale electronic structure calculation. The method gives an iterative solver algorithm of the Green's function and the density matrix without calculating eigenstates. The problem is reduced to independent linear equations at many energy points and the calculation is actually carried out only for a single energy point. The method is robust against the round-off error and the calculation can reach the machine accuracy. With the observation of residual vectors, the accuracy can be controlled, microscopically, independently for each element of the Green's function, and dynamically, at each step in dynamical simulations. The method is applied to both semiconductor and metal. 71.15.Nc, 71.15.Pd

We report an experimental demonstration and theoretical analysis of electromagnetically induced transparency in a GaAs quantum well, in which the absorption of an exciton resonance is reduced by more than twentyfold. The destructive quantum interference in this scheme is set up by a control pulse that couples to a resonance of biexcitons. These studies illustrate that many-particle interactions, which are inherent in semiconductors and are often detrimental to quantum coherences, can also be harnessed to manipulate these coherences.

For large scale electronic structure calculation, the Krylov subspace method is introduced to calculate the one-body density matrix instead of the eigenstates of given Hamiltonian. This method provides an efficient way to extract the essential character of the Hamiltonian within a limited number of basis set. Its validation is confirmed by the convergence property of the density matrix within the subspace. The following quantities are calculated; energy, force, density of states, and energy spectrum. Molecular dynamics simulation of Si(001) surface reconstruction is examined as an example, and the results reproduce the mechanism of asymmetric surface dimer.

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In nonlinear semiconductor optics, two-particle scattering is often being modeled successfully within the second Born approximation (2nd BA) of the Coulomb interaction. It is shown in this paper that, at low energies, such a perturbative treatment of Coulomb correlations applied to exciton-exciton scattering in two-dimensional systems fails even qualitatively (unless phenomenological or self-consistent dephasing processes are included in the theory). We show that the failure of the 2nd BA in two dimensions can be inferred from a comparison of our theoretical results with reported experiments of four-wave mixing signals from semiconductor microcavities.Linear excitonic absorption effects (see, e.g., [1]) and optical nonlinearities arising from exciton-exciton interactions in quasi-one-, two-, and three-dimensional semiconductors are well established (see, e.g., [2][3][4]). While the dimensionality dependence of linear excitonic effects is well understood (the simplest example being the increase of exciton binding energy with decreasing dimensionality), that of nonlinear excitonic effects is in general not clearly established. In this Letter, we discuss one aspect of this issue which concerns exciton-exciton scattering at low kinetic energies. Such scattering processes are commonly treated within the second Born approximation (2nd BA), because this approximation can already account, at least qualitatively, for all observable signatures of excitonexciton scattering in nonlinear optical experiments. Moreover, numerous experiment-theory comparisons (including cases involving exciton-free-carrier scatterings) seem to validate the 2nd BA. Examples include the line shape of optical gain spectra in semiconductor lasers [5], photoluminescence from semiconductor quantum wells [6], and optical Stark shifts in semiconductor quantum wells [7].While we do not dispute the validity of the model assumptions underlying those experiment-theory comparisons, we will show in the following that the 2nd BA in two dimensions should be used with caution. In fact, if the theoretical results are not smoothened by phenomenological or self-consistently calculated [6] dephasing rates, the 2nd BA T matrix (or scattering amplitude) governing low-energy exciton-exciton scattering would diverge in the limit of zero exciton center-of-mass-motion energies, while the exact scattering amplitude is known to vanish as 1͞ln͑energy͒ in the same limit [8]. These behaviors result from the dimensionality of the system and hold for any generic short-ranged potential independent of strength and other details. In analyzing semiconductor experiments, including the ones referenced above, dephasing introduced into the theory regularizes these nonanalytic behaviors, but their presence is still indicated by the large deviation of the 2nd BA T matrix from the exact one even for only moderately strong potentials (below, we will show this in more detail, cf. Fig. 2). Admittedly, since this deviation is quantitative instead of qualitative, its effects may not be ascertai...

We report the experimental observation of coherently coupled heavy-hole-light-hole Stark shifts, i.e., light-hole exciton shifts under heavy-hole exciton pumping conditions, in InGaAs quantum wells. The theoretical analysis of the data is based on a full many-body approach (dynamics-controlled truncation formalism) in the third-order nonlinear optical regime. It is shown that the Stark shift data can be interpreted as strong evidence of suitably defined nonradiative intervalence band coherences in a semiconductor quantum well. Hence, the observations establish a semiconductor analog of Raman coherences in three-level atoms.

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