Screened Hartree-Fock Approximation Research Articles

Coupled-Mode Theory for Semiconductor Nanowires

We present a model to describe the spatiotemporal evolution of guided modes in semiconductor nanowires based on a coupled mode formalism. Light-matter interaction is modelled based on semiconductor Bloch equations, including many-particle effects in the screened Hartree-Fock approximation. Appropriate boundary conditions are used to incorporate reflections at waveguide endfacets, thus allowing for the simulation of nanowire lasing. We compute the emission characteristics and temporal dynamics of CdS and ZnO nanowire lasers and compare our results both to Finite-Difference Time-Domain simulations and to experimental data. Finally, we explore the dependence of the lasing emission on the nanowire cavity and on the materials relaxation time.

Effectivegfactor in black phosphorus thin films

We theoretically investigate the effective $g$ factor in the black phosphorus (BP) thin films (TFs) based on a multiband $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ theory. We demonstrate that the effective single particle $g$ factor in pristine BP TF is anisotropic arising from its anisotropic band structure with ${g}_{xx}^{*}\ensuremath{\approx}{g}_{yy}^{*}\ensuremath{\approx}2.0$ and ${g}_{zz}^{*}$ sensitively depending on the interband coupling and the band gap. The ${g}_{zz}^{*}$ approaches 2.0 with increasing hole doping density and gate electric field since both of them minish the interband coupling by reducing the overlap integral between the electron and hole wave functions. We also estimate the exchange interaction enhancement on the effective single particle $g$ factor by using the screened Hartree-Fock approximation. The exchange interaction enhanced $g$ factor (${g}_{\text{ex}}$) shows maxima (minima) at odd (even) filling factors. The effective $g$ factor (${g}^{*}$) oscillates with the increase of magnetic field and sensitively depends on the Landau level broadening as well as the gate electric field since both of them affect the interband coupling and the electron-electron interactions.

Temperature-dependent investigation of carrier transport, injection, and densities in AlGaAs-based multi-quantum-well active layers for vertical-cavity surface-emitting lasers

The electro-optical efficiency of vertical-cavity surface-emitting lasers (VCSELs) strongly depends on the efficient carrier injection into the quantum wells (QWs) in the laser active region. Carrier injection degrades with increasing temperature, which limits VCSEL performance in high-power applications where self-heating imposes high-operating temperatures. In a numerical model, we investigate the transport of charge carriers in an 808-nm AlGaAs multi-quantum-well structure with special attention to the temperature dependence of car- rier injection into the QWs. Experimental reference data were extracted from oxide-confined, top-emitting VCSELs. The transport simulations follow a drift-diffusion-model complemented by an energy-resolved car- rier-capture model. The QW gain was calculated in the screened Hartree-Fock approximation. With the combi- nation of the gain and transport model, we explain experimental reference data for the injection efficiency and threshold current. The degradation of the injection efficiency with increasing temperature is not only due to increased thermionic escape of carriers from the QWs, but also to state filling in the QWs initiated from higher threshold carrier densities. With a full opto-electro-thermal VCSEL model, we demonstrate how changes in VCSEL properties affecting the threshold carrier density, like mirror design or optical confinement, have con- sequences on the thermal behavior of the injection and the VCSEL performance. © 2015 Society of Photo-Optical

Light-matter interaction and lasing in semiconductor nanowires: A combined finite-difference time-domain and semiconductor Bloch equation approach

We present a time-domain model for the simulation of light-matter interaction in semiconductors in arbitrary geometries and across a wide range of excitation conditions. The electromagnetic field is treated classically using the finite-difference time-domain method. The polarization and occupation numbers of the semiconductor material are described using the semiconductor Bloch equations including many-body effects in the screened Hartree-Fock approximation. Spontaneous emission noise is introduced using stochastic driving terms. As an application of the model, we present simulations of the dynamics of a nanowire laser including optical pumping, seeding by spontaneous emission and the selection of lasing modes.

Model for direct-transition gain in a Ge-on-Si laser

This paper describes a laser gain model for the direct, Γ-point transition in bulk Ge. The model allows calculation of gain and spontaneous-emission spectra for arbitrary strain, as well as doping and injected carrier densities. Many-body effects are included at the level of the screened Hartree-Fock approximation to account for energy renormalization modifications, especially to the impact of n-doping on magnitude and spectral extension of laser gain. Application of the model is illustrated by predicting the net material peak gain versus injected current density under different combinations of tensile strain and n-doping density.

Quasiparticle velocities in two-dimensional electron/hole liquids with spin-orbit coupling

We study the influence of spin-orbit interactions on quasiparticle dispersions in two-dimensional electron and heavy-hole liquids in III-V semiconductors. To obtain closed-form analytical results, we restrict ourselves to spin-orbit interactions with isotropic spectrum and work within the screened Hartree-Fock approximation, valid in the high-density limit. For electrons having a linear-in-momentum Rashba (or, equivalently, Dresselhaus) spin-orbit interaction, we show that the screened Hartree-Fock approximation recovers known results based on the random-phase approximation and we extend those results to higher order in the spin-orbit coupling. While the well-studied case of electrons leads only to a weak modification of quasiparticle properties in the presence of the linear-in-momentum spin-orbit interaction, we find two important distinctions for hole systems (with a leading nonlinear-in-momentum spin-orbit interaction). First, the group velocities associated with the two hole-spin branches acquire a significant difference in the presence of spin-orbit interactions, allowing for the creation of spin-polarized wavepackets in zero magnetic field. Second, we find that the interplay of Coulomb and spin-orbit interactions is significantly more important for holes than for electrons and can be probed through the quasiparticle group velocities. These effects should be directly observable in magnetotransport, Raman scattering, and femtosecond-resolved Faraday rotation measurements. Our results are in agreement with a general argument on the velocities, which we formulate for an arbitrary choice of the spin-orbit coupling.

Interwall screening and excitons in double-wall carbon nanotubes

Exciton properties of double-wall carbon nanotubes are studied in the static screened Hartree-Fock approximation within a k ·p scheme. The intrawall electron-hole interaction is largely suppressed by interwall screening effects. The suppression is sensitive to the effective interwall distance between the inner and outer tubes and reduces the exciton binding energy as well as the band gap. As a result, the exciton energy levels are redshifted from those in the single-wall tube with the same diameter. The energy shift of the ground exciton has little dependence on the tube diameter, in contrast to that of the excited excitons. In the case of a metallic outer and inner tube, excited exciton states in the semiconducting tube disappear due to strong screening.

Trions in semiconducting single-walled carbon nanotubes

We study trions (charged excitons), a complex of an electron-hole pair and an additional electron or hole, in semiconducting single-walled carbon nanotubes (s-SWCNT), by means of the exact diagonalization of the realistic Hamiltonian based on the $\mathbit{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbit{p}$ scheme and on the screened Hartree-Fock approximation. By comparing different classes of models that partially or fully include the band nonparabolicity, the form factors in the density operators, the screening effects on interaction, and the self-energy correction in the energy bands, we succeed in capturing the essential features of s-SWCNT. It turns out that the trion binding energy is significantly suppressed by the form factor as well as by the screening effect. Further, an unconventional feature of s-SWCNT is found: the trion has a larger binding energy than the biexciton, since the biexcitons are more strongly affected by screening than trions. We also consider the effects of the short-range part of the Coulomb interaction, and clarify the fine structures in the trion energy levels. It is shown that the bright (optically allowed) trion with the lowest energy can be interpreted as a bound state of a dark (optically forbidden) exciton and an extra electron or hole.

Carbon nanotube Bloch equations: A many-body approach to nonlinear and ultrafast optical properties

Carbon nanotube Bloch equations are proposed to analyze the many-body electron dynamics for optical interband transitions in carbon nanotubes. As a first approach, the Bloch equations for microscopic transitions and occupations are discussed within the screened Hartree-Fock approximation. The potential of the Bloch equation approach is illustrated for linear and nonlinear optical spectra and ultrafast electron dynamics in carbon nanotubes.

Spontaneous spin polarization in doped semiconductor quantum wells

We calculate the critical density of the zero-temperature, first-order ferromagnetic phase transition in n-doped GaAs/AlGaAs quantum wells. We find that the existence of the ferromagnetic transition is dependent upon the choice of well width. We demonstrate rigorously that this dependence is governed by the interplay between different components of the exchange interaction and that there exists an upper limit for the well width beyond which there is no transition. We predict that some narrow quantum wells could exhibit this transition at electron densities lower than the ones that have been considered experimentally thus far. We use a screened Hartree-Fock approximation with a polarization-dependent effective mass, which is adjusted to match the critical density predicted by Monte Carlo calculations for the two-dimensional electron gas.

Determination of the piezoelectric field in InGaN quantum wells

In many studies, the value of the experimentally determined internal piezoelectric field has been reported to be significantly smaller than theoretical values. We believe this is due to an inappropriate approximation for the electric field within the depletion region, which is used in the analysis of experimental data, and we propose an alternative method. Using this alternative, we have measured the strength of the internal field of InGaN p-i-n structures, using reverse bias photocurrent absorption spectroscopy and by fitting the bias dependent peak energy using microscopic theory based on the screened Hartree-Fock approximation. The results agree with those using material constants interpolated from binary values.

Screening and electronic correlations in quantum wires in strong magnetic fields: Filling factor dependence

The screening of the Coulomb interaction in quantum wires, subjected to strong perpendicular magnetic fields, is assessed for integer filling factors $\ensuremath{\nu}l~3$ and low temperatures. Correlations due to bulk screening are rather weak whereas those due to screening at the edges are very strong and smoothen considerably the energy dispersion. The group velocity at the Fermi edge ${v}_{g}{(k}_{\mathrm{F}\ensuremath{\nu}})$ can be one order of magnitude larger than the Hartree velocity ${v}_{g}^{\mathrm{H}}{(k}_{\mathrm{F}\ensuremath{\nu}}).$ The exchange-correlation contribution ${v}_{g}^{\mathrm{ec}}{(k}_{\mathrm{F}})$ to ${v}_{g}{(k}_{\mathrm{F}})$ is proved to be nonsingular and for sufficiently strong magnetic fields ${v}_{g}^{\mathrm{ec}}{(k}_{\mathrm{F}})$ is proportional to ${v}_{g}^{\mathrm{H}}{(k}_{\mathrm{F}\ensuremath{\nu}})$ with a proportionality constant that depends on $\ensuremath{\nu}.$ The dispersion relation, obtained in the screened Hartree-Fock approximation, is in line with the observed strong suppression of the spin splitting for $\ensuremath{\nu}=1$ and helps explain the observed destruction or absence of some quantum Hall states. For $\ensuremath{\nu}=2$ the effective ${g}_{\mathrm{op}}^{*}$ factor is constant whereas for $\ensuremath{\nu}=1(3)$ varies strongly across the channel. In addition, the calculated activation energies agree well with those determined experimentally.

Ultrafast pump–probe dynamics in ZnSe-based semiconductor quantum wells

Pump–probe experiments are used as a controllable way to investigate the properties of photoexcited semiconductors, in particular, the absorption saturation. We present an experiment–theory comparison for ZnSe quantum wells, investigating the energy renormalization and bleaching of the excitonic resonances. Experiments were performed with spin-selective excitation and above-bandgap pumping. The model, based on the semiconductor Bloch equations in the screened Hartree–Fock approximation, takes various scattering processes into account phenomenologically. Comparing numerical results with available experimental data, we explain the experimental results and find that the electron spin-flip occurs on a time scale of 30 ps.

Hydrodynamic theory for spatially inhomogeneous semiconductor lasers. I. A microscopic approach

Starting from the microscopic semiconductor Bloch equations including the Boltzmann transport terms in the distribution function equations for electrons and holes, we derived a closed set of diffusion equations for carrier densities and temperatures with self-consistent coupling to Maxwell's equation and to an effective optical polarization equation. The coherent many-body effects are included within the screened Hartree-Fock approximation, while scatterings are treated within the second Born approximation including both the in- and out-scatterings. Microscopic expressions for electron-hole $(e$-$h)$ and carrier--LO-phonon $(c$-LO) scatterings are directly used to derive the momentum and energy relaxation rates. These rates, expressed as functions of temperatures and densities, lead to microscopic expressions for self- and mutual-diffusion coefficients in the coupled density-temperature diffusion equations. Approximations for reducing the general two-component description of the electron-hole plasma to a single-component one are discussed. In particular, we show that a special single-component reduction is possible when e-$h$ scattering dominates over $c$--LO-phonon scattering. The ambipolar diffusion approximation is also discussed and we show that the ambipolar diffusion coefficients are independent of e-$h$ scattering, even though the diffusion coefficients of individual components depend sensitively on the e-$h$ scattering rates. Our discussions lead to deeper insights into the roles played in the single-component reduction by the electron-hole correlation in momentum space induced by scatterings and the electron-hole correlation in real space via internal static electrical field. Finally, the theory is completed by coupling the diffusion equations to the lattice temperature equation and to the effective optical polarization, which in turn couples to the laser field.

Enhanced magnetization at integer quantum Hall states

We report on enhancements in the magnetization of two-dimensional electron systems in the quantum Hall regime. The observed discontinuities in the magnetization exceed the predictions for interacting electrons calculated in the Hartree-Fock approximation where only the exchange enhancement of the energy gaps is taken into account. We attribute the further enhancement to many-body correlation effects, i.e., filling factor dependent screening within the screened Hartree-Fock approximation. With this, the discontinuities in the magnetization no longer reflect the discontinuities of the chemical potential, but its behavior in the vicinity of integer filling factors.

Electron correlation effects in a wide channel from theν=1quantum Hall edge states

The spatial behavior of Landau levels (LL's) for the $\ensuremath{\nu}=1$ quantum Hall regime at the edge of a wide channel is studied in a self-consistent way by using a generalized local density approximation proposed here. Both exchange interaction and strong electron correlations, due to edge states, are taken into account. They essentially modify the spatial behavior of the occupied lowest spin-up LL in comparison with that of the lowest spin-down LL, which is totally empty. The contrast in the spatial behavior can be attributed to a different effective one-electron lateral confining potentials for the spin-split LL's. Many-body effects on the spatially inhomogeneous spin splitting are calculated within the screened Hartree-Fock approximation. It is shown that, far from the edges, the maximum activation energy is dominated by the gap between the Fermi level and the bottom of the spin-down LL, because the gap between the Fermi level and the spin-up LL is much larger. In other words, the maximum activation energy in the bulk of the channel corresponds to a highly asymmetric position of the Fermi level within the gap between spin-down and spin-up LL's in the bulk. We have also studied the renormalization of the edge-state group velocity due to electron correlations. The results of the present theory are in line with those suggested and reported by experiments on high-quality samples.

Screening and strain effects on the ground-state energy of a quasi-two-dimensional quantum well system

We discuss the screening and strain effects on the ground-state energy of the strained-layer semiconductor quantum wells, which forms a quasi-two-dimensional electron-hole plasma within the screened Hartree-Fock approximation. The exchange self-energy is evaluated within the Thomas-Fermi screening scheme for variation of the sheet density and the biaxial compressive strain. Such evaluation includes the solving of the Luttinger-Kohn Hamiltonian, which leads to obtaining the valence band structure [Phys. Rev. 97, 869 (1955)]. The dependence of the exchange self-energy on the sheet density and the strain is shown to be significantly reduced as the screening effects are taken into account. Also, the screening plays an important role in determining the ground-state energy and the renormalization of the single-particle energies. In addition, we observe that the ground-state energy increases with the biaxial compressive strain.

Memorization of short-range potential fluctuations in Landau levels

We calculate energy spectra of a two-dimensional electron system in a perpendicular magnetic field and periodic potentials of short periods. The Coulomb interaction is included within a screened Hartree-Fock approximation. The electrostatic screening is poor and the exchange interaction amplifies the energy dispersion. We obtain, by numerical iterations, self-consistent solutions that have a hysteresis-like property. With increasing amplitude of the external potential the energy dispersion and the electron density become periodic, and they remain stable when the external potential is reduced to zero. We explain this property in physical terms and speculate that a real system could memorize short-range potential fluctuations after the potential has been turned off.

Strong suppression of spin splitting in quantum wires due to correlations induced by edge state screening

A modified local-density approximation is developed to treat self-consistently exchange and correlations in a quantum wire (QW) subjected to a strong perpendicular magnetic field. The influence of many-body interactions on the spin splitting between the two lowest Landau levels (LLs) is calculated within the screened Hartree-Fock approximation (SHFA), for filling factor , and the strong spatial dependence of the screening properties of electrons is taken into account. In comparison with the Hartree-Fock result, the spatial behaviour of the occupied LLs in a QW is strongly modified when correlations are included. Correlations caused by bulk screening are very weak whereas those caused by screening at the edges are very strong. The latter strongly suppress the exchange splitting and smoothen the energy dispersion at the edges. The theory is in reasonable agreement with the observed strong suppression of the spin splitting pertinent to the quantum Hall effect (QHE) state and the destruction of this state in long QWs.

Coulomb effects on the quantum transport of a two-dimensional electron system in periodic electric and magnetic fields

The magnetoresistivity tensor of an interacting two-dimensional electron system with a lateral and unidirectional electric or magnetic modulation, in a perpendicular quantizing magnetic field, is calculated within the Kubo formalism. The influence of the spin splitting of the Landau bands and of the density of states (DOS) on the internal structure of the Shubnikov--de Haas oscillations is analyzed. The Coulomb electron-electron interaction is responsible for strong screening and exchange effects and is taken into account in a screened Hartree-Fock approximation, in which the exchange contribution is calculated self-consistently with the DOS at the Fermi level. This approximation describes both the exchange enhancement of the spin splitting and the formation of compressible edge strips, unlike the simpler Hartree and Hartree-Fock approximations, which yield either one or the other.