Exciton-Boson Formalism in the Theory of Laser-Excited Semiconductors and Its Application in Coherent Four-Wave-Mixing Spectroscopy

By the use of a bosonization transformation and group-theoretical arguments, the Hamiltonian of an electron–hole–photon system in a laser-excited direct two-band semiconductor is transcribed into that of an exciton–photon system with the particle spins rigorously taken into consideration. It is shown that the third-order optical nonlinearities in the spectral region below the band edge have their microscopic origin in two-exciton correlations, which are expressed in terms of the effective exciton–exciton and anharmonic exciton–photon interactions. The dependence of the interparticle interactions on the spin states of quasiparticles is behind the polarization dependence of the semiconductor nonlinear optical response. On the example of the system of heavy hole excitons in quantum wells, grown from compounds with the zinc blende type of symmetry, it is demonstrated that the effective exciton–exciton interaction in two-exciton states with nonzero total spin is repulsive, while in zero-spin states it is attractive, which may result in the biexciton formation. The derived Heisenberg equations of motion for the exciton and biexciton operators form the basis for a theoretical study of the coherent four-wave-mixing in GaAs and ZnSe quantum wells. It is readily apparent from the equations that in different polarization configurations the coherent four-wave-mixing is generated by different ingredients of two-exciton Coulomb correlations: in the co-circular configuration, it is the interexciton repulsion, in the cross-linear configuration, the formation of the biexciton and its coupling to excitons, and in the collinear configuration, both of them jointly. The obtained expressions for the time-resolved and frequency-resolved four-wave-mixing signals adequately describe the main characteristics and various details of wave mixing phenomena, including a biexciton signature in the appropriate polarization configurations. Results of the work clarify the microscopic mechanism of the polarization dependence in coherent four-wave-mixing spectroscopy in semiconductor quantum wells.     

Influence of acoustic phonons on dephasing of free excitons in quantum wells

A theory of the dephasing rate of quasi-2D free excitons due to acoustic phonon interaction at low exciton densities is presented. Both deformation potential and piezoelectric couplings are considered for the exciton–phonon interaction in quantum wells. Using the derived interaction Hamiltonian obtained recently by us, exciton linewidth and dephasing rate are calculated as a function of the exciton density, exciton temperature, exciton momentum and lattice temperature.     

Theory of the excitonic Mott transition in quasi-two-dimensional systems

The excitonic Mott transition in single and double quantum wells is studied using the Green’s function technique. An abrupt jump in the value of the ionization degree, which happens with an increase of the carrier density or temperature, is found in a certain density–temperature region. The opposite effect–the collapse of the electron–hole plasma into an insulating exciton system–is predicted to occur at lower densities. The critical density of the Mott transition for spatially indirect excitons may be much smaller than that for direct excitons.     

Phase transitions of indirect excitons in coupled quantum wells: The role of disorder

The theory of what happens to a superfluid in a random field, known as the “dirty boson” problem, directly relates to a real experimental system presently under study by several groups, namely excitons in coupled semiconductor quantum wells. We consider the case of bosons in two dimensions in a random field, when the random field can be large compared to the repulsive exciton–exciton interaction energy, but is small compared to the exciton binding energy. The interaction between excitons is taken into account in the ladder approximation. The coherent potential approximation (CPA) allows us to derive the exciton Green's function for a wide range of the random field strength, and in the weak-scattering limit CPA results in the second-order Born approximation. For quasi-two-dimensional excitonic systems, the density of the superfluid component and the Kosterlitz–Thouless temperature of the superfluid phase transition are obtained, and are found to decrease as the random field increases.     

Millisecond fluorescence in InAs quantum dots embedded in AlAs

The temperature dependence of steady-state and time-resolved photoluminescence from self-assembled InAs quantum dots embedded in AlAs has been studied. Millisecond-long nonexponential photoluminescence decay is observed in the temperature range of 4.2–50 K. At higher temperatures, the decay time decreases to a few nanoseconds. The experimental results are interpreted using a model of singlet–triplet splitting of exciton levels in small dots in a dense quantum dot system with local carrier transfer between dots.     

On the origin of time-resolved pump–probe differential signal from excitons in quantum wells

We investigate the origin and nature of femtosecond time-resolved (TR) pump–probe differential (PPD) signal from the exciton resonance in semiconductor quantum wells (QWs) in the coherent regime. The excitonic PPD signal is expressed as a sum of interferences of the excitonic nonlinear polarization with the incident probe field and the linear polarization induced by the probe. A nonzero excitonic TR-PPD signal from QWs can occur for time t larger than the pulse width (t_p) when the exciton dephasing time is longer than t_p, and this signal can originate only from the second interference term for both the negative and positive pump–probe delays, the contribution from the first interference term being zero for t>t_p. This is in contrast with the case of PPD signal in the spectral domain where the first interference term plays a major role. We discuss the effects of many body interactions on the TR-PPD signal. It is shown that excitation-induced dephasing can cause a significant increase in the rise time of the TR-PPD signal.     

Magnetooptical investigations of single self assembled In0.3Ga0.7As quantum dots

We present results from magnetooptical investigations of large elongated single self assembled In_0.3Ga_0.7As quantum dots with a low surface density of . Compared to conventional In_0.6Ga_0.4As quantum dots the dimension of the investigated dots is enlarged by nearly one order of magnitude using a low strain In_0.3Ga_0.7As nucleation layer. In addition, the exciton exhibits a smaller g-factor of 0–0.4 and a larger diamagnetic coefficient of 20– in Faraday geometry, reflecting the increased extension of the exciton wavefunction, with respect to In_0.6Ga_0.4As quantum dots. From power dependent investigations we observe biexciton binding energies ranging from 1.7 to 1.9 meV. Excited state emission appears typically 2–5 meV above the ground state which is consistent with the increased dimensions of the structure. Furthermore we find linear polarization degrees of up to 0.6 from exciton emission of the elongated quantum dot structure.     

Rotating metrics admitting non-perfect fluids

In this paper an application of Newman-Janis algorithm in spherically symmetric metrics with the functions M(u,r) and e(u,r) has been discussed. After the transformation of the metric via this algorithm, these two functions M(u,r) and e(u,r) will be transformed to depend on the three variables u,r,. With these functions of three variables, all the Newman–Penrose (NP) spin coefficients, the Ricci as well as the Weyl scalars have been calculated from the Cartans structure equations. Using these NP quantities, we first give examples of rotating solutions of Einsteins field equations like Kerr–Newman, rotating Vaidya solution and rotating Vaidya–Bonnor solution. It is found that the technique developed by Wang and Wu can be used to give further examples of embedded rotating solutions, that the rotating Kerr–Newman solution can be combined smoothly with the rotating Vaidya solution to derive the Kerr–Newman–Vaidya solution, and similarly, Kerr–Newman–Vaidya–Bonnor solution of the field equations. It has also shown that the embedded universes like Kerr–Newman de Sitter, rotating Vaidya–Bonnor–de Sitter, Kerr–Newman–Vaidya–de Sitter can be derived from the general solutions with Wang–Wu function. All rotating embedded solutions derived here can be written in Kerr–Schild forms, showing the extension of Xanthopouloss theorem. It is also found that all the rotating solutions admit non-perfect fluids.     

Electron–hole complexes in self-assembled quantum dots in strong magnetic fields

We present results of calculations and experiments on electron–hole complexes in InGaAs/GaAs self-assembled quantum dots in high magnetic field (B). Due to hidden symmetries, the chemical potential of an N-exciton system at special B fields becomes insensitive to the exciton number as well as the magnetic field. This results in plateau regions of high intensity in measured magneto-PL spectrum. Theoretical calculations using exact diagonalization techniques successfully explain the measured magneto-photoluminescence spectrum with B fields up to 28 T.     

The symmetries of the Manton superconductivity model

The symmetries and conserved quantities of Manton’s modified superconductivity model with non-relativistic Maxwell–Chern–Simons dynamics (also related to the Quantized Hall Effect) are obtained in the “Kaluza–Klein type” framework of Duval et al.     

Solution of Duffin–Kemmer–Petiau Equation for the Step Potential

The Duffin–Kemmer–Petiau (DKP) equation for spin 0 and 1 in the pressence of the step potential is solved. The problem is reduced to the solution of an equation of Feshbach–Villars type.The reflection and transmission coefficients are correctly deduced. The Klein paradox persists and is discussed using the charge interpretation.     

Lowering the Hartree–Fock Minimizer by Electron–Positron Pair Correlation

We prove by a simple computation that a suitable coupling to the positronic sector lowers the energy of the purely electronic minimizer of the electron–positron Hartree–Fock functional.     

Boundary G/G Theory and Topological Poisson–Lie Sigma Model

We study a boundary version of the gauged WZW model with a Poisson–Lie group G as the target. The Poisson–Lie structure of G is used to define the Wess–Zumino term of the action on surfaces with boundary. We clarify the relation of the model to the topological Poisson sigma model with the dual Poisson–Lie group G ^* as the target and show that the phase space of the theory on a strip is essentially the Heisenberg double of G introduced by Semenov–Tian–Shansky.     

A Spin-Shift Operator of the Multi-particle Ruijsenaars–Schneider Hamiltonian

We obtain a spin-shift operator for the multi-particle trigonometric Ruijsenaars–Schneider Hamiltonian. This result is a generalization of the argument in Phys. Lett. B 375 (1996), 89–97, where the integrability of the one-particle Ruijsenaars–Schneider system is shown by using the existence of a spin-shift operator.     

A new form of the Sutton–Chen potential for the Cu–Ag alloys

The analytic construction of a many-body potential inspired from the Sutton–Chen parametrization is presented for copper and silver. A new approach is used to model the cross interaction for the Cu–Ag alloys. The parameters are fitted to first principles calculations based on the full potential linear plane wave method. The structural properties of the order and disorder Cu–Ag alloys in the B₂and fcc structures are presented for different concentration.     

Influence of a Photoconductive Polymer Matrix on the Photoluminescence of Cationic Polymethine Dyes

Using symmetric cationic indopolycarbocyanines HIC and HIDC as an example, the authors detected the enhancement of their photoluminescence in films of photoconductive polymers poly–N–epoxypropyl carbazole and poly–N–vinyl carbazole as compared to nonphotoconductive polymers, i.e., polyvinyl butyral, polystyrene, and polyethylene. The excitation was carried out on the shortwave edge of the absorption band of the dye and did not affect the absorption region of the polymer. It is shown that the effect of enhancement of the luminescence increases with decrease in the excitation wavelength and becomes weaker with increase in the molecular mass of carbazole–containing polymers. Its enhancement is interpreted as the recombination luminescence of electron–hole pairs formed in photogeneration of charge from the dye molecules.     

A Construction of Berezin–Toeplitz Operators via Schrödinger Operators and the Probabilistic Representation of Berezin–Toeplitz Semigroups Based on Planar Brownian Motion

First we discuss the construction of self-adjoint Berezin–Toeplitz operators on weighted Bergman spaces via semibounded quadratic forms. To ensure semiboundedness, regularity conditions on the real-valued functions serving as symbols of these Berezin–Toeplitz operators are imposed. Then a probabilistic expression of the sesqui-analytic integral kernel for the associated semigroups is derived. All results are the consequence of a relation of Berezin–Toeplitz operators to Schrödinger operators defined via certain quadratic forms. The probabilistic expression is derived in conjunction with the Feynman–Kac–Itô formula.     

Investigations of the exciton condensate

Recent experiments on quantum Hall bilayers in the vicinity of total filling factor 1 (ν_T=1) have revealed many exciting observations characteristic of a superfluidic exciton condensate. We report on our experimental work involving the ν_T=1 exciton condensate in independently contacted bilayer two-dimensional electron systems. We observe previously reported phenomena as a zero-bias resonant tunneling peak, a quantized Hall drag resistivity, and in counter-flow configuration, the near vanishing of both ρ_xx and ρ_xy resistivity components. At balanced electron densities in the layers, we find for both drag and counter-flow current configurations, thermally activated transport with a monotonic increase of the activation energy for d/ℓ_B<1.65 with activation energies up to 0.4 K. In the imbalanced system the activation energies show a striking asymmetry around the balance point, implying that the gap to charge excitations is considerably different in the separate layers that form the bilayer condensate. This indicates that the measured activation energy is neither the binding energy of the excitons, nor their condensation energy.     

On the magnetic ordering implemented by the s–d exchange interaction

The RKKY perturbation scheme for the spin s–d exchange model is reexamined in the case of a finite number of electrons per impurity. The distribution of impurities is assumed to be random. The free electron gas representing the unperturbed system in the RKKY approach is replaced by a mean-field system h_r asymptotically equivalent to the reduced s–d model H_r which includes part of the s–d exchange. Below the transition temperature T_c of h_r the lowest energy levels of the s–d exchange Hamiltonian H_K resulting from second-order perturbation theory prove to be ordered in the same manner as those of h_r in the limit of weak s–d exchange, favouring the same definite parallel alignment of any pair of impurity spins. It follows therefore that in the low temperature, weak coupling regime, the s–d model exhibits ferromagnetic ordering of impurities. At temperatures above T_c there is no ordering and impurity–impurity exchange has the RKKY form. These observations are consistent with the presence of a low-temperature ferromagnetic phase in numerous compounds with s–d exchange interaction.     

Simultaneous formation of contacts and diffusion barriers for VLSI by rapid thermal silicidation of TiW

The formation of (Ti_xW_1–x)Si₂/(Ti_xW_1–x)N, by rapid thermal processing of Ti_xW_1–x on Si in an N₂ ambient is investigated. An activation energy of 1.7 eV is obtained for silicide formation. A distinct snow-ploughing of As atoms is observed during silicide formation whereas the interfacial B concentration decreases with increasing silicide formation temperature. The diffusion barrier properties of the (Ti_xW_1–x)Si₂/(Ti_xWi_1–x)N stack in contact with Al is investigated upon post-metal annealing. No interaction between the layers is found for temperatures as high as 475°C after 60 min. The improved thermal stability of the (Ti_xW_1–x)N layer in contact with Al is attributed to nitrogen blocking of the grain boundaries.