The longitudinal magnetophonon effect in semiconductors containing magnetic impurities

The dependence of longitudinal magnetoresistance on magnetic field in semiconductors containing magnetic impurities is investigated theoretically. The calculation takes into account the scattering of electrons on magnetic impurities and on optical phonons. The inelastic optical phonon scattering itself is responsible for magnetophonon oscillations of the magnetoresistance, the extremes of these oscillations occuring when energy distance between Landau levels is equal to the energy of optical phonon, $\text{h}\text{?}$ω₀. The scattering on magnetic impurities may lead to spin flip electronic transitions. The spin flip electronic transitions manifest themselves as additional minima on the oscillatory picture of magnetoresistance. These new minima occur when the energy separation between spin-split Landau levels is equal to $\text{h}\text{?}$ω₀.     

Indirect exciton absorption and Raman scattering in GaAs-AlGaAs superlattices

Longitudinal optic (LO) phonon assisted indirect exciton creation (X_LO), hot carrier relaxation ((e-h)_LO) and Raman scattering phenomena are reported in the optical spectra of GaAs-AlGaAs superlattices. Structures of the same dimensions both with and without double heterostructure confining barriers are studied. For the structures without confining barriers, continuum transitions are suppressed in photoluminescence excitation (PLE) spectra, and as a result the X_LO, (e-h)_LO and Raman peaks are observed. The X_LO absorption peaks are identified from the observation of a clear threshold in PLE at ℏω_LO (36.4 meV) above the heavy hole exciton peak. The intensity of X_LO is a maximum at 6 meV above the threshold, probably due to dissociation into free carriers at the exciton binding energy (6meV) above ℏω_LO. The influence of non-radiative processes on incoherent (PLE) and coherent (Raman) processes is compared.     

Time domain capacitance spectroscopy of tunneling electrons in the two-dimensional electron gas

We have developed a technique capable of measuring the tunneling current into both localized and conducting states in a 2D electron system (2DES). The method yields I-V characteristics for tunneling with no distortions arising from low 2D in-plane conductivity. We have used the technique to determine the pseudogap energy spectrum for electron tunneling into and out of a 2D system and, further, we have demonstrated that such tunneling measurements reveal spin relaxation times within the 2DEG. Pseudogap: In a 2DEG in perpendicular magnetic field, a pseudogap develops in the tunneling density of states at the Fermi energy. We resolve a linear energy dependence of this pseudogap at low excitations. The slopes of this linear gap are strongly field dependent. No existing theory predicts the observed behavior. Spin relaxation: We explore the characteristics of equilibrium tunneling of electrons from a 3D electrode into a high mobility 2DES. For most 2D Landau level filling factors, we find that electrons tunnel with a single, well-defined tunneling rate. However, for spin-polarized quantum Hall states (ν=1, 3 and 1/3) tunneling occurs at two distinct rates that differ by up to two orders of magnitude. The dependence of the two rates on temperature and tunnel barrier thickness suggests that slow in-plane spin relaxation creates a bottleneck for tunneling of electrons.     

Carrier kinetics and population inversion in Landau level system in cascade GaAs/AlGaAs quantum well structures

The carrier distribution over Landau levels was studied in resonant tunneling GaAs/AlGaAs quantum well structures under tunneling pumping of the upper subband. The numerical calculations of the Landau levels population for various values of pumping intensity (tunneling time), magnetic field and the structure doping were carried out. The effect of various scattering mechanisms, as two-electron (electron–electron scattering) as single-electron (acoustic phonon and interface roughness scattering) ones on level population was studied. The population inversion between the zeroth Landau level of the upper subband and the first Landau level of the lowest subband was shown to exist in wide range of the magnetic field strength thus providing the possibility of wide range tunable stimulated terahertz emission.     

On the dynamic conductivity for an electron-impurity system

The correlation function formula for the dynamic conductivity of a system of non-interacting electrons in the field of impurities is analyzed in terms of proper connected diagrams. By selecting those diagrams appropriate in the region of weak coupling and low impurity concentration, a set of coupled equations for the energy broadening γ (ω, ε, n_s) and the energy shift Δ(ω, ε, n_s) is derived, where both γ and Δ depend on the frequency ω of a probing field, the energy ε of the electron, and the concentration, n_g, of impurities. With the assumption of a finite range potential, these equations are solved. It is found that γ (ω, n_s) is smaller than that extrapolated value which the conventional expression γ₀ for the low-concentration collision frequency would predict, in the entire region studied, that the difference γ₀-γ becomes appreciable when the ratio of the average time between scatterings, τ_c, to the average duration of a scattering, τ_d, is 100 or less, that γ (ω, n_s) decreases monotonically from its static value γ (0, n_s), and becomes vanishingly small in the region ω≈1/τ_d, and that in the static limit (ω=0), γ=γ₀[1?(2/π) (γ₀τ_d)+…], that the energy shift Δ is positive, and increases from 0 and reach a peak of magnitude γ₀ as ω is raised from 0. By using the γ and Δ obtained, the dynamic conductivity σ(ω, n_s) for degenerated electrons is calculated. The deviation, σ-σ₀, from the conventional expression σ₀=(?i) (n_ee²/M) [ω-iΓ₀]^?1, (n_e]=number density of electrons), for 0°K, is appreciable when the ratio τ_c/τ_d is 100 or less. The field-term correction, which arises from the modification of the scattering due to the probing field, is found to be negligible in the entire region studied.     

Free carrier absorption in quantizing magnetic fields: Nonpolar optical phonon scattering

A quantum theory of free carrier absorption in nondegenerate semiconductors and in strong magnetic fields which was previously developed to treat the case when acoustic phonon scattering dominates the free carrier absorption process [1] is extended to treat the case when nonpolar optical scattering is important. When the electromagnetic radiation field is polarized parallel to the direction of the applied magnetic field, results are obtained which are similar to those when acoustic phonon scattering is dominant. The free carrier absorption is an oscillatory function of the magnetic field which on the average increases in magnitude with the magnetic field. However, more structure in the free carrier absorption occurs when nonpolar optical phonon scattering dominates. This is due to the fact that there are two periods in the oscillatory magnetic field dependence associated with the emission or the absorption of optical phonons during the intraband transitions. When the cyclotron frequency exceeds the sum of the photon and optical phonon frequencies, i.e. ω_c > θ + ω_o, the free carrier absorption is predicted to increase linearly with magnetic field when ?ω_c? k_BT. The magnetic field dependence of the free carrier absorption can be explained in terms of phonon-assisted transitions between the various Landau levels in a band involving the emission and absorption of optical phonons.     

Resonance Compton scattering in an external magnetic field

The scattering of a photon by an electron in an external magnetic field under resonant conditions, when the photon energy is close to the splittings between the Landau levels, is investigated. Formulas are obtained for the cross section of the process taking account of the polarization of the electron. For external fields ～10¹² G the resonant Compton cross section is several orders of magnitude greater than the Thompson cross section, and the width of the resonance is tens of electron volts.     

Fractional features in radiation-induced oscillations of the magnetoresistance of two-dimensional electron systems

The magnetoresistance of two-dimensional electron systems irradiated by microwave radiation is calculated. It exhibits oscillatory features at fractional values of the ratio ω/ω_c of the circular frequency of microwave radiation to the cyclotron frequency. The calculation explains existing experimental data by nonequilibrium population of electron states that appears due to one-photon processes and predicts ω/ω_c values near which the basic features in magnetoresistance are expected. In the framework of the mechanism under consideration, the fractional features can be observed only in the crossover from strongly overlapping to separate Landau levels and only at radiation frequencies below the threshold frequencies depending on a fractional value.     

On resonant tunneling

Localized electron states in oxides adjacent to metals hybridize with conduction electron states forming interface states, which at the localized site have an amplitude resonantly enhanced over the amplitude of the conduction electron states. The interface states mediate a continuous transition between the metal and the semiconducting or insulating oxide. Resonant tunneling via these interface states to an opposing metal surface can dominate over direct and intermediate-state tunneling. Resonant tunneling is obstructed by the correlation (Coulomb) energy which causes voltage, temperature and time dependencies. The obstruction increases with distance of the localized state from the metal and this increased obstruction causes the transition from resonant to intermediate-state tunneling. This corresponds to a space-wise metal-insulator transition. In oxides, like Nb₂O₅, the correlation energy is small and the hybridization is strong and thus resonant tunneling through localized states at the Fermi energy can account for various tunnel anomalies observed in the normal or superconducting state.     

Point impurities remove degeneracy of the Landau levels in a two-dimensional electron gas

The density of states of a two-dimensional electron gas in a magnetic field has been studied taking into account the scattering on point impurities. It is demonstrated that allowance for the electron-impurity interaction completely removes degeneracy of the Landau levels even for a small volume density of these point defects. The density of states is calculated in a self-consistent approximation taking into account all diagrams without intersections of the impurity lines. The electron density of states ρ is determined by the contribution from a cut of the one-particle Green’s function rather than from a pole. In a wide range of the electron energies ω (measured from each Landau level), the value of ρ(ω) is inversely proportional to the energy |ω| and proportional to the impurity concentration. The obtained results are applicable to various two-dimensional electron systems such as inversion layers, heterostructures, and electrons on the surface of liquid helium.     

Magnetic field effects on THz quantum cascade laser: A comparative analysis of three and four quantum well based active region design

We consider the influence of additional carrier confinement, achieved by application of strong perpendicular magnetic field, on inter Landau levels electron relaxation rates and the optical gain, of two different GaAs quantum cascade laser structures operating in the terahertz spectral range. Breaking of the in-plane energy dispersion and the formation of discrete energy levels is an efficient mechanism for eventual quenching of optical phonon emission and obtaining very long electronic lifetime in the relevant laser state. We employ our detailed model for calculating the electron relaxation rates (due to interface roughness and electron–longitudinal optical phonon scattering), and solve a full set of rate equations to evaluate the carrier distribution over Landau levels. The numerical simulations are performed for three- and four-well (per period) based structures that operate at 3.9 THz and 1.9 THz, respectively, both implemented in GaAs/Al_0.15Ga_0.85As. Numerical results are presented for magnetic field values from 1.5 T up to 20 T, while the band nonparabolicity is accounted for.     

Resonant tunneling transport through GaAs/AlGaAs superlattices in strong tilted magnetic field

An analysis is presented of the transverse resonant tunneling transport through GaAs/AlGaAs superlattices due to tunneling between Landau levels in quantum wells in a strong tilted magnetic field. A high tunneling rate is demonstrated between Landau levels with Δn ≠ 0 in a magnetic field with a nonzero in-plane component. This leads to substantial broadening and shift of the tunneling resonance and significant changes in the current-voltage characteristics of superlattices. The predicted behavior of the current-voltage characteristics of superlattices in tilted magnetic fields is demonstrated experimentally.     

Free electron laser study of the suppression of non-radiative scattering processes in semiconductors

A brief review is given of pump–probe studies of far infrared inter-sub-level relaxation between conduction band states in doped `quasi' quantum dots (created by the application of a magnetic field along the growth direction of an InAs/AlSb quantum well) and of mid-infrared (MIR) interband recombination in narrow gap semiconductors, using the free electron laser at FOM-Rijnhuizen (FELIX). In the former case, the longitudinal optic (LO) phonon scattering rate is shown to be suppressed by a factor of about 100 when the Landau level separation is off-resonance with the optical phonon energy; in the latter case, Auger recombination is shown to be substantially suppressed in the lead salts due to their `mirror' energy band structure.     

Strong effect of resonant impurities on Landau-level quantization

We investigate experimentally the effect of a random distribution of nitrogen (N) impurities on the Landau-level spectrum of a GaAs quantum well. Our magnetotunneling study reveals complex and nonequally spaced Landau levels and a quenching of the Landau states at a well-defined bias and electron energy which is resonant with that of the N atoms. Analysis of the magnetic field dependence of the tunnel current into the Landau levels of the well also provides quantitative information about the nonresonant component of the N-related scattering potential.     

Energy relaxation of two-dimensional electrons in the quantum Hall effect regime

The mm-wave spectroscopy with high temporal resolution is used to measure the energy relaxation times τ_e of 2D electrons in GaAs/AlGaAs heterostructures in magnetic fields B=0–4 T under quasi-equilibrium conditions at T=4.2 K. With increasing B, a considerable increase in τe from 0.9 to 25 ns is observed. For high B and low values of the filling factor ν, the energy relaxation rate τ _e ^?1 oscillates. The depth of these oscillations and the positions of maxima depend on the filling factor ν. For ν>5, the relaxation rate τ _e ^?1 is maximum when the Fermi level lies in the region of the localized states between the Landau levels. For lower values of ν, the relaxation rate is maximum at half-integer values of τ _e ^?1 when the Fermi level is coincident with the Landau level. The characteristic features of the dependence τ _e ^?1 (B) are explained by different contributions of the intralevel and interlevel electron-phonon transitions to the process of the energy relaxation of 2D electrons.     

Charge-magnetic interference resonant scattering studies of ferromagnetic crystals and thin films

The element- and site-specificity of X-ray resonant magnetic scattering (XRMS) makes it an ideal tool for furthering our understanding of complex magnetic systems. In the hard X-rays, XRMS is readily applied to most antiferromagnets where the relatively weak resonant magnetic scattering (10⁻²–10⁻⁶ I _c ) is separated in reciprocal space from the stronger, Bragg charge scattered intensity, I _c . In ferro(ferri)magnetic materials, however, such separation does not occur and measurements of resonant magnetic scattering in the presence of strong charge scattering are quite challenging. We discuss the use of charge-magnetic interference resonant scattering for studies of ferromagnetic (FM) crystals and layered films. We review the challenges and opportunities afforded by this approach, particularly when using circularly polarized X-rays. We illustrate current capabilities at the Advanced Photon Source with studies aimed at probing site-specific magnetism in ferromagnetic crystals, and interfacial magnetism in films.     

Magnetic-impurity states of electron in two-dimensional semiconductor structures

Electron states on an attractive center of small-radius r _c ? l (l = $\sqrt {\frac{{c\hbar }}{{eH}}} $ is the magnetic length) located in a two-dimensional structure are investigated in a uniform magnetic field H applied perpendicularly to the structure surface. The spectrum of magnetic-impurity (MI) particle states with an arbitrary moment projection on the direction H for Landau bands 0 ≤ N < l ²/r _c ² is derived in the approximation that mixing of Landau levels is weak. The dependence of the electron energy states on magnetic field, the layer thickness, and the impurity position are studied. It is shown that dimension lowering leads to a qualitatively different spectrum of MI states compared to the three-dimensional case [1]. A comparison of the obtained binding energy of the D ^? center with experimental data is performed.     

Theory of transient two-photon resonant up-conversion with non-synchronized excitation

The theory of the two-photon resonant up-conversion process (ω_a + ω_a) + ω_c ? ω_d is developed for short pulse excitation. Prominence is given to the case where the pulse at frequency ω_c is not time-synchronized with the pulse ω_a but travels immediately behind it. Not only is the conversion efficiency thereby maximized, but the associated theoretical simplification enables several analytical formulae to be derived which provide new insight into the mechanism of resonant non- linear interactions. In particular, an expression is derived for the maximum useful energy per unit area of the pulse at ω_c. Exceeding this value is of little or no advantage in the non-synchronized case and is positively detrimental when the a- and c-pulses are coincident. The results are supported by computer solutions.     

Carrier dynamics and stimulated radiative terahertz transitions between Landau levels in cascade GaAs/AlGaAs quantum well structures

The carrier distribution over Landau levels was studied in resonant tunneling GaAs/AlGaAs quantum well structures under tunneling pumping of the upper subband. The numerical calculations of the Landau level populations for various values of pumping intensity (tunneling time), magnetic field and structure doping were carried out. The population inversion between zeroth Landau level of the upper subband and the first Landau level of the lowest subband was shown to exist in wide range of the magnetic field strength. The effect of various scattering mechanisms, both two-particle (electron-electron scattering) and single-particle (acoustic phonon and interface roughness scattering) ones, on level population was studied. The way of lifting the selection rule forbidding the inter-Landau level terahertz transitions of interest and achieving considerable values of the dipole matrix element is proposed.     

Prediction of strong magnetic quantum oscillations of the nuclear spin relaxation in a quasi-two-dimensional metal

The nuclear spin lattice relaxation rate in a quasi-two-dimensional (2-D) metal under strong magnetic fields is studied in a special case where the electronic cyclotron mass is small compared with the free electron mass. In the pure limit (ω_cτ ? 1) and for sufficiently low temperatures ($\text{h}\text{?}\text{ω}{}_{\mathrm{c}}\text{> 2π}{}^2\text{k}{}_{\mathrm{B}}\text{T}$) we find remarkable quantum oscillations of the relaxation rate as a function of the magnetic field. The period of these oscillations is identical to that of the de Haas-van Alphen oscillations and their amplitude grows linearly with the magnetic field. The possibility of observing such oscillations experimentally in the quasi-2-D mercury chain compound Hg_3?δAsF₆ is discussed.