Landau quantization of a two-dimensional electron with the nonparabolic dispersion law, pseudospin components and chirality terms

The Landau quantization of a two-dimensional electron in a perpendicular magnetic field on the basis of a Hamiltonian with two pseudospin components is considered. The diagonal elements of the Hamiltonian have non-parabolic but circular symmetric dispersion laws, whereas the off diagonal elements contain the chirality terms of different degrees. The solution of the matrix form Schrödinger equation was found following the method proposed by Rashba in his theory of spin-orbit coupling, taking into account different degrees of chirality and deviations on the parabolic dispersion law. The Landau quantization Hamiltonians were obtained by substituting the canonical momentum operators by the kinetic momentum operators. Two concrete examples were discussed. One of them concerns the Mexican hatlike dispersion law in the biased bilayer graphene with second order chirality, when the Landau quantization levels except two are characterized by two quantum numbers (n−2) and n for n≥2, corresponding to different pseudospin projections. They differ by 2 as the degree of chirality is. There are two energy levels E^±(n−2,n) with the same numbers (n−2) and n. The lower energy levels E⁻(n−2,n) have a linear decreasing behavior with dependence on the magnetic field strength H with different slopes and minima for different values of n≥2. At the intersection point H_th, two energy levels E⁻(1,3) and E⁻(0,2) have the same energy forming two degenerate LLLs. Touching the minima at different values of H, the energy branches gradually transform in the increasing quadratic dependences proportional to (2n+1)²H². The similar results were obtained in the case of cosine-type dispersion law in the frame of one-band model.     

Exact Solutions Describing Collapse of Landau Levels in Graphene

The eigenequation for single-layer graphene in transverse electric and perpendicular magnetic fields is investigated at a critical value |E| = υ _F B. The critical solutions are not bound states and contain two unknown constants. Different from the case of the “classical” Hall effect, the electric current in the direction perpendicular to the electric and magnetic fields could be positive or negative depending on the values of the unknown constants.     

Influence of Magnetic Confinement on the Yellow Excitons in Cuprous Oxide Subject to an Electric Field

We study the spectrum of the yellow exciton series in crossed electric and magnetic fields. The electric field, applied along the optical axis, tilts the Coulomb potential between electron and hole, so that at sufficiently high fields exciton dissociation becomes possible, roughly when the electric dipole interaction energy exceeds the binding energy of an exciton state with principal quantum number n. For an applied voltage of U = 20 V all excitons above n = 6 are dissociated. Additional application of a magnetic field normal to the optical axis introduces magnetic confinement, due to which above a threshold field strength around B = 2.5 T the exciton lines re-emerge. The complex dispersion with increasing fields suggests quantum chaotic behavior in this crossed field configuration, so that the search for exceptional points may be promising.     

Cyclotron resonance study of conduction electrons in n-type indium antimonide under a strong magnetic field—II: Hot electrons

A system of hot electrons in the n-InSb under the application of a strong magnetic field has been studied by far IR cyclotron resonance. A three band model and an energy independent scattering time were assumed in analyzing the line shape variation with electric field applied either parallel or perpendicular to the magnetic field. Two kinds of electron temperature, inter- and intra-subband, were introduced to describe the electron distribution in energy space. The electron distribution function was found to deviate from an essentially Maxwellian form in the manner predicted by Yamada and Kurosawa. A remarkable difference exists between the two geometries: E∥H and E⊥U. A brief survey of cyclotron emission, and the reverse process of hot electron cyclotron absorption, is summarized at the end as an addendum.     

Instability of electromagnetic waves in transversely magnetised semiconductor-plasmas

Using the hydrodynamic model of plasmas the general dispersion relation is derived in the collisiondominated regime when a d.c. magnetic field is applied (Y-axis) transversly to the propagation vector k (Z-axis), and the d.c. electric field is inclined to the Z-axis in the X-Z plane. The dispersion relation is solved for intrinsic and extrinsic semiconductors to explore the possibility of wave instability. The threshold conditions of wave oscillations are obtained. In n-InSb the frequency of the oscillation attains a maximum value when the electron cyclotron frequency is equal to the electron collision frequency. In intrinsic InSb instability is possible only in the long wavelength region for E₀ ? 10 kVm^?1 when B₀> 0.2 T, while for lower values of B₀, E₀ should be greater 20kVm^?1. The energy dependent collision frequency has a significant effect on the threshold frequency of oscillation.     

Electric-field-induced energy spectra and dispersions of ZnO/MgxZn1−xO MQWs

The energy spectra and dispersion relations of carriers in the presence of an electric field applied along the growth direction in ZnO/Mg_xZn_1−xO multiple quantum wells (MQW) are calculated using the asymptotic transfer method (ATM) on the basis of the quasistationary state approximation. The energy spectra of the carriers induce some quasi-bound levels under electric fields. The dispersion relations for the energy of the ground state and lower excitation states still have parabolic shapes for both the electrons and the heavy holes in the presence of a moderate electric field. Our results also reveal that the number of energy levels increases with increasing number of ZnO quantum wells and that the energies increase with both increasing Mg composition x and electric field strength.     

Magnetic Bloch states and Hall conductivity of a two-dimensional electron gas in a periodic potential without inversion center

Quantum states of 2D electrons are studied in a periodic potential without inversion center in the presence of a magnetic field. It is shown that the energy spectrum in magnetic subbands is not symmetric about the center of magnetic Brillouin zone E(k)≠E(?k). Singularities (phase branching points) of the electron wave function, which determine the quantization law of Hall conductivity σ_xy, are studied in the k space. It is found that a sharp change takes place in the number of points in the magnetic Brillouin zone and in the corresponding values of topological invariants determining the Hall conductivity of filled subbands. It is noted that the longitudinal conductivity of a lattice without inversion center placed in a magnetic field is not invariant with respect to a change in sign of the electric field, and a photovoltaic effect must arise in an ac electromagnetic field.     

Dynamics of magnetic insulation failure and self-organization of an electron flow in a magnetron diode

The dynamics of back cathode bombardment (BCB) instability in a magnetron diode (a coaxial diode in a magnetic field, B ≡ B _0z ≡ B ₀) is numerically simulated. The quasi-stationary regime of electron leakage across the high magnetic field (B ₀/B _cr > 1.1, where B _cr is the insulation critical field) is realized. An electron beam in the electrode gap is split into a series of bunches in the azimuthal direction and generates the electric field component E _θ(r, θ, t), which accelerates some of the electrons. Having gained an extra energy, these electrons bombard the cathode, causing secondary electron emission. The rest of the electrons lose kinetic energy and move toward the anode. Instability is sustained if the primary emission from the cathode is low and the secondary emission coefficient k _se=I _se/I _{e, BCB} is greater than unity. The results of numerical simulation are shown to agree well with experimental data. A physical model of back-bombardment instability is suggested. Collective oscillations of charged flows take place in the gap with crossed electric and magnetic fields (E × B field) when the electrons and E × B field exchange momentum and energy. The self-generation and self-organization of flows are due to secondary electron emission from the cathode.     

Electrical properties of SrBi2(Nb0.5Ta0.5)2O9 ceramics

Aurivillius SrBi₂(Nb_0.5Ta_0.5)₂O₉ (SBNT 50/50) ceramics were prepared using the conventional solid-state reaction method. Scanning electron microscopy was applied to investigate the grain structure. The XRD studies revealed an orthorhombic structure in the SBNT 50/50 with lattice parameters a=5.522 Å, b=5.511 Å and c=25.114 Å. The dielectric properties were determined by impedance spectroscopy measurements. A strong low frequency dielectric dispersion was found to exist in this material. Its occurrence was ascribed to the presence of ionized space charge carriers such as oxygen vacancies. The dielectric relaxation was defined on the basis of an equivalent circuit. The temperature dependence of various electrical properties was determined and discussed. The thermal activation energy for the grain electric conductivity was lower in the high temperature region (T>303.6 °C, E_a−ht=0.47 eV) and higher in the low temperature region (T<303.6 °C, E_a−lt=1.18 eV).     

Superparamagnetic behavior of La0.67Sr0.33MnO3 nanoparticles prepared via sol-gel method

Magnetic nanoparticles of La_0.67Sr_0.33MnO₃ (LSMO) manganite were prepared by sol-gel method. Phase formation and crystal structure of the synthesized powder were examined by the X-ray diffraction (XRD) using the Rietveld analysis. The mean particle size was determined by the transmission electron microscopy (TEM). Infrared transmission spectroscopy revealed that stretching and bending modes are influenced by calcinations temperature. The temperature dependence of the ac magnetic susceptibility was measured at different frequencies and ac magnetic fields in the selected ranges of 40-1000 Hz and 80-800 A/m, respectively. The temperature dependence of ac susceptibility shows a characteristic maxima corresponding to the blocking temperature near room temperature. The frequency dependence of the blocking temperature is well described by the Vogel-Fulcher law. By fitting the experimental data with this law, the relaxation time τ₀=1.7×10⁻¹² s, characteristic temperature T₀=262±3 K, anisotropy energy E_a/k=684±15 K and effective magnetic anisotropy constant k_eff=2.25×10⁴ erg/cm³ have been obtained. dc Magnetization measurement versus magnetic field shows that some of LSMO nanoparticles are blocked at 293 K. The role of magnetic interparticle interactions on the magnetic behavior is also investigated.     

Zeeman and spin–orbit effects on the spin-Hall conductance

We show that when a two-dimensional interacting electron gas is submitted to a perpendicular magnetic field, the application of an in-plane electric field E induces a spin current perpendicular to E whose conductivity is quantized. This current can lead to spin accumulation that might be detected by means of optical experiments. The appearance of this intrinsic spin-Hall effect is crucially based on the validity of Kohn's theorem and on the presence of the Zeeman term in the electron Hamiltonian. The possibility of resonant effects in the spin-Hall conductivity due to the combined effect of Rashba and Dresselhaus spin–orbit couplings is discussed.     

EPR and optical absorption study of Cr-doped ammonium oxalate monohydrate single crystals

The electron paramagnetic resonance (EPR) study of the Cr³⁺-doped ammonium oxalate monohydrate (AOM) single crystal is done at room temperature. Two magnetically inequivalent sites for chromium are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The spin Hamiltonian parameters are evaluated as: D=(309±2)×10⁻⁴ cm⁻¹, E=(103±2)×10⁻⁴ cm⁻¹, g=1.9820±0.0002, A=(161±2)×10⁻⁴ cm⁻¹ for site I and D=(309±2)×10⁻⁴ cm⁻¹, E=(103±2)×10⁻⁴ cm⁻¹, g=1.9791±0.0002, A=(160±2)×10⁻⁴ cm⁻¹ for site II, respectively. On the basis of EPR data the site symmetry of Cr³⁺ doped single crystal is discussed. The optical absorption spectra are recorded in 195-925 nm wavelength range at room temperature. The energy values of different orbital levels are determined. On the basis of EPR and optical data, the nature of bonding in the crystal is discussed. The values of different parameters are B=803, C=3531, D_q=2208 cm⁻¹, h=0.59 and k=0.21, where B and C are Racah parameters, D_q is crystal field parameter and h and k are nephelauxetic parameters, respectively.     

Density fluctuation spectrum in whistler turbulence

We develop a nonlinear two-dimensional fluid model of whistler turbulence that includes effect of electron fluid density perturbations. The latter is coupled nonlinearly with wave magnetic field. This coupling leads essentially to finite compressibility effects in whistler turbulence model. We find from our simulations that despite strong compressibility effects, the density fluctuations follow the evolution of the wave magnetic field fluctuations. In a characteristic regime where large scale whistlers are predominant, the coupled density fluctuations are found to follow a Kolmogorov-like phenomenology in the inertial range turbulence. Consequently, the turbulent energy is dominated by the large scale (compared to electron inertial length) eddies and it follows a Kolmogorov-like k−7/3 spectrum, where k is a characteristic wavenumber.     

Dependence of the interband transitions on the in mole fraction and the applied electric field in InxGa1−xAs/In0.52Al0.48As multiple quantum wells

Transmission electron microscopy (TEM) and photocurrent (PC) measurements were carried out to investigate the microstructural properties and excitonic transitions in In_xGa_1−xAs/In_0.52Al_0.48As multiple quantum wells (MQWs) for x = 0.54, 0.57 and 0.60. TEM images showed that high-quality 11-period In_xGa_1−xAs/In_0.52Al_0.48As MQWs had high-quality heterointerfaces. The results for the PC spectra at 300 K showed that the peaks corresponding to the excitonic transitions from the ground state electronic sub-band to the ground state heavy-hole band (E₁-HH₁) and the ground state electronic sub-band to the ground state light-hole band (E₁-LH₁) became closer to each other with decreasing In mole fraction and that E₁-HH₁ and E₁-LH₁ excitonic peaks shifted to longer wavelength with increasing applied electric field. The calculated values of the E₁-HH₁ interband transition energies were in qualitative agreement with those obtained form the PC measurements with and without applied electric field. These results can be helpful in understanding potential applications of In_xGa_1−xAs/In_yAl_1−yAs MQWs dependent on In mole fraction and applied electric field in long-wavelength optoelectronic devices.     

Edge current switch of two-dimensional electron gas using carrier density control

We have investigated the effects of electron density discontinuity on the transports of edge currents of two-dimensional electron gas (2DEG). The electric field applied to a gate, which covers the 2DEG partially, gives rise to change in the carrier density and results in a density gradient, which deforms the edge currents. The transverse and longitudinal resistances were measured as functions of gate voltage V_G in the quantum Hall regime. The deviations of the longitudinal resistances from the normal quantum Hall resistances are attributed to the reflections of the edge currents under the influence of the abrupt density discontinuity. A switching behavior of the transverse resistance by controlling the gate voltage was observed when V_G=−2.2 and −2.0 V for magnetic field H=5 and 7.2 T, respectively.     

Deformation of NaCl crystals under combined action of magnetic and electric fields

The paper reports observation of a strong macroplastic effect of weak magnetic and electric fields (B≤0.4 T, E～1 kV/m) when applied simultaneously to NaCl samples in the course of their active deformation at constant rate ?=const. In the absence of magnetic field, electric effects in the macroplasticity of the same crystals become manifest at fields E≥10³ kV/m. Quantitative dependences of the macroplasticity on magnetic and electric fields and on the strain rate have been measured. A physical interpretation of the observed phenomena is proposed.     

Electrical properties of KTiOPO4 single crystal in the temperature range from −100 °C to 100 °C

The electrical property of a KTiOPO₄ single crystal was studied by means of a dielectric spectroscopy method in the temperature range from −100 to 100 °C. Dielectric dispersion began at a temperature, T_S=−80 °C. It is believed that this dielectric dispersion is related to the ionic hopping conduction, which arises mainly from the jumping of K⁺ ions. The activation energy concerned with hopping conduction is E_a∼0.20 eV above T_S. T_S=−80 °C can be the minimum temperature for the hopping K⁺ ion.     

Strange anisotropy in amorphous metals

The spin orientation in ferromagnetic amorphous Fe₈₃P₅C₁₂ in an external magnetic field, H_ext, applied perpendicular to the ribbon sample has been determined by magnetoresistance measurements and by the angular dependence of the hyperfine interaction. In small fields, H_ext ? 4 kOe, the spins tend to orient themselves perpendicular to H_ext due to the influence of the demagnetizing field and in large fields, H_ext ≈ 50 kOe, a complete alignment was not obtained.     

Attenuation and escape depths of low-energy electron emission

Electron transport and emission is simulated by two Monte Carlo (MC) programs. The first version is based on elastic Mott cross sections and inelastic loss functions with full dispersion ΔE=ℏω(q), including electron impact and subsequent cascading processes. Surface effects like surface plasmons and the quantum mechanical surface transmittivity have been taken into account too. Especially for dielectric materials like SiO₂ and applied electric fields a second MC version is developed based on the electron scattering with acoustic and optical phonons, intra- and intervalley scattering and impact valence band ionization. A comparison of both versions results in a good agreement still in the energy region of several eV, but a predominance of the phonon-based second version is found for very low electron energies, e.g., for hot and ballistic electrons in dielectric materials.     

Mössbauer study of CoFeRhO4

CoFeRhO₄ has been studied by Mössbauer spectroscopy and X-ray diffraction. The crystal is found to have a cubic spinel structure with the lattice constant a₀=8.451±0.005 Å. The iron ions are in ferric states. The temperature dependence of the magnetic hyperfine field is analyzed by the Néel theory of ferrimagnetism. The intersublattice superexchange interaction is antiferromagnetic and strong with a strength of J_AB=−12.39k_B while the intrasublattice superexchange interactions are weak with strengths of J_AA=−4.96k_B and J_BB=6.20k_B. As the temperature increases toward the Néel temperature T_N, a systematic line broadening effect in the Mössbauer spectrum is observed and interpreted to originate from different temperature dependences of the magnetic hyperfine fields at various iron sites.