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.     

Non-Abelian Chern-Simons particles in an external magnetic field

The quantum mechanics and thermodynamics of SU(2) non-Abelian Chern-Simons particles (non-Abelian anyons) in an external magnetic field are addressed. We derive the N-body Hamiltonian in the (anti-) holomorphic gauge when the Hilbert space is projected onto the lowest Landau level of the magnetic field. In the presence of an additional harmonic potential, the N-body spectrum depends linearly on the coupling (statistics) parameter. We calculate the second virial coefficient and find that in the strong magnetic field limit it develops a step-wise behavior as a function of the statistics parameter, in contrast to the linear dependence in the case of Abelian anyons. For small enough values of the statistics parameter we relate the N-body partition functions in the lowest Landau level to these of SU(2) bosons and find that the cluster (and virial) coefficients dependence on the statistics parameter cancels.     

Influence of quantization of band states on the effective electron mass in quaternary alloys

Summary An attempt is made to study the effective electron mass in quaternary alloys, taking a In_1−x Ga _x As _y P_1−y lattice matched to InP, by using the three-band Kane model under different physical conditions,e.g. bulk specimens, magnetic quantization, cross-field configuration, quantum well, electric-field-aided quantum well, magnetic-field-aided quantum well, quantum well under cross fields, quantum well wires, electric-field-aided quantum well wires, magnetic-field-aided quantum well wires and quantum well wires under cross fields by formulating the respective expressions. We have plotted the effective Fermi level mass with various physical variables under different conditions. In the presence of a quantizing magnetic field the effective mass depends on the spin splitting of Landau levels due to the spin-orbit splitting parameter of the valence bands. Under cross-field configuration and the various quantum confined low-dimensional systems, the effective masses depend on the respective quantum numbers in addition to the Fermi energies even for parabolic models because of the inherent features of such systems. In addition, the corresponding results for relatively wide-gap materials have also been obtained from our generalized formulations under certain limiting conditions.     

Tunneling conductivity oscillations in a magnetic field in metal-insulator-narrow-gap-HgCdTe structures: The energy spectrum and spin-orbit splitting of 2D states

We study tunneling conductivity oscillations in a magnetic field in narrow-gap p-HgCdTe-oxide-metal (Yb, Al) structures. In tunnel structures with Yb we detect two types of tunneling conductivity oscillations. The first is related to the crossing of the Landau levels of two-dimensional (2D) states localized in the surface quantum well of the semiconductor, and has an energy E _F+eV, where E _F is the Fermi energy of the semiconductor and V is the bias voltage; the second has an energy E _F. We find that in such structures with an asymmetric quantum well there is strong spin-orbit splitting in the spectrum of the 2D states. In p-HgCdTe-oxide-Al tunnel structures the surface potential is much weaker and only oscillations of the first type are observed. We find that in such structures there is only one spin state of the 2D carriers, while the second is pushed into the continuous spectrum because of strong spin-orbit coupling. To analyze the experimental results we calculate the spectrum of 2D states localized in the surface quantum well in a semiconductor with a Kane dispersion law. We find that all the experimental results are in good agreement with the results of calculations. Finally, we discuss the features of “kinematically coupled” states in an asymmetric quantum well. Zh. éksp. Teor. Fiz. 112, 537–550 (August 1997)     

Energy level of an electron in a saddle-potential quantum dot under a uniform magnetic field obtained by the invariant eigenoperator method

We show that the recently proposed invariant eigenoperator method can be successfully applied to solving the energy levels of an electron in a saddle-potential quantum dot under a uniform magnetic field. The Landau diamagnetism decreases with the value ω_y² - ω_x² due to the existence of the saddle potential.     

Quasi-one-dimensional quantum spin liquid in the Cu(C<Subscript>4</Subscript>H<Subscript>4</Subscript>N<Subscript>2</Subscript>)(NO<Subscript>3</Subscript>)<Subscript>2</Subscript> insulator

We analyze measurements of the magnetization, differential susceptibility and specific heat of quasi-onedimensional insulator Cu(C₄H₄N₂)(NO₃)₂ (CuPzN) subjected to magnetic fields. We show that the thermodynamic properties are defined by quantum spin liquid formed with spinons, with the magnetic field tuning the insulator CuPzN towards quantum critical point related to fermion condensation quantum phase transition (FCQPT) at which the spinon effective mass diverges kinematically. We show that the FCQPT concept permits to reveal and explain the scaling behavior of thermodynamic characteristics. For the first time, we construct the schematic T–H (temperature-magnetic field) phase diagram of CuPzN that contains Landau–Fermi-liquid, crossover and non-Fermi liquid parts, thus resembling that of heavy-fermion compounds.     

Role of electron spin in integer quantum hall photoluminescence

We investigate numerically the photoluminescence (PL) spectrum in the integer quantum Hall regime and find that the electron spins play important roles. The spectra for the left circularly polarized light show peak splittings when the Fermi levels lies in the excited Landau level, which is caused by the inter Landau level scattering between electrons with anti-parallel spins. At around ν_e∼1 the PL energy is strongly affected by the interplay between the screening and multiple spin flipping (skyrmion) effects.     

GaAsδ-doped quantum wire superlattice characterization by quantum Hall effect and Shubnikov–de Haas oscillations

Quantum wire superlattices (1D) realized by controlled dislocation slipping in quantum well superlattices (2D) (atomic saw method) have already shown Magneto-phonon oscillations. This effect has been used to investigate the electronic properties of such systems and prove the quantum character of the physical properties of the wires. By cooling the temperature and using pulsed magnetic field up to 35 T, we have observed both quantum Hall effect (QHE) and Shubnikov–de Haas (SdH) oscillations for various configurations of the magnetic field. The effective masses deduced from the values of the fundamental fields are coherent with those obtained with Magneto-phonon effect. The field rotation induces a change in the resonance frequencies due to the modification of the mass tensor as in a (3D) electron gas. In view the QHE, the plateaus observed in ρ_YZare dephased relatively toρ_ZZ minima which seems to be linked to the dephasing of the minima of the density of states of the broadened Landau levels.     

Properties of parallel upper critical field within continuous Ginzburg–Landau model

In this paper, we employ a continuous Ginzburg–Landau model to study the behaviors of the parallel upper critical field of an intrinsically layered superconductor. Near T_c where the order parameter is nearly homogeneous, the parallel upper critical field is found to vary as (1−T/T_c)^1/2. With a well-localized order parameter, the same field temperature dependence holds over the whole temperature range. The profile of the order parameter at the parallel upper critical field is of a Gaussian type, which is consistent with the usual Ginzburg–Landau theory. In addition, the influences of the unit cell dimension and the average effective masses on the parallel upper critical field and the associated order parameter are also addressed.     

外场调控下硼磷烯量子点的电子结构和光学性质研究

采用紧束缚近似方法对锯齿状六边形硼磷烯量子点在平面电场和垂直磁场调控下的电子结构和光学性质进行了研究. 研究表明,硼磷烯量子点作为直接带隙半导体,在无外加电场和磁场作用时,能隙不随尺寸的改变而变化. 在平面电场调控下,能隙随电场强度的增加逐渐减小直至消失,平面电场方向几乎不会对硼磷烯量子点体系产生影响, 且随量子点尺寸的增大,能隙消失所需电场强度逐渐减小. 在垂直磁场调控下,表现为体态的能级在磁场作用下形成朗道能级,而能隙边缘处的朗道能级近似为一个平带,不随磁通量的改变而变化,态密度主要分布于朗道能级处. 另外,垂直磁场作用下的光吸收主要是由朗道能级之间的跃迁引起的.     

Zener tunneling between the landau levels in quasi-two-dimensional electronic Corbino disks at large filling factors

The magnetotransport characteristics of quasi-two-dimensional electronic Corbino disks based on a wide GaAs quantum well with two filled subbands of size quantization are studied. At low temperatures and high magnetic fields, the Corbino disks exhibit the oscillations of differential conductivity, which are periodic with respect to dc electric field E _dc. It is shown that the observed oscillations are related to the Zener tunneling induced by E _dc. The tunneling occurs between the filled and empty Landau levels under conditions corresponding to the absence of the Hall field.     

Fisher Information of Free-Electron Landau States

An electron in a constant magnetic field has energy levels, known as the Landau levels. One can obtain the corresponding radial wavefunction of free-electron Landau states in cylindrical polar coordinates. However, this system has not been explored so far in terms of an information-theoretical viewpoint. Here, we focus on Fisher information associated with these Landau states specified by the two quantum numbers. Fisher information provides a useful measure of the electronic structure in quantum systems, such as hydrogen-like atoms and under some potentials. By numerically evaluating the generalized Laguerre polynomials in the radial densities, we report that Fisher information increases linearly with the principal quantum number that specifies energy levels, but decreases monotonically with the azimuthal quantum number m. We also present relative Fisher information of the Landau states against the reference density with m=0, which is proportional to the principal quantum number. We compare it with the case when the lowest Landau level state is set as the reference.     

Saturation spectroscopy of electronic states in a magnetic field in InAs/AlxGa1−xSb single quantum wells

We have carried out saturation spectroscopy of cyclotron resonance in a semiconducting InAs/Al_0.5Ga_0.5Sb single quantum well using the UCSB free electron laser and have extracted an effective Landau level lifetime using an n-level rate equation model. The effective lifetime shows strong oscillations (>an order of magnitude) with frequency. Minima are shifted to higher frequencies than those given by the simple parabolic magnetophonon resonance condition due to large nonparabolicity in the InAs conduction band. We have also used this technique to investigate the origins of two lines: the X-line and cyclotron resonance in a “semimetallic” InAs/Al_0.1Ga_0.9Sb single quantum-well structure. Results show that the two lines are of different origin.     

A Mathematical Representation of Quantizing the Motion of Relativistic Electrons in a Magnetic Field

It is shown that the quadratic component of the kinetic energy of continuous longitudinal motion of relativistic electrons in the external magnetic field is varied continuously between 0 and 2(2m _e c ²_B H) within each Landau energy level, undergoing an abrupt change at the boundaries of the levels. This results in the fact that in the quantum limit of a superstrong magnetic field where all electrons are at the zero Landau level, the maximum quadratic component of the kinetic energy of free longitudinal electron motion along the direction of the magnetic field is twice as high as the maximum quadratic component of the kinetic energy of its bound transverse motion.     

Quantum galvanomagnetic properties of n-type inversion layers on Si(100) MOSFET

Transverse magnetoconductivity σ_xx and Hall effect in n-type inversion layers of Si(100) MOSFET are measured for various source-drain fields between 0.08 and 40 V/cm under magnetic fields up to 150 kOe at 1.4 K. Conductivity peaks in low Landau levels are in good agreement with theory. Effect of the source-drain field in the magnetoconductivity is found to be very important in higher Landau levels as well as in the appearance of the lowest Landau level peak. Immobile electrons are clearly observed in conductivity bottoms. Electrode geometry effect for Hall effect measurement under strong magnetic fields is discussed.     

Photodetachment of H- near an elastic surface in a magnetic field

This paper investigates the photodetachment of the negative hydrogen ion H near an elastic wall in a magnetic field.The magnetic field confines the perpendicular motion of the electron,which results in a real three-dimensional well for the detached electron.The analytical formulas for the cross section of the photodetachment in the threedimensional quantum well are derived based on both the quantum approach and closed-orbit theory.The magnetic field and the elastic surface lead to two completely different modulations to the cross section of the photodetachment.The oscillation amplitude depends on the strength of the magnetic field,the ion-wall distance and the photon polarization as well.Specially,for the circularly polarized photon-induced photodetachment,the cross sections display a suppressed(E E th) 1/2 threshold law with energy E in the vicinity above Landau energy E th,contrasting with the(E E th) 1/2 threshold law in the presence of only the magnetic field.The semiclassical calculation fits the quantum result quite well,although there are still small deviations.The difference is attributed to the failure of semiclassical mechanics.     

Distribution functions for a two-dimensional non-interacting quantum electron gas in an external magnetic field

The exact n-body distribution functions are calculated for a two-dimensional, non-interacting quantum electron gas in an external magnetic field for any temperature and density. At low tempertures and filled lowest Landau level (LLL), these functions are identical to the exact distribution functions obtained by Jancovici [1981, Phys. Rev. Lett., 46, 386] for the classical two-dimensional one-component plasma (2DOCP) at the special plasma parameter Γ = 2, thus establishing that the 2DOCP provides an exact classical Boltzmann factor which describes the ideal LLL quantum state associated with the integral quantum Hall effect.     

Critical magnetic field ratio of anisotropic magnetic superconductors

The upper critical field, the lower critical field and the critical magnetic field ratio of anisotropic magnetic superconductors are calculated by Ginzburg–Landau theory analytically. The effect of the Ginzburg–Landau parameter (κ₀), magnetic susceptibility (χ) and magnetic-to-anisotropic parameter ratio (θ) on the critical field ratio are considered. We find that the value of critical field ratio increases with increasing κ₀ and θ, and decreases with increasing χ. The highest and the lowest value of critical field ratio is found in the diamagnetic superconductors and the ferromagnetic superconductors, respectively.     

New polaron effect in magnetooptic phenomena in a quantum well

It is predicted that resonance coupling between two discrete electron energy levels corresponding to different size-quantization quantum numbers and different Landau quantum numbers can occur in a quantum well in a quantizing magnetic field. The resonance coupling is due to the interaction of an electron with LO phonons and results in the formation of polaron states of a new type. It is shown that for a certain value of the magnetic field, which depends on the splitting of the electron size-quantization levels, the absorption peak and the two-phonon resonance Raman scattering peak split into two components, the separation between which is determined by the electron-phonon coupling constant. The resonance coupling between size-quantization levels with the same Landau quantum numbers is also studied. The splitting of the peaks in this case is virtually independent of the magnetic field and can be observed in much weaker fields. The experimental observation of the effect will make it possible to determine the relative position of the electronic levels and the electron-phonon coupling constant. Pis’ma Zh. éksp. Teor. Fiz. 65, No. 7, 511–515 (10 April 1997)     

Magneto-dimensional resonance. Pseudospin phase and hidden quantum number

The Schrödinger operator for a spinless charge inside a layer with parabolic confinement profile and homogeneous magnetic field is considered. The Lorentz (cyclotron) and the confinement frequencies are assumed to be equal to each other. After inclination of the layer normal from the magnetic field direction there appears a pseudospin su(2)-field removing the resonance degeneracy of Landau levels. Under deviations of the layer surface from the plane shape, a longitudinal geometric current is created. In circulations around surface warping, there is a nontrivial quantum phase transition generated by an element of the π₁-homotopy group and a hidden degree of freedom (spectral degeneracy) associated with a “charge” of geometric poles on the layer. The quantization rule contains an additional parity index related to the algebraic number of geometric poles and the Landau level number. The resonance pseudospin phase-shift represents an example of general Aharonov–Bohm type topologic phenomena in quantum (semiclassical or adiabatic) systems with delta-function singularities in symplectic structure.