A Similar Change in the Kinetic-Energy Components of Longitudinal Continuous Motion of Magnetized Electrons within the Landau Levels and Determination of the Characteristics of a Degenerate System

Account is taken of a similar change in the kinetic-energy components of a longitudinal electron motion along the magnetic field within each Landau energy level. The maximum electron energy is found as well as the kinetic energy of a transverse electron motion in the magnetic field. The electron concentrations are determined depending on the magnetic-field strength, whose intrinsic magnetic moments are directed along and opposite the field. The magnetic-field strengths for which a certain number of Landau quantum levels is realized in an electron degenerate system of a specified concentration are also found.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 18–22, March, 2005.     

Relativistic Landau quantization in the spiral dislocation spacetime

We analyse the interaction of a relativistic electron with a uniform magnetic field in the spiral dislocation spacetime.We show that analytical solutions to the Dirac equation can be obtained,where the spectrum of energy corresponds to the relativistic Landau levels.We also analyse the influence of the spiral dislocation on the relativistic Landau levels by showing that there exists an analogue of the Aharonov–Bohm effect for bound states.     

Topological and non inertial effects on the interband light absorption

In this work, we investigate the combined influence of the nontrivial topology introduced by a disclination and non inertial effects due to rotation, in the energy levels and the wave functions of a noninteracting electron gas confined to a two-dimensional pseudoharmonic quantum dot, under the influence of an external uniform magnetic field. The exact solutions for energy eigenvalues and wave functions are computed as functions of the applied magnetic field strength, the disclination topological charge, magnetic quantum number and the rotation speed of the sample. We investigate the modifications on the light interband absorption coefficient and absorption threshold frequency. We observe novel features in the system, including a range of magnetic field without corresponding absorption phenomena, which is due to a tripartite term of the Hamiltonian, involving magnetic field, the topological charge of the defect and the rotation frequency.     

Charged particle with magnetic moment in a space with a screw dislocation

In this work we study the interaction of a charged quantum mechanical particle with magnetic moment in a space with a screw dislocation. We focus on the influence of the screw dislocation on the energy spectrum and eigenfunctions of the electron with spin-1/2 in a uniform magnetic field. We use the approach of the continuum theory of defects that is isomorphic to three-dimensional gravity.     

光学极化子性质对耦合强度和磁场的依赖性

应用线性组合算符和幺正变换方法,研究磁场和耦合强度对光学极化子性质的影响。数值计算表明:当电子接近晶体表面时,光学极化子的振动频率、基态能量和第一激发能仅与磁场有关,且随磁场强度的增强而增大;当电子远离晶体表面时,基态能量和第一激发能与磁场强度和耦合参数均有关,且随磁场强度和耦合参数的增加而增加。     

Stable Pfaffian state in bilayer graphene

Here, we show that the incompressible Pfaffian state originally proposed for the 5/2 fractional quantum Hall states in conventional two-dimensional electron systems can actually be found in a bilayer graphene at one of the Landau levels. The properties and stability of the Pfaffian state at this special Landau level strongly depend on the magnetic field strength. The graphene system shows a transition from the incompressible to a compressible state with increasing magnetic field. At a finite magnetic field of ~10 T, the Pfaffian state in bilayer graphene becomes more stable than its counterpart in conventional electron systems.     

Quantum-mechanical substantiation of a similar change in the kinetic energy component of an electron along the magnetic field within each Landau level

A detailed solution to the Schr?dinger equation for an electron in the presence of a quantizing magnetic field is considered using the method of separation of variables. The discrete energy levels occurring in this case are regarded as the potential barriers of finite height, with an electron moving normal to them along the magnetic-field direction. A similar change in the difference between the energy values within the neighboring Landau levels allows us to show, basing on the general properties of one-dimensional electron motion in the magnetic field, that within each quantum energy level, the kinetic-energy component of a longitudinal electron motion continuously is varied between 0 and 2μ_BH, whereas the probability density of particle location is practically damped into the potential-barrier depth as it moves along the magnetic-field direction. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 3–7, October, 2006.     

Screw dislocation-induced influence of transverse modes on Hall conductivity

The Hall conductivity of an electron gas on an interface showing a topological defectcalled screw dislocation is investigated. This kind of defect induces a singular torsionon the medium which in turn induces transverse modes in the quantum Hall effect. It isshown that this topology decreases the plateaus’ widths and shifts the steps in the Hallconductivity to lower magnetic fields. The Hall conductivity is neither enhanced nordiminished by the presence of this kind of defect alone. We also consider the presence oftwo defects on a sample, a screw dislocation together with a disclination. For a specificvalue of deficit angle, there is a reduction in the Hall conductivity. For an excess ofangle, the steps shift to higher magnetic fields and the Hall conductivity is enhanced.Our work could be tested only in common semiconductors but we think it opens a road to theinvestigation on how topological defects can influence other classes of Hall effect.     

Threading dislocation densities in semiconductor crystals: A geometric approach

In this Letter, we introduce a geometric model to explain the origin of the observed shallow levels in semiconductors threaded by a dislocation density. We show that a uniform distribution of screw dislocations acts as an effective uniform magnetic field which yields bound states for a spin-half quantum particle, even in the presence of a repulsive Coulomb-like potential. This introduces energy levels within the band gap, increasing the carrier concentration in the region threaded by the dislocation density and adding additional recombination paths other than the near band-edge recombination.     

Landau Diamagnetism,Pauli Paramagnetism,and Determination of Longitudinal and Transverse Kinetic Energy Components of a Degenerate Nonrelativistic Electron Gas

The Fermi energy, density of average kinetic energy, and average density of kinetic energy of the transverse finite motion of an electron gas of a specified concentration are calculated taking into account Landau diamagnetism and Pauli paramagnetism. The kinetic energy of a longitudinal continuous electron motion along the direction of the external magnetic field H is estimated. It is shown that the kinetic energy of the longitudinal continuous motion vanishes with increase in the external magnetic field strength in the quantum limit where the maximum Landau quantum number N _m = 0. For N _m > 0, the longitudinal kinetic energy component of a degenerate electron gas somewhat increases with magnetic field strength. The cause of the erroneous result is discussed.     

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.     

Landau levels in a simple hexagonal bilayer graphene

A new approach, which makes the Hamiltonian of the Peierls tight-binding model change into a band matrix, is used to investigate the Landau levels in a AA-stacked bilayer graphene. The interlayer atomic hoppings could induce an energy gap, the asymmetry of the Landau levels about the chemical potential, the random variation in the level spacing, more fourfold degenerate Landau levels at low energy, and the oscillatory Landau levels and the complicated state degeneracies at moderate energy. For the low-energy Landau levels, their dependence on the quantum number and the field strength cannot be well characterized by a simple power law. They exhibit a anomalous oscillation during the variation of the magnetic field. The main features of the magnetoelectronic states are directly reflected in density of states.     

Screw dislocations in the field theory of elastoplasticity

A (microscopic) static elastoplastic field theory of dislocations with moment and force stresses is considered. The relationship between the moment stress and the Nye tensor is used for the dislocation Lagrangian. We discuss the stress field of an infinitely long screw dislocation in a cylinder, a dipole of screw dislocations and a coaxial screw dislocation in a finite cylinder. The stress fields have no singularities in the dislocation core and they are modified in the core due to the presence of localized moment stress. Additionally, we calculated the elastoplastic energies for the screw dislocation in a cylinder and the coaxial screw dislocation. For the coaxial screw dislocation we find a modified formula for the so‐called Eshelby twist which depends on a specific intrinsic material length.     

Donor-bound electron states in a two-dimensional quantum ring under uniform magnetic field

The electron states in a two-dimensional GaAs/AlGaAs quantum ring are theoretically studied in effective mass approximation. On-centre donor impurity and uniform magnetic field perpendicular to the ring plane are taken into account. The energy spectrum with different angular momentum changes dramatically with the geometry of the ring. The donor impurity reduces the energies with an almost fixed value; however, the magnetic field alters energies in a more complex way. For example, energy levels under magnetic field will cross each other when increasing the inner radius and outer radius of the ring, leading to the fact that the arrangement of energy levels is distinct in certain geometry of the ring. Moreover, energy levels with negative angular momentum exhibit the non-monotonous dependence on the increasing magnetic field.     

Giant quantum oscillations of the skin layer in semimetals

We study theoretically the effect of electron energy quantization in a magnetic field on the penetration of radio waves into a semimetal in a geometry in which a constant magnetic field H is directed along the trigonal axis of a crystal. In this geometry, strong magnetic Landau damping in semimetals prevents wave propagation and is responsible for the skin effect. It is shown that quantization of the transverse energy of electrons considerably influences the effectiveness of collisionless absorption of the wave. As a result, the magnetic Landau damping and the skin depth experience giant oscillations upon a change in magnetic field H.     

Effects of rotation on Landau states of electrons on a spherical shell

Based on a previously observed analogy between electromagnetic and non-inertial effects, we investigate the competition between magnetic field and rotation in the quantum motion of an electron constrained to the surface of a sphere. We solve numerically the Schrödinger equation of the problem for the energy eigenvalues and the eigenfunctions and compare the effects of the magnetic field and rotation. We obtain that, for a weak magnetic field, an electron can not distinguish between magnetic field and rotation, since they lead to equivalent behavior. But this is no longer true for strong magnetic fields. However, surprisingly, even though the rotation and magnetic fields play different roles in the electronic properties of the system, when together, each influence of the magnetic field on the energy levels can be separately balanced by rotation. We also show that no matter the intensity of the magnetic field, it is always possible to destroy the Landau levels in the sphere by rotation.     

Doped graphene in a quantizing magnetic field: Hall conductivity

The energy spectrum of electrons in doped graphene corresponding to the Landau levels in an external transverse magnetic field has been calculated in the low-energy approximation. The magnetic-field dependence of the electrical conductivity has been determined based on the derived dispersion relation of electrons in the doped graphene. The behavior of the conductivity has been analyzed for different impurity parameters, such as the hybridization potential and energy of adsorbed atoms.     

Magnetic-field-induced motion of disclinations in a twisted nematic layer

In a twisted nematic layer oppositely twisted regions can exist, separated by a disclination line, as demonstrated by the orientation of Williams domains. The disclination line can move under the influence of a magnetic field. Measurements of the velocity as a function of magnetic field strength and sample thickness lead to an estimate of the size of the disclination core.     

Addition to the Solution of the Problem on the Motion of a Free Nonrelativistic Electron in a Magnetic Field

In addition to the solution of the quantum mechanical problem on the motion of a free electron in a magnetic field, given by L. D. Landau in his pioneering work, this quantum mechanical problem is solved in view of the fact that the sum of the components of the free kinetic energy of an electron along two axes is a periodic quantity varying identically within the boundaries of every Landau energy level. This periodicity is a consequence of the quantized motion of an electron in a plane normal to the direction of the external magnetic field.