Zitterbewegung of electrons in quantum wells and dots in the presence of an in-plane magnetic field

We study the effect of an in-plane magnetic field on the zitterbewegung (ZB) of electrons in a semiconductor quantum well (QW) and in a quantum dot (QD) with the Rashba and Dresselhaus spin-orbit interactions (SOIs). We obtain a general expression of the time-evolution of the position vector and current of the electron in a semiconductor QW. The amplitude of the oscillatory motion is directly related to the Berry connection in momentum space. We find that in presence of the magnetic field the ZB in a QW does not vanish when the strengths of the Rashba and Dresselhaus SOIs are equal. The in-plane magnetic field helps to sustain the ZB in QWs even at a low value of k(0)d (where d is the width of the Gaussian wavepacket and k(0) is the initial wavevector). The trembling motion of an electron in a semiconductor QW with high Landé g-factor (e.g. InSb) is sustained over a long time, even at a low value of k(0)d. Further, we study the ZB of an electron in QDs within the two sub-band model numerically. The trembling motion persists in time even when the magnetic field is absent as well as when the strengths of the SOI are equal. The ZB in QDs is due to the superposition of oscillatory motions corresponding to all possible differences of the energy eigenvalues of the system. This is an another example of multi-frequency ZB phenomenon.     

Effect of an in-plane magnetic field on magnetoresistance hysteresis of the two-dimensional electron gas in the integer quantum Hall effect regime

Effect of an in-plane magnetic field on the features of the magnetoresistance of a narrow conducting channel placed in the bath of a macroscopic two-dimensional electron gas has been studied. These features are manifested in the hysteretic behavior of the magnetoresistance in the quantum Hall effect regime. It has been found that the hysteresis loops observed in different ranges of the filling factor may be separated into two groups that differ in both the response to the in-plane magnetic field and the temperature dependence. The basic features observed near the integer filling factors ν = 1 and 2 are almost independent of the in-plane magnetic field. Therefore, their origin is not associated with spin effects. At the same time, additional features that appear at ν ≈ 1.8 and 2.2 are suppressed by the in-plane magnetic field B _‖ ≈ 6 T and almost temperature-independent from 45 mK to 1 K.     

Dependence of electron spin g-factor on magnetic field in quantum wells

The dependence of electron spin g-factor on magnetic field has been investigated in GaAs/AlGaAs quantum wells. We have estimated the electron g-factor from spin precession frequency in time-resolved photoluminescence measurements under a magnetic field in different configurations; the magnetic field perpendicular (g_⊥) and parallel (g_∥) to the quantum confinement direction. When the angle between the magnetic field and the confinement direction is 45°, we have found that g-factor varies depending on the direction of magnetic field and the circular polarization type of excitation light (σ⁺ or σ^?). These dependences of g-factor exhibit main features of Overhauser effect that nuclear spins react back on electron spin precession. The value of g_⊥ and g_∥ corrected for the nuclear effects agree well with the results of four-band k·p perturbation calculations.     

Effect of magnetic field on the impurity binding energy of the excited states in spherical quantum dot

The effect of external magnetic field on the excited state energies in a spherical quantum dot was studied. The impurity energy and binding energy were calculated using the variational method within the effective mass approximation and finite barrier potential. The results showed that by increasing the magnetic field, the energy would be increased. The results obtained by this method were compared with the previous investigations.     

Detecting the Anomalous Quantum Hall phase under magnetic field

Detecting the charming topological phase has been an ongoing topic. In this work, we take the square lattice as an example and try to detect the anomalous quantum Hall (AQH) phase under magnetic field. We analyze the topological energy levels of the system, the quantum Hall effect and quantum valley Hall effect, and the number of scattered electrons after a laser pulse, from which the unambiguous signals to characterize the AQH phases can be obtained. Meanwhile the corresponding valley polarizations of electrons are investigated. Our study opens new perspectives for the applications of valleytronics in the future.     

Effect of vacuum fluctuations on the motion of an electron in the magnetic field of an accelerator

The Langevin form of the quasiclassical approximation for an electron in a magnetic field is used to find the most general expression in the first order in fa for the vacuum-fluctuation Lorentz force. It is shown that besides the mechanism of excitation of fluctuation oscillations due to the recoil momentum there also exists a transverse (relative to the photon wave vector) fluctuation force due to the incomplete compensation of the electric force and the transverse component of the magnetic Lorentz force.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 42–46, March, 1981.     

Effect of the in-plane magnetic field on the recombination radiation spectrum of spatially-separated electron-hole layers

Changes in the recombination radiation spectrum of spatially-separated electron-hole layers has been studied under variation of the in-plane magnetic field and interlayer distance. It has been found that a change in the spectral position of the luminescence line in the low-field limit is proportional to the square of the magnetic field with the proportionality coefficient depending on the interlayer distance. The observed dependence has been shown to agree with the theoretical conceptions, according to which the line shift is quadratic in the magnetic field and interlayer distance and inversely proportional to the sum of the electron and hole masses. This total mass obtained in the experiment has been found to depend on the electric field that separates the layers and may substantially differ from the expected value.     

Rippled graphene in an in-plane magnetic field: effects of a random vector potential

We report measurements of the effects of a random vector potential generated by applying an in-plane magnetic field to a graphene flake. Magnetic flux through the ripples cause orbital effects: Phase-coherent weak localization is suppressed, while quasirandom Lorentz forces lead to anisotropic magnetoresistance. Distinct signatures of these two effects enable the ripple size to be characterized.     

Interplay of Rashba- and Dresselhaus spin-orbit interactions in a quasi-two-dimensional electron gas of a finite thickness under in-plane magnetic field

Interplay of Rashba- and Dresselhaus spin-orbit interactions and in-plane magnetic field is studied in a quasi-two-dimensional electron gas with finite thickness. The transverse confinement is modeled by means of a parabolic potential. An orbital effect of the in-plane magnetic field is shown to mix a transverse quantized spin-up state with nearest-neighboring spin-down states. A controllable changes of the spin-orbital interactions, orbital- and Zeeman effects of the in-plane magnetic field yield a multivalley energy subbands, where a negative differential resistance can be observed. The out-off-plane component of the equilibrium spin current appears to be not zero in the presence of an in-plane magnetic field, provided at least two transverse-quantized levels are filled. In the absence of the magnetic field the obtained results coincide with the well-known results, yielding cubic dependence of the equilibrium spin current on the spin-orbit coupling constants. The persistent spin-current vanishes in the absence of the magnetic field if Rashba- and Dresselhaus spin-orbit coefficients, α and β, are equal each other. In-plane magnetic field destroys this symmetry, and yields a finite spin-current as α → β. Magnetic field is shown to change strongly the equilibrium current of the in-plane spin components, and gives new contributions to the cubic-dependent on spin-orbit constants terms. These new terms depend linearly on the spin-orbit constants.     

Influence of the intrinsic magnetic moment of an electron on the filling of energy levels of a nonrelativistic degenerate electron gas in a quantizing magnetic field

The effect of a quantizing magnetic field on the filling of energy subbands of a degenerate nonrelativistic electron gas, whose magnetic moments are parallel and antiparallel to the direction of the field, is studied. Calculations are made under the assumption that the Fermi kinetic energy of the electron system increases as a result of Pauli's paramagnetism as compared to the kinetic energy calculated without taking this effect into account. Numerical values of the electron concentration are calculated as a function of the magnetic moment direction for magnetic fields under which the electrons are in states with given numbers of the Landau quantum level.A. S. Pushkin State Education Institute, Brest. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 9–13, June, 1992.     

Stability of energy gaps under variations of the magnetic field

It is proved that the location of the spectrum of the one-body Schrödinger operator is stable under small variations of the magnetic field. It is not supposed that the potential or the magnetic field vanishes at infinity. The potential is not supposed to be periodic so the results applies to crystalline and amorphous solids as well.     

Impurity effects on the magnetization and magnetic susceptibility of an electron confined in a quantum ring under the presence of an external magnetic field

The magnetization and the magnetic susceptibility of a single electron confined in a two-dimensional (2D) parabolic quantum ring under the effect of external uniform magnetic field and in the presence of an acceptor impurity have been studied. The shifted 1/N expansion method was used to solve the Hamiltonian quantum ring within the effective mass approximation. The computed energy spectra, the magnetization and magnetic susceptibility have been displayed as a function of the quantum ring parameters: confinement strength ω₀, magnetic field strength (ω_c), and temperature (T). The obtained energy results show level-crossings, in the absence and presence of acceptor impurity, which are manifested as oscillations in the magnetization and magnetic susceptibility curves.     

Quantum interference effects in field ionization: Application to the measurement of the fine structure splitting of highly excited Na2 D states

Quantum beats between the fine structure levels of highly excitedn ² D levels of sodium atoms have been measured by investigating the field electrons. The states were populated by stepwise excitation with two dye lasers and an electric field pulse was applied a certain time after the laser excitation. The quantum beat signal is observed when the time delay between excitation and ionization is varied. The fine structure splitting forn=21 to 31 has been measured.     

Shallow impurity binding energy in lateral parabolic confinement under an external magnetic field

We have described the calculation of hydrogenic impurity binding energies in cylindrical GaAs–Ga_1−xAl_xAs quantum well wires (QWWs) with lateral parabolic confinement in the presence of an axial magnetic field. The numerical calculations of this system have been performed with the use of a variational procedure in the effective mass approximation. We observed sharp changes in binding energy for critical spatial confinement radius and B$B$ magnetic field values.     

Effect of sample shape on nonlinear magnetization dynamics under an external magnetic field

Effect of sample shape on the nonlinear collective dynamics of magnetic moments in the presence of oscillating and constant external magnetic fields is studied using the Landau–Lifshitz–Gilbert (LLG) approach. The uniformly magnetized sample is considered to be an ellipsoidal axially symmetric particle described by demagnetization factors and uniaxial crystallographic anisotropy formed some angle with an applied field direction. It is investigated as to how the change in particle shape affects its nonlinear magnetization dynamics. To produce a regular study, all results are presented in the form of bifurcation diagrams for all sufficient dynamics regimes of the considered system. In this paper, we show that the sample's (particle's) shape and its orientation with respect to the external field (system configuration) determine the character of magnetization dynamics: deterministic behavior and appearance of chaotic states. A simple change in the system's configuration or in the shapes of its parts can transfer it from chaotic to periodic or even static regime and back. Moreover, the effect of magnetization precession stall and magnetic moments alignment parallel or antiparallel to the external oscillating field is revealed and the way of control of such “polarized” states is found. Our results suggest that varying the particle's shape and fields’ geometry may provide a useful way of magnetization dynamics control in complex magnetic systems.