Self-consistent theory of screening in a two dimensional electron gas under strong magnetic field

The dielectric response of a two dimensional electron gas under a strong transverse magnetic field is obtained within a self-consistent procedure in which the broadening of Landau levels due to collisional damping from the impurities both determines and is determined by the static dielectric function of the system. The dielectric function is evaluated in random phase approximation with the impurity scattering treated in a self-consistent Born approximation. Explicit results are presented for the zero temperature, extreme quantum limit. It is found that this “no parameter” theory is in good qualitative agreement with experimental results for the broadening as extracted from magnetotransport data.     

Interacting electron gas in a strong magnetic field

The density response function of an electron gas in a strong magnetic field shows logarithmic singularities due to scattering across the Fermi surface. We analyze the parquet equations for the vertex function in leading logarithmic order for a general interaction potential. The parquet equations are solved for a special interaction potential (Schulz and Keiter model). The divergence of the density response function at extremely high fields is discussed in connection with a possible transition to a Wigner lattice.     

Power-law electron and ion distributions in a strong magnetic field

The possibility of establishing steady-state power-law distributions with constant fluxes in systems comprised of two kinds of particles is investigated. A local distribution n_e= p _e ^3/2 , which is established in pulsar magnetospheres, is derived for magnetized electrons interacting with ions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenij, Radiofizika, Vol. 21, No. 11, pp. 1549–1557, November, 1978.     

Space-charge-limited 2D electron flow between two flat electrodes in a strong magnetic field

An approximate analytic solution is constructed for the 2D space-charge-limited emission by a cathode surrounded by nonemitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.     

Two-dimensional electron-hole liquid in the strong magnetic field

The Matsubara diagram technique is used to study the formation and thermodynamic properties of an electron-hole liquid (EHL) in the two-dimensional system in the transverse strong magnetic field. The system has discrete energy spectra, i.e. a motion of particles becomes “zero-dimensional”. Therefore, the exchange interaction alone is sufficient to form EHL, the correlation correction being negligible.     

Skyrmions in electron gas with nonlocal exchange in a strong magnetic field

The energy and action for skyrmions in two-dimensional electron gas with nonlocal exchange have been calculated. The energy of positively charged skyrmions is considerably lower than the energy of negatively charged skyrmions and does not contain an exchange contribution. The action has been calculated taking into account collective skyrmion null modes. Zh. éksp. Teor. Fiz. 115, 716–725 (February 1999)     

Two-dimensional electron liquid with disorder in a weak magnetic field

We present the effective theory for the low-energy dynamics of two-dimensional interacting electrons in the presence of a weak short-range disorder and a weak perpendicular magnetic field, with the filling factor γ ? 1. We investigate the exchange enhancement of the g factor, the effective mass, and the decay rate of the simplest spin wave excitations at γ=2N+1. We obtain the enhancement of the field-induced gap in the tunneling density of states and the dependence of the tunneling conductivity on the applied bias.     

Quasi-two-dimensional electron gas in a non-quantizing magnetic field and strong non-quantizing electric field

A calculation is performed to determine the transverse electric field E_y formed in quasi-two-dimensional superlattices in a strong drift field E_x and a weak magnetic field that is perpendicular to the plane of the superlattice (H‖OZ). When the electronic energy spectrum is nonadditive, the field E_y includes both the Hall factor and a spontaneous transverse electric field that exists whetherH is present or not. The situation when the specimen is in a closed circuit with a resistor on the OY axis is examined. As the function E_x, the field E_y is multivalued (multistable) and variable. The stability of the branches of the function E_y(E_x) is determined using a specially introduced (kinetic) “potential” whose minimum corresponds to the steady state of a nonequilibrium electron gas. Volgograd State Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–51, July, 1996.     

Hydrodynamic theory of electron transport in a strong magnetic field

The mode coupling contribution to the transverse transport coefficients of a three-dimensional one-component plasma in a strong external magnetic field is calculated. For very strong fields it is found that the tagged particle diffusion rate, the thermal diffusion rate, and the coefficient of viscosity in the plane orthogonal to the field have a Bohm-like B ^–1 behavior. The mode coupling mechanism responsible for such an effect is always one that involves the finite-frequency upper hybrid modes.     

CDW instability of electron gas in a strong magnetic field

It is shown that within the Hartree-Fock approximation the electron gas in the quantum limit of a strong magnetic field has an instability as the temperature is lowered toward the charge density wave state with an wave-vector which has finite components in the directions not only parallel but also perpendicular to the field. The critical temperature, T_c, is estimated under the assumption of T_c??_F?ω_c, where ?_F and ω_c are the Fermi energy of the non-interacting system and the cyclotron frequency respectively.     

Tunneling between two-dimensional electron systems in a strong magnetic field

We calculate the tunnel current between two parallel two-dimensional electron systems in a strong perpendicular magnetic field. We model the strongly correlated electron systems by Wigner crystals, and describe their low-energy dynamics in terms of magnetophonons. The effects of the magnetophonons on the tunneling processes can be described by an exactly solvable independent-boson model. A tunneling electron shakes up magnetophonons, which results in a conductance peak that is displaced away from zero voltage and broadened compared with the case of no magnetic field. At low temperatures and low enough voltages the tunneling conductance is strongly suppressed, and the I–V characteristics exhibit a power-law behavior. The zero-voltage conductance is thermally activated with an activation temperature 10 K. The results are in very good agreement with experiment.     

Two-dimensional electron gas in a strong magnetic field. I

We obtain expressions for the thermodynamic potential, concentration, and magnetic moment of an ideal two-dimensional electron gas in a strong (quantizing the motion) magnetic field at low temperatures. The results are used to explain the integer quantum Hall effect.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 101–106, January, 1990.     

Two-dimensional electron gas in a strong magnetic field. II

The quantum mechanical problem on the motion of electrons in a strong (quantizing the motion) magnetic field is considered, taking into account the Coulomb interaction between charges. It is shown how, on the basis of the solutions found, it is possible to obtain the fractional filling factor of the Landau levels that enters into the expression for the Hall conductivity of a two-dimensional electron gas.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 25–29, March, 1990.     

Anomalous Hall effect in a two dimensional electron gas with magnetic impurities

Magnetic impurities play an important role in many spintronics-related materials. Motivated by this fact, we study the anomalous Hall effect in the presence of magnetic impurities, focusing on two-dimensional electron systems with Rashba spin-orbit coupling. We find a highly nonlinear dependence on the impurity polarization, including possible sign changes. At small impurity magnetizations, this is a consequence of the remarkable result that the linear term is independent of the spin-orbit coupling strength. Near saturation of the impurity spins, the anomalous Hall conductivity can be resonantly enhanced, due to interference between potential and magnetic scattering.     

The recursion method for a two-dimensional electron system in a strong magnetic field

We study the tight-binding model of non-interacting electrons on a two-dimensional square lattice within a strong magnetic field. The recursion method is applied to this problem, and the asymptotic behaviour of the continued fraction coefficients and the appropriate termination of the continued fractions are discussed. For an ordered system the local density of states at bulk sites can efficiently and accurately be calculated. For any rational number =p/q of magnetic flux quanta per lattice site the spectral function is splitted in up toq different (Landau-like) subbands. At edge sites the gaps between the Landau subbands disappear. For a disordered system an appropriate termination of the continued fractions is more difficult. Nevertheless, reasonable results for the (bulk) density of states in the presence of disorder can be obtained by averaging over different system realizations. The corresponding result obtained within the coherent potential approximation (CPA) is in good agreement with the exact (averaged) density of states of the disordered system. It is shown that the broadening of each subband due to the disorder is considerably smaller than the disorder strength. The site off-diagonal matrix elements of the one-particle Green function can also be calculated and their unusual properties are discussed. Finally it is discussed, why a determination of the transport coefficients _xx and _xy from the Kubo formula was not yet possible within this method, not even within the CPA transport theory.     

Finite temperature investigations of a two dimensional electron liquid

We investigate the spin dependent local field corrections and correlation functions of an electron layer at intermediate degeneracies. The results are obtained within the Singwi-Tosi-Land-Sjølander approximation by solving the corresponding set of coupled integral equations. Analytic expressions are given for the asymptotic limiting behavior. In addition, the free exchange-and correlation energy, which is in good agreement with Monte Carlo results at full degeneracy, is calculated for various temperatures.