Electron Gas In Magnetic Field Research Articles

Simple edge-state models of two-dimensional electron gas in magnetic field

Electron states localized to the edges of the twodimensional electron gas in perpendicular magnetic field are investigated on simple models. Two kinds of states are discussed: states which only exist due to the magnetic field and states which are localized to edges even in the absence of the magnetic field. Methods, enabling to treat cases with comparable strengths of the magnetic and crystalline potential fields, are used. Interesting behaviour of electron structure dispersions, consisting in flat plateau regions closely approaching the neighbouring branches has been found.

Anomalous classical diffusion of high mobility 2D electron gas in magnetic field.

It is well known that in a classically strong magnetic field, ${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$${\mathrm{\ensuremath{\tau}}}_{\mathit{t}}$\ensuremath{\gg}1 (${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$ is the cyclotron frequency and ${\mathrm{\ensuremath{\tau}}}_{\mathit{t}}$ is the transport relaxation time), the transverse conductivity is inversely proportional to magnetic field squared, ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{x}}$=${\mathrm{\ensuremath{\sigma}}}_{0}$/(${\mathrm{\ensuremath{\omega}}}_{\mathit{c}}$${\mathrm{\ensuremath{\tau}}}_{\mathit{t}}$${)}^{2}$, wher ${\mathrm{\ensuremath{\sigma}}}_{0}$ is the conductivity without magnetic field. Such a dependence results from the lack of correlation of scattering events of an electron. This condition can be violated in a high mobility 2D gas, where the correlation length of the scattering potential is large. A strong correlation between scattering events results in an anomalous dependence of ${\mathrm{\ensuremath{\sigma}}}_{\mathit{x}\mathit{x}}$ on magnetic field.

Applications of virial theorem and moment sum rules to 2D electron gas in magnetic field

We derive the virial theorem and frequency moment sum rules for electron gas systems in a magnetic field and utilize these results to study the characteristics of electron correlations in the magnetic field, such as the ground state energy and the collective excitation, in the two-dimensional situation. A general relation is obtained for the ground state energy. The collective excitation is examined within the single mode approximation and is found to be in agreement with the RPA.

Ideal Two‐Dimensional Electron Gas in a Magnetic Field and at Non‐Zero Temperatures. An Alternative Approach

AbstractA new exact expression is derived for the free energy of an ideal two‐dimensional electron gas (2DEG) in a uniform magnetic field and at low, but finite, temperatures. The approach eliminates a 2D‐peculiarity that neither the weak nor the strong magnetic field limit can be easily taken in the result derived from the standard Sondheimer‐Wilson treatment. In the strong magnetic field limit, the result reduces to an existing one, for which a misunderstanding needs to be clarified. In the weak field limit, it agrees with a result obtainable through Euler's summation formula. The conditions are discussed under which the nondegenerate situation may occur.

Dielectric response of a two-dimensional electron gas in a quantizing magnetic field

Focusing on screening effects we demonstrate drastic differences between the isothermal and the isolated response properties of a two-dimensional electron gas in a magnetic field at low temperatures. These differences occur both in bounded and unbounded samples and are caused by their peculiar Landau quantized and highly degenerate energy spectrum.

Density of states of a two dimensional electron gas in a high magnetic field studied with photoluminescence

The density of states of a quasi two dimensional electron gas in magnetic fields up to 25 T is determined directly from photoluminescence measurements and can be described by Gaussian broadened Landau levels superimposed on a constant background. A model for electron - acoustic phonon scattering is presented to explain the observed filling factor (ν) dependence of the width of the partially filled first Landau level Γ 1, while it is suggested that the ν dependence of the width of the completely filled zeroth Landau level Γ 0 can be attributed to long range impurity scattering. Finally, the background is found to be independent of ν and is assumed to have the same origin as Γ 0 because of the resemblance in their dependence on electron temperature.

Longitudinal dielectric behavior of a two-dimensional electron gas in a uniform magnetic field

A new exact closed-form expression is given for the random-phase-approximation longitudinal polarizability function of a two-dimensional electron gas in a magnetic field. Detailed approximations are given for several limiting cases. Static screening and the nonretarded plasmon dispersion relation are examined in detail.

Spectroscopy of Landau transitions of two-dimensional electron gases

We have employed resonant inelastic light scattering spectroscopy to study electronic transitions in multilayer two-dimensional electron gases in magnetic fields of 4–14 T. From polarized spectra, we have evidence for both single particle Landau transitions (Δl = 1 and Δl = 2) as well as their collective counterparts. We show the variation of intensities with B and the resonant behavior, but are unable to identify a scattering mechanism.

Hartree-Fock solution of CDW of two-dimensional electron gas in magnetic field

Temperature dependence of the amplitude of the charge density wave of two-dimensional electron gas in strong magnetic field is calculated within Hartree-Fock approxiimation. The density of states is investigated, too, and it is shown that there is not an energy gap at Fermi level when the lowest Landau level is half filled.

Noninteracting electron gas in high magnetic fields

A closed-form expression is obtained for a free electron gas in a magnetic field. The resulting formulation is valid for fields less than 10 8 gauss and temperatures where de Haas-Van Alphen effects can be neglected.

Quantum Theory of an Electron Gas in Intense Magnetic Fields

In this paper we have developed the quantum theory of a relativistic electron gas in magnetic fields of arbitrary strength, and we have obtained the equation of state for such a gas. Intense magnetic fields (of field strengths \ensuremath{\sim}${10}^{13}$ G) are believed to exist during gravitational collapse and in collapsed astronomical objects. Our results show that the stress tensor is very anisotropic when $\frac{〈{{p}_{z}}^{2}〉}{{m}^{2}{c}^{2}}$ [${p}_{z}=(z \mathrm{momentum})=(\mathrm{momentum}\mathrm{parallel}\mathrm{to}\mathrm{the}\mathrm{field})$] is smaller than ${(\frac{2H}{{H}_{c}})}^{\frac{1}{2}}$, where $H$ is the field and ${H}_{c}=\frac{{m}^{2}{c}^{3}}{\ensuremath{\hbar}e}=4.414\ifmmode\times\else\texttimes\fi{}{10}^{13}$ G. At a temperature of ${10}^{9}$ \ifmmode^\circ\else\textdegree\fi{}K or a density of ${10}^{5}$ g/${\mathrm{cm}}^{3}$, the theory developed here must be used if $H\ensuremath{\gtrsim}{10}^{12}$ G.

Ground State of an Electron Gas in a Magnetic Field

Abstract : The ground state of an electron gas in a uniform magnetic field is found to be not the customary uniform state, but rather one in which a spin density wave exists, directed along the field. This conclusion is reached through what is essentially a Hartree-Fock calculation with a repulsive interaction, but in which no restrictive assumptions are made about either the strength or the range of the exchange interaction. Thus static screening does not eliminate the spin density wave in the presence of a magnetic field, as it does in the electron gas when no magnetic field is present. The temperature at which the transition to a spin density wave state occurs approaches zero as the field vanishes. The pertinent question is therefore not the nature of the ground state, but whether there is a range of field strengths and electronic densities for which the transition temperature is observably high. It is found that spin density wave formation is most favorable when only a few Landau levels are occupied, corresponding to large field strengths and low electronic densities. A rough calculation indicates that in InSb a transition temperature as high as 10 millidegrees can be realized. (Author)