Two-dimensional Wigner crystal in magnetic fields

Orbital magnetic moment and the frequency dependent conductivities of the Wigner crystal are examined in the harmonic approximation. The effects of scattering on the collective modes are also discussed.     

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 10⁸ gauss and temperatures where de Haas-Van Alphen effects can be neglected.     

The Wigner crystal in a semimetal film in a high magnetic field

The possibility of existance of a super-crystalline (Wigner) phase in a semimetal or impurity semiconductor film placed in a high magnetic field, is discussed and a comparison is made with a crystal in a three-dimensional specimen.

Such a phase exists in a succession of magnetic field or particle density intervals. The vibrational spectrum depends on magnetic field, while the bind energy is only density-dependent. The mean-square displacement x² of the particles in the lattice sites are also independent on the magnetic field over a wide temperature range.     

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.     

Accuracy of the Hartree-Fock method for Wigner molecules at high magnetic fields

Few-electron systems confined in two-dimensional parabolic quantum dots at high magnetic fields are studied by the Hartree-Fock (HF) and exact diagonalization methods. A generalized multicenter Gaussian basis is proposed in the HF method. A comparison of the HF and exact results allows us to discuss the relevance of the symmetry of the charge density distribution for the accuracy of the HF method. It is shown that the energy estimates obtained with the broken-symmetry HF wave functions become exact in the infinite magnetic-field limit. In this limit the charge density of the broken-symmetry solution can be identified with the classical charge distribution.Received: 24 October 2003, Published online: 6 January 2004PACS: 73.20.Qt Electron solids - 73.21.-b Electron states and collective excitations in multilayers, quantum wells, mesoscopic, and nanoscale systems     

Orbital magnetic moment of two-dimensional Wigner crystal

The orbital magnetic moment is calculated for the two-dimensional Wigner crystal within the harmonic approximation. It is shown that the temperature dependence of the magnetic moment in the crystalline state is in the marked contrast with that of the liquid state.     

Real-space observation of drift States in a two-dimensional electron system at high magnetic fields

The local density of states of the adsorbate-induced two-dimensional electron system is studied in magnetic fields up to B=6 T. Landau quantization is observed and drift states with a width of about the magnetic length are found in agreement with theoretical predictions. At the tails of the Landau levels the states form closed paths indicating localization. These states show the expected energy dependence. A multifractal analysis applied to the data results in a nice parabolic shape of the characteristic f(alpha) spectra, but we find only a slight displacement of the origin from alpha=2.0 for the states in the center of the Landau level.     

Two-dimensional liquid crystal laser array

A two-dimensional liquid crystal (LC) laser array has been demonstrated by photopumping a single LC sample using a lenslet array consisting of plano-convex microlenses. A 5 x 5 array of LC lasers (displaying evidence of mutual coherence) spaced by 1 mm inactive regions has been generated, which could be combined to yield a single monomode output and allows an almost 50-fold increase in energy density in comparison to a single-focus LC cavity. Furthermore, we have demonstrated how the individual and recombined emission spectra vary with different sample topologies and how polydomain samples can be used to generate a multiwavelength laser emission.     

Correlation lengths of the wigner-crystal order in a two-dimensional electron system at high magnetic fields

The insulator terminating the fractional quantum Hall series at low Landau level filling nu is generally taken to be a pinned Wigner crystal (WC), and exhibits a microwave resonance that is interpreted as a WC pinning mode. For a high quality sample at several densities, n, we find maxima in resonance peak frequency, f(pk), vs magnetic field, B. L, the correlation length of WC order, is calculated from f(pk). For each n, L vs nu tends at low nu toward a line with positive intercept; the fit is accurate over as much as a factor of 5 range of nu. The linear behavior is interpreted as due to B compressing the electron wave functions, to alter the effective electron-impurity interaction.     

Wigner liquid conductivity in a parallel magnetic field

It is assumed that comparatively low-mobility objects (clusters of a small number of electrons) can appear in a two-dimensional strongly correlated electronic system (Wigner liquid) against the background of mobile Fermi-type carriers. These formations can get “pinned” to inhomogeneities and play the role of additional scatterers. Clusters of two and three electrons are discussed (for a short-range order in the arrangement of electrons, as in a triangular lattice). The number of these clusters depends on both temperature and the parallel magnetic field. This results in the temperature and field dependences of the resistance and magnetization of the system. According to a simple model, resistance increases and the metal-dielectric transition occurs as the parallel magnetic field grows stronger. The model predicts a nonlinear magnetic field dependence of magnetization.     

Photon-drag effect in a two-dimensional electron gas in high magnetic fields

We present the first measurements concerning the photon drag effect in a two-dimensional electron gas based on intersubband transitions in high magnetic fields. It is shown that the excitation mechanism of the drag voltage in a magnetic field differs obviously from the case of zero magnetic field. The longitudinal as well as the Hall drag voltage show strong oscillations around zero when the magnetic field is swept. Both consist of a B-symmetrical and an antisymmetrical part with the same periodicity in B as the magnetoresistanceR_xx. The drag voltage oscillations are strongly correlated to the relative position of Fermi energy and Landau levels and are independent of the photon energy in the range of usable laser lines.     

Two-dimensional excitonic phase in strong magnetic fields

The excitonic phase of the coupled electron-hole system which consists of p- and n-channel inversion layers separated by a thin insulating layer and subjected to a strong magnetic field, is investigated in the mean field approximation. The spectrum of the symmetry-restoring collective excitation mode is shown to be consistent with the possible superfluidity of excitons.     

Two-dimensional electron crystal in magnetic field. Topological phase transitions and stability region.

The phase diagram of a 2-dim. electron system in the magnetic field $\text{H}$ is analyzed. We obtain ab initio the free energy F{U_iκ} of a deformed electron crystal when the long-range Coulomb forces and $\text{H}$ are taken into account. Using F{u_iκ} we find H-dependent interaction between the dislocations and the curve of the topological melting due to the dissociation of dislocation pairs. The topological melting curve for H → ∞ asimptotically approaches to the melting curve of a classical crystal. This result is obtained using Feynman variational technique as well. We examine also the electron liquid crystal phase and the stability region of a 2-dim. crystal at $\text{H}$ ≠ 0. The first-order phase transitions from the crystal and liquid crystal to the isotropic liquid are predicted to take place in a definite region of the phase diagram. We find the increase of the crystal and liquid crystal region on the T-n phase diagram with H increase. The various phenomenological stability criteria are ånaylzed.     

Simulation of relaxation processes in electron beams at high magnetic fields

Molecular-dynamics simulations of relaxation processes in electron beams at high magnetic fields are presented. The result of the longitudinal–longitudinal relaxation and the rate of the transverse–longitudinal relaxation are calculated for magnetic fields between 0.006 and 0.1 T for electron beam parameters typical of those in low-energy electron coolers. Comparisons with theoretical and experimental values are made. This revised version was published online in July 2006 with corrections to the Cover Date.     

Two-dimensional wigner crystal under magnetic field

Dispersion relations of phonons are obtained in the harmonic approximation for the two-dimensional Wigner crystal under the magnetic field. For small wave vector, the eigen-energies of two modes are ω₊ = ω_c = eH/mc and ω_? → ω_lω_t/ω_c, where ω_l and ω_t are frequencies of longitudinal and transverse phonons in the absence of the field.