Dynamical properties of the 2D wigner crystal in a strong magnetic field

Summary The dispersion relations and the shear modulus of the 2D Wigner crystal (WC) in the presence of a strong magnetic field are evaluated using a density functional method which includes the effect of electronic correlations. Comparison is made with previous theoretical results on the magnetophonons and the shear modulus. The effect of correlation on the stability of the crystal is discussed. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Two dimensional wigner crystallization caused by magnetic field

It is discussed that two dimensional electrons can crystallize by the application of magnetic field. The critical field, H_c, above which the crystalline state is expected, is evaluated at absolute zero as a function of the carrier density, n, by use of the Lindeman's Law. The theoretical results are discussed in connection to the recent experiment by Kawaji and Wakabayashi.     

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.     

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.     

Two-dimensional oscillator in a magnetic field

The energy and eigenstate spectrum of a charged particle in the electric field of a 2D anisotropic oscillator and in a uniform magnetic field is considered. The exact analytic solution to the problem is obtained for an arbitrary magnetic field strength. The characteristic features of variation of the energy spectrum depending on the magnetic field strength are analyzed. The results of this study are of interest for the quantum-mechanical theory of magnetism and can be used to simulate the magnetic properties of atoms and molecules.     

Two-dimensional metal in a parallel magnetic field

We have investigated the effect of an in-plane parallel magnetic field (B(axially) on two high mobility metallic-like dilute two-dimensional hole gas systems in GaAs quantum wells. The experiments reveal that, while suppressing the magnitude of the low temperature resistance drop, B(axially) does not affect E(a), the characteristic energy scale of the metallic resistance drop. The field B(c) at which the metallic-like resistance drop vanishes is dependent on both the width of the quantum well and the orientation of B(axially). It is unexpected that E(a) is unaffected by B(axially) up to B(c) despite the fact that the Zeeman energy at B(c) is roughly equal to E(a).     

Two-dimensional exciton-phonon system in a magnetic field

The properties of an exciton at the surface of a polar crystal in a weak magnetic fieldB, which is perpendicular to the surface and is constant, are discussed by a perturbational method. Taking account of the effects from the surface modes of the lattice vibrations and on ground of a slow motion of the exciton, the self-energy of an exciton, the effective potential and renormalized masses are derived. The self-energy of the exciton becomes higher under the action of the magnetic field.Center of Theoretical Physics, CCAST (World Laboratory)     

Two-dimensional NMR spectroscopy in Earth's magnetic field

We demonstrate the first two-dimensional correlation NMR (COSY) spectra obtained at ultra low frequencies (ULF) using the Earth's magnetic field. Using a specially developed spectrometer with multiple audio-frequency pulses under controlled pulse phase, we observe magnetisation transfer arising from heteronuclear J-couplings in trifluoroethanol and para-difluorobenzene. The 2D COSY spectra exhibit all diagonal and off-diagonal multiplets consistent with known J-couplings in these molecules.     

Cyclotron resonance of two-dimensional electrons forming wigner crystal

The cyclotron resonance peak shape is analysed for two-dimensional electrons interacting with surface vibrations of a medium. Explicit expressions for the broadening and shift of the peak are obtained at low and high electron densities.     

Two-dimensional electron gas in a periodic magnetic field

We study the energy spectrum and electronic properties of a two-dimensional (2D) spinless electron gas in a periodic magnetic field which has the symmetry of a triangular lattice. We show that the energy bands depend strongly on the value of the magnetic field. For large field the low-energy electrons are localized on closed rings where the magnetic field vanishes. This results in the appearance of persistent currents around these rings. We also calculate the intrinsic Hall conductivity, which is quantized when the Fermi level is in a gap.     

Two-dimensional spherical oscillator in a constant magnetic field

We study the equations of motion of a spherical oscillator model suggested by Bellucci and Nersessian, in the presence of a constant magnetic field. This model is shown to be exactly solvable classically in contrast to the Higgs oscillator which is not exactly solvable in magnetic fields.     

Two-dimensional electron-hole system in a strong magnetic field

A theory of a 2-D e-h-system in a strong magnetic field is presented. Its properties drastically depend on the existence of the e-h-symmetry in it. In an asymmetric system excitons interact with each other and as a result can from magnetic biexcitons. The system is unstable to the formation of a charge-density waves (CDW) at low temperatures.     

Two-dimensional quasi-exactly solvable models with a magnetic field

New classes of quasi-exactly solvable models are found. They possess SO(3) hidden symmetry and describe the quantum motion of a particle on a curved two-dimensional manifold under influence of a scalar potential and a magnetic field.     

Two-dimensional quantum antiferromagnet in a strong magnetic field

The behaviour of the two-dimensional quantum antiferromagnet of arbitrary spin in a strong transversal magnetic field on a square lattice is studied in terms of the equivalent Bose gas problem. The existence of phase transition from the state characterized by “quasi-long-range” magnetic order to the disordered ferromagnetic state is demonstrated. The expressions for correlation functions, thermodynamical and magnetic characteristics are derived.     

Two-dimensional hydrogen negative ion in a magnetic field

Making use of the adiabatic hyperspherical approach, we report a calculation for the energy spectrum of the ground and low-excited states of a two-dimensional hydrogen negative ion H^{-} in a magnetic field. The results show that the ground and low-excited states of H^{-} in low-dimensional space are more stable than those in three-dimensional space and there may exist more bound states.     

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.