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.     

Nonlinear surface polaritons in 2D electron system in high magnetic field

The paper deals with the theoretical investigation of nonlinear surface polaritons (NSP) in isolated two-dimensional electron system (2DES) arranged at the interface between linear and nonlinear media and placed into the external quantizing magnetic field directed perpendicularly to 2DES. We consider that nonlinear medium dielectric permeability depends upon the tangential component of electric field only. It is shown that under the integer quantum Hall effect conditions all NSP characteristics are represented by the quantized values. It is found that the NSP spectrum contains two NSP modes - high-frequency and low-frequency ones. It is shown that the NSP can exist only in the case where the value of tangential component of electric field at the interface is less than a certain critical value. It is found that the resonant interaction between the NSP high-frequency mode and surface polariton mode occurs in the vicinity of the cyclotron resonance subharmonic. Received 23 September 2001 / Received in final form 31 January 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: bludov@ire.kharkov.ua     

Time evolution of initially localized states in two-dimensional quantum dot arrays in a magnetic field

The evolution of non-stationary localized states |Ψ(t=0) is investigated in two-dimensional tight binding systems of N potential wells with and without a homogeneous field perpendicular to the plane. Most results are presented in analytical form, what is almost imperative if the patterns are as complex as for rings in a magnetic field, where the qualitatively different features arise depending on rational or irrational numbers. The systems considered comprise finite linear chains (N=2,3), finite rings (N=3–6), infinite chains, finite rings (N=3–6) in a magnetic field, and rings with leads attached to each ring site. The position of the particle at time t is described by the projection of the wave function P_m(t)=|m|Ψ(t)|² onto the localized basis function at site m. For finite chains and rings with N=3,4,6 the time evolution is periodic, whereas it is non-periodic for N=5 and N greater then 6. Rings in a magnetic field show a rich spectrum of different features depending on N and the number of flux quanta through the ring, including periodic oscillation and rotation of the charge as well as non-periodic charge fluctuations.     

On some singularities in the dielectric properties of an electron gas in a uniform magnetic field

The effects of a magnetic field on the self-shielding of an electron gas against small electrostatic perturbations V are studied by use of Bloch wave functions and by the random phase approximation. V is taken to be periodic along the field lines. It is demonstrated that in the weak field limit, $\text{μ}{}_0\text{B}\text{eV}\text{→ 0}$, magnetic effects become negligible. For μ₀B ? eV such effects may be important only under limited physical conditions. Singularities discussed by Glasser and Kaplan [1] are replaced by peaks of finite amplitude and width, appearing with the frequency of neck orbit oscillations. Peak profiles and the Lindhard singularity are investigated for the case V ≠ 0.     

Donor-bound electron states in a two-dimensional quantum ring under uniform magnetic field

The electron states in a two-dimensional GaAs/AlGaAs quantum ring are theoretically studied in effective mass approximation. On-centre donor impurity and uniform magnetic field perpendicular to the ring plane are taken into account. The energy spectrum with different angular momentum changes dramatically with the geometry of the ring. The donor impurity reduces the energies with an almost fixed value; however, the magnetic field alters energies in a more complex way. For example, energy levels under magnetic field will cross each other when increasing the inner radius and outer radius of the ring, leading to the fact that the arrangement of energy levels is distinct in certain geometry of the ring. Moreover, energy levels with negative angular momentum exhibit the non-monotonous dependence on the increasing magnetic field.     

Compressibility of a two-dimensional electron gas in a parallel magnetic field

The thermodynamic compressibility of a two-dimensional electron system in the presence of an in-plane magnetic field is calculated. We use accurate correlation energy results from quantum Monte Carlo simulations to construct the ground state energy and obtain the critical magnetic field B_c required to fully spin polarize the system. Inverse compressibility as a function of density shows a kink-like behavior in the presence of an applied magnetic field, which can be identified as B_c. Our calculations suggest an alternative approach to transport measurements of determining full spin polarization.     

Quantum theory of high-electric-field magnetotransport for a two-dimensional electron gas in microstructures

Summary Nonlinear response to an electric field applied in the plane of a two-dimensional electron gas (2DEG) subjected to a perpendicular magnetic field is expressed in terms of an electric-field (F)-dependent magnetoconductivity in which the effect of the electric field is incorporated in the resolvent of the Liouville operator. This electric-field-dependent Kubo-type formula is calculated in the presence of the simultaneous scattering by disorder and phonons and is expressed in terms of the electric-field-dependent broadening and shifting of the Landau levels. It is found to be essential to treat the two interactions simultaneously and self-consistently at low temperatures. High-field effects such as ?collisional broadening? and ?intracollisional field effects? as manifested through the electric-field-dependent tetradic self-energy of 2DEG in a perpendicular magnetic field are calculated and shown to be much more pronounced in 2DEG as compared to the same phenomenon in three-dimensional semiconductors. The present results are found to be useful in the calculation of the effects of the temperature (T), magnetic field (B) and the electric field (F) as well as the interplay of the two interactions on the quantum effects as manifested in the Landau level broadening due to the relaxation and acceleration of the electrons in an applied electric field. In the limitF→0 the present results reduce to the usual formulae as known from the linear response theory.     

Magnetoresistance of a two-dimensional electron gas in a parallel magnetic field

The conductivity of a two-dimensional electron gas in a parallel magnetic field is calculated. We take into account the magnetic-field-induced spin-splitting, which changes the density of states, the Fermi momentum, and the screening behavior of the electron gas. For impurity scattering, we predict a positive magnetoresistance for low electron density and a negative magnetoresistance for high electron density. The theory is in qualitative agreement with recent experimental results found for Si inversion layers and Si quantum wells.     

Wigner function of a two-dimensional electron gas in a magnetic field

The Wigner function of a two-dimensional electron gas in an arbitrary magnetic field perpendicular to the plane in which the electrons are confined is constructed rigorously. The function is useful in taking various statistical averages and illuminates the roles played by the hyperbolic functions of the field which appear in the expressions of the susceptibility and other physical quantities.     

Dephasing in the presence of a two-dimensional electron gas at high magnetic fields

By means of degenerate four-wave mixing (FWM), we investigate the quantum coherence of electron–hole pairs in the presence of a two-dimensional electron gas in modulation-doped GaAs–AlGaAs quantum wells in the regime of the integer quantum-Hall effect. We observe large jumps in the decay time of the FWM signal at even Landau level filling factors. The main features of the experimental observations can be qualitatively reproduced by a model which takes into account the number of unoccupied states within the highest partially occupied Landau level. Furthermore, we observe quantum beats between up to three different Landau level transitions.     

Analytical thermodynamical properties of a two-dimensional electron gas in a magnetic field

Analytical expressions for the thermodynamical properties of a two-dimensional electron gas in a perpendicular magnetic field are derived.This is accomplished by first deriving the general expression for the thermodynamical potential,and then employing this result to obtain the corresponding expression for the two-dimensional gas.The chemical potential and magnetization are studied as a function of temperature and magnetic field,and shown to be in agreement with prior work.It is also shown that the results are close to those obtained by assuming a Gaussian density of states for the Landau levels.     

DHVA magnetic susceptibility of a 2D free electron gas

Summary The grand potential and energy of a noninteracting uncorrelated two-dimensional electron gas subject to Landau quantization in a magnetic field are examined here at low temperatures. The DeHaas-Van Alphen oscillatory magnetic susceptibility for the free 2D gas is calculated and the results presented here incorporate the effects of spin (by allowing that spin splitting may not, in general, equal Landau level separation) in formulae that have the same analytic structure for both even and odd numbers of filled Landau levels.

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Riassunto Il gran potenziale e l'energia di un gas elettronico bidimensionale non correlato non interagente, soggetto a quantizzazione di Landau in un campo magnetico, sono esaminate qui a basse temperature. La suscettibilità magnetica oscillatoria di De Haas-Van Alphen per il gas libero 2D è calcolata e i risultati presentati qui incorporano gli effetti di spin (tenendo conto che il taglio di spin non può, in generale, eguagliare uguale separazione del livello di Landau) in formule che hanno la stessa struttura analitica per numeri sia pari che dispari dei livelli completi di Landau.

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Резюме В зтой работе при низких температурах исследуется потенсиал и знергия невзаимодействующего некоррелированного двумерного злектроннного газа, подчинющегося квантованию Ландау в магнитном поле. Вычисляется осцилляторная магнитная восприимчивость де Гааза-ван Альфена для свободнго двумерного газа. Полученные результаты учитывают спиновые зффекты (допуская, что спиновое расщепление в общем случае может быть не равно интервалу между уровнями Ландау) в формулах, которые имеют ту же аналитическую структуру для четного и нечетного числа заполненных уровней Ландау.

     

Transport studies of localized and extended states of a two-dimensional electron gas in low magnetic fields

We have observed the quantum Hall effect in a high mobility two-dimensional electron gas to filling factors up to 80 at 0.3 K. This demonstrates the presence of both localized and extended states at low field, and explains the failure of the standard semi-classical analysis of Shubnikov–de Haas (SdH) oscillations in this regime. We go on to derive a general expression for the conductivity due to rectangular bands of extended states, and show that the observed temperature dependence of the SdH oscillations is consistent with this picture. An analysis of the oscillations using this expression reveals the predicted levitation of the extended states as the magnetic field is reduced.     

Cancellation of fine-structure splitting in quantum dots by a magnetic field

We demonstrate control of the fine-structure splitting of the exciton emission lines in single InAs quantum dots by the application of an in-plane magnetic field. The composition of the barrier material and the size and symmetry of the quantum dot are found to determine decrease or increase in the linear polarization splitting of the dominant exciton emission lines with increasing magnetic field. This enables the selection of dots for which the splitting can to be tuned to zero, within the resolution of our experiments. General differences in the g-factors and exchange splittings are found for different types of dot.     

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.     

Completely bound motion of a positive-energy electron in the coulomb field of a motionless nucleus and a uniform magnetic field

We show that the completely bound classical motion of a positive-energy electron is realized in the Coulomb field of a motionless nucleus and a uniform magnetic field. Such a motion exists due to conservation of the so-called invariant tori in the phase space of the system for not only the negative, but also for the positive energy of an electron. The completely bound trajectories occupy a much larger interval of the velocity directions compared with free trajectories for the same energy in a range of distances from the nucleus in which the typical time of the electron transit near the nucleus is larger than the cyclotron-gyration period, while the negative energy of Coulomb interaction is larger (in absolute value) than the total electron energy. The indicated range of distances is realized in the case of a low electron energy or a strong magnetic field when the Larmor radius of the electron is smaller than the characteristic impact parameter of the close Coulomb collisions in the absence of a magnetic field. The required conditions are realized in the photospheres of isolated magnetic white dwarfs and in the experiments on creation of antihydrogen.     

Crossover behavior of disordered interacting two-dimensional electron systems in a parallel magnetic field

The crossover behavior of disordered interacting two-dimensional electron systems in a parallel magnetic field is analyzed. Using the so-called crossover one-loop renormalization group equations for the resistance and electron-electron interaction amplitudes, experimentally observed transformation of the temperature dependence of the resistance from a reentrant (nonmonotonic) behavior in relatively weak fields to an insulating-type behavior in stronger fields is qualitatively explained. The text was submitted by the authors in English.     

Long-time behavior of the Lorentz electron gas in a constant,uniform electric field

The long-time behavior of the Lorentz electron gas is studied in the presence of a uniform external field. A discussion of the rigorous solution of the one-dimensional Boltzmann equation is followed by the derivation of the asymptotic form of the velocity distribution in an arbitrary number of dimensions. The system is shown to absorb energy from the field without bounds, which excludes the usually assumed steady state with finite thermal energy density.Supported by the Polish Ministry of Higher Education, Science and Technology, Project MR.I.7.The authors are very grateful to Dr. Y. Pomeau for many valuable comments.