Magnetic moment of a two-dimensional degenerate electron gas in mesoscopic samples

The orbital magnetism of two-dimensional electrons in mesoscopic samples is studied in models where the interaction between electrons is neglected. Various geometries are considered as there are disc, plaquette, bracelet with hard wall confinement and also a confinement with a parabolic potential. We calculate the average magnetic moment which means an average with respect to size fluctuations and de Haas-van Alphen oscillations which arise in the case of a sharp Fermi cutoff. We see three distinct ranges in the magnetic field: (i) small field region where perturbation theory applies; (ii) moderate fields where edge currents play a prominent role; and (iii) the high field range with a Landau type susceptibility. In a quasiclassical picture, the electronic orbits are not qualitatively changed by a magnetic field in (i); skipping orbits are important in (ii); and in (iii), the cyclotron radius is smaller than the sample size. As a rule, we find an enhancement of the magnetic response which increases with k_FL, that is, with sample size divided by the Fermi wave length. Also, we have found out that the quasiclassical approximation fails in the calculation of the magnetic properties; on the other hand, we have seen no essential differences between the canonical ensemble (fixed particle number) and the grand canonical ensemble (chemical potential given). In the case of plaquettes, in particular for samples in the form of squares, we have found agreement with experimental results by Lévy, Reich, Pfeiffer and West.     

Magnetic ratchet effects in a two-dimensional electron gas

The effect of the magnetic field on the generation of an electric current in a two-dimensional electronic ratchet is theoretically studied. Mechanisms of the formation of magnetically induced photocurrent are proposed for a structure with a two-dimensional electron gas (quantum well, graphene, or topological insulator) with a lateral asymmetric superlattice consisting of metallic strips on the external surface of the structure. The ratchet with the spatially oscillating magnetic field generated by the ferromagnetic lattice, as well as the nonmagnetic ratchet placed in the uniform magnetic field both classically weak and strong quantizing, is considered. It is established that the ratio of the amplitude of the magnetic oscillations of photocurrent to the ratchet photocurrent in zero field can exceed two orders of magnitude.     

Observation of an interedge magnetoplasmon mode in a degenerate two-dimensional electron gas

We study the propagation of edge magnetoplasmons by time-resolved current measurements in a sample which allows for selective detection of edge states in the quantum Hall regime. At filling factors close to nu=3 we observe two decoupled modes of edge excitations, one of which is related to the innermost compressible strip and is identified as an interedge magnetoplasmon mode. From the analysis of the propagation velocities of each mode the internal spatial parameters of the edge structure are derived.     

Magnetoexcitons in nanostructures exhibiting cylindrical symmetry

The problem of an exciton in the cylindrical nanostructure exposed to an external static magnetic field is investigated. The theoretical model assumes anisotropic masses which are different inside and outside the nanostructure. The confinement potential has finite value at the boundaries and magnetic field is parallel to the axis of the cylinder. The screened Coulomb interaction between an electron and a hole is assumed. The consistent mathematical procedure is developed to calculate the magnetoexciton eigenfunctions and eigenenergies. Our method applies to the systems exhibiting cylindrical symmetry where, due to confinement effects accompanied by the e-h Coulomb interaction, the separation of relative- and center-of-mass motion is not possible. Numerical calculations have been performed for the quantum disk, the cylinder and the quantum rod. The magnetic field dependent energy spectrum and corresponding wave functions, expressed in terms of known one-particle electron and hole eigenfunctions, are calculated. Additionally, we point out the different role of Coulomb interaction in every case.     

Spin polarization of two-dimensional electron gas in hybrid ferromagnetic/semiconductor nanostructures

We present a theoretical study on the spin-dependent transport of electrons in hybrid ferromagnetic/semiconductor nanosystem under an applied bias voltage. Experimentally, this kind of nanosystem can be realized by depositing a magnetized ferromagnetic stripe with arbitrary magnetization direction on the surface of a semiconductor heterostructure. It is shown that large spin-polarized current can be achieved in such a nanosystem. It is also shown that the spin polarity of the electron transport can be switched by adjusting the applied bias voltage. These interesting properties may provide an alternative scheme to realize spin injection into semiconductors, and such a nanosystem may be used as a tunable spin-filter by bias voltage.     

Retarded transverse current-current response functions of a two-dimensional electron gas

The retarded transverse current-current response functions of an ideal two-dimensional electron gas at zero temperature are calculated. Introducing a new approximation scheme which allows one to take account of the reaction of the electromagnetic field to the induced current, i.e. the influence of the electronic induced current on the dynamics of the electromagnetic field, within the framework of the conventional linear response theory in a self-consistent way, a possible form of the dispersion relation for the transverse plasmon in the system is obtained. It is found that the energy of the transverse plasmon has a gap at k=0, if the thickness of the system is finite, in contrast to the longitudinal case.     

Disordered two-dimensional electron systems with chiral symmetry

We review the results of our recent numerical investigations on the electronic properties of disordered two dimensional systems with chiral unitary, chiral orthogonal, and chiral symplectic symmetry. Of particular interest is the behavior of the density of states and the logarithmic scaling of the smallest Lyapunov exponents in the vicinity of the chiral quantum critical point in the band center at E=0. The observed peaks or depressions in the density of states, the distribution of the critical conductances, and the possible non-universality of the critical exponents for certain chiral unitary models are discussed.     

Solitons in a two-dimensional electron gas

The non-linear spectrum of a two-dimensional electron gas (2-DEG) formed at the interface of a heterostructure is investigated. This spectrum is found to contain a new type of localized excitation exhibiting soliton behavior. A matrix formulation of the model equations permits the extraction of the equation of evolution in space for these excitations. Results are presented for the boundary value problem excited by temporal Gaussian pulses.     

Dielectric response of cylindrical nanostructures in a magnetic field

We study the magnetic field dependence of the dielectric response of large cylindrical molecules such as nanotubes. When a field-induced level crossing takes place, an applied electric field has two effects: it may cause a linear instead of the usual quadratic Stark effect or the difference in the quadratic Stark coefficient of the two levels leads to a discontinuity in the polarization. Explicit calculations are performed for doped nanotubes and a rich structure in the real part of the low-frequency dielectric function is found when a magnetic field is applied along the cylinder axis. It is suggested that studies of can serve as a spectroscopic tool for the investigation of large ring-shaped or cylindrical molecules. Received 11 January 2000 and Received in final form 19 May 2000     

On the thermodynamics of a degenerate two-dimensional electron gas in a strong magnetic field: density of states

Systematic expansions, in powers ofB ^–1, for the free energy and the density of states, are derived for a two-dimensional degenerate electron gas in the presence of a strong magnetic field and an arbitrary potential. They are then applied to a system involving random impurities. Landau levels are shown to be broadened, with level widths related to the impurity concentration and potential. We show that level broadenings, induced by long range electron-impurity ineractions, do not depend on the magnetic field in the strong field limit, confirming the existing theories. But broadened Landau levels can have a large variety of shapes as one changes the impurity potential, distribution and concentration. Our theory, with a Gaussian potential, leads to a good agreement with the recent experiment on the de Haas-van Alphen effect in Br₂-graphite intercalation compounds     

The specific heat of a degenerate electron gas

The internal energy of a degenerate electron gas is evaluated for finite temperature to first order ine ² by applying the Sommerfeld method to the grand partition function. The specific heat is obtained correctly by temperature differentiation in which the shift of the Fermi momentum from the ideal gas value is taken into consideration. Thus, this theory differs from those given previously by Pines, Gell-Mann and others. In fact, there appears no divergence such as encountered by Gell-Mann in his approximate approach. The specific heat thus evaluated increases slightly withr _s in agreement with recent experimental data on alkali metals. This work was supported by the National Science Foundation.     

Solitons in semiconductor microstructures with a two-dimensional electron gas

Nonlinear waves in a two-dimensional electronic plasma with metal screening gates are investigated. It is shown that solitons described by the KdV equation exist in such a system. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 7, 479–481 (10 October 1999)     

Magnetic susceptibility of a two-dimensional electron gas in the quantum strong magnetic field limit

It is shown that the peak values of the magnetic susceptibility of a two-dimensional electron gas in the quantum strong magnetic field limit are integral multiples of $\text{μ}{}^2{}_{\mathrm{B}}\text{2π}$.     

High-frequency conductivity of a two-dimensional electron gas with impurity electron states

The high-frequency conductivity tensor for a two-dimensional electron gas with short-range-acting impurity atoms has been computed. Spatial dispersion of the conductivity was taken into account. The threshold and maxima of the dissipative part of the conductivity arising from ionization of the impurity atoms by the field of electromagnetic waves were found. Numerical calculations of the conductivity were carried out for semiconductor structures with a two-dimensional electron gas. Khar’kov State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 91–94, July, 1997.     

Magnetic barrier in a two-dimensional hole gas

Transport properties of a magnetic barrier in a Ga_xAl_1−xAs based two-dimensional hole gas are reported. A ferromagnetic cobalt film, separated by an AlO_x layer from the semiconductor in order to prevent leakage currents, is magnetized in-plane, such that the fringe field generates a localized perpendicular magnetic field acting as a magnetic barrier. The resistance as a function of the in-plane magnetic field shows a characteristic minimum at the coercive field of the ferromagnetic film. Semiclassical simulations based on the Landauer–Büttiker formalism show good agreement with the experiment.     

Dynamical response properties of a two-dimensional electron gas in a weak periodic magnetic modulation

Calculating the dynamical dielectric response function for a two-dimensional electron gas (2D EG) under a perpendicular magnetic field and subjected to an additional weak unidirectional periodic magnetic field within the random-phase approximation (RPA), we find that not only is the response function broadened in the presence of the magnetic modulation, but it is also found to contain a series of subsingularities at the band edges which are attributed to the magnetic modulation induced broadening of the energy spectrum.     

Hybrid semiconductor/metal nanostructures with two-dimensional electron systems

A brief account of our recent work on InAs/metal hybrids is given. In particular we discuss Josephson field-effect transistors with niobium source and drain contacts, first spin transistor structures with permalloy electrodes, and devices with gold shunts exhibiting the extraordinary magnetoresistance effect.