Mesoscopic conductance fluctuations of a two-dimensional electron gas in a one-dimensional lattice of antidots

Mesoscopic conductance fluctuations of a two-dimensional electron gas in a one-dimensional periodic array of antidots have been studied experimentally, for the first time. The fluctuations show a quasiperiodic behaviour on magnetic field, with period corresponding to the quantization of magnetic flux through the area of a unit cell of the one-dimensional array. The existence of the quasiperiodic component is explained by an anomalous area distribution of interfering trajectories.     

Quantum magnetic flux through helical molecules in optically active media

After study of an electron moving in a loop of wire in an uniform external magnetic field with its velocity vector perpendicular to the field and quantization of the angular momentum of the moving electron in the equilibrium state, we find the quantum magnetic flux through the solenoids or loops of wire, like the quantum magnetic flux trapped in hollow superconducting cylinders. Optically active media have the helical molecular structure, which acts as the natural micro-solenoid for the electromagnetic waves passing through them. Applying the result of the quantized magnetic field in the propagation direction induced by helical molecules, we find that optic activity is the natural Faraday effect, when the optical rotation of a plane-polarized wave through an optically active medium is caused by the quantized magnetic field induced by the incident light, which has been confirmed by the experimental observations on α-quartz. Through measurements of the rotatory power and the Verdet constant of an optically active substance, we can determine the quantized magnetic field. PACS 03.70.+k; 33.55.Ad; 74.25.Ha; 78.20.Ek; 78.20.Ls     

Calculation of electric transport close to a Lifshitz transition in a high magnetic field

The effects of the Landau quantization and interactions on a Lifshitz transition are studied. The Landau quantization leads to a quasi-one-dimensional behavior for the direction parallel to the field. The repulsive Coulomb interactions give rise to a gas of strongly correlated carriers. Consequently, in the ground state, an electron pocket is emptied in a discontinuous fashion as a function of the chemical potential or magnetic field. This discontinuity is gradually smeared by temperature, in agreement with experiments for CeIn₃. We further calculate the conductivity and the Hall conductivity in the presence of nonmagnetic impurities, the Landau quantization and interactions.     

Self-assembled nanocrystalline CdSe thin films

The topic of this contribution is the investigation of quantum states and quantum Hall effect in electron gas subjected to a periodic potential of the lateral lattice. The potential is formed by triangular quantum antidots located on the sites of the square lattice. In such a system the inversion center and the four-fold rotation symmetry are absent. The topological invariants which characterize different magnetic subbands and their Hall conductances are calculated. It is shown that the details of the antidot geometry are crucial for the Hall conductance quantization rule. The critical values of lattice parameters defining the shape of triangular antidots at which the Hall conductance is changed drastically are determined. We demonstrate that the quantum states and Hall conductance quantization law for the triangular antidot lattice differ from the case of the square lattice with cylindrical antidots. As an example, the Hall conductances of magnetic subbands for different antidot geometries are calculated for the case when the number of magnetic flux quanta per unit cell is equal to three.     

A new approach to the quantized electrical conductance

The quanta of electrical conductance is derived for a one-dimensional electron gas both by making use of the quasi-classical motion of a quantum fluid and by using arguments related to the uncertainty principle. The result is extended to a nanowire of finite cross section area and to electrons in magnetic field, and the quantization of the electrical conductance is shown. An additional application is made to the two-dimensional electron gas.     

Mechanism of plateau formation in the quantum Hall effect

As the magnetic flux is increased (decreased) relative to the mid-plateau value by a given number of flux quanta, the 2-dimensional electron liquid responds by forming the same number of vortices (antivortices). Assuming the vortices (antivortices) to be pinned, we show that with a transport current flowing by, the pinning centres exert a force on the electron liquid. Inclusion of this force in a force balance equation for the electron liquid explains the formation of plateaus within the FQHE. The possibility of generalizing the theory to the IQHE is discussed.     

Theory of Quantum Magneto-Transport in Two-Dimensional Electron Systems

By making use of the concept of phase slippage originally proposed by Anderson, we present a theoretical study of the boundary between two contiguous twodimensional electron systems in a strong magnetic field based on the conclusion that the number of flux quanta (h/e) pertaining to a electron is the inverse Landau filling factor. The magneto-transportation is related to the superfluidity analogy of the two-dimensional electron system. It is shown that voltages on the perimeters are determined explicitly by the Landau indices of the two contiguous regions. Then we apply to systems with many region in series and obtain results which are in good agreement with experiments associated with both the integer and fractional quantum Hall effects. Finally we discuss the quantization of the source-drain two-terminal resk tances.     

Landau quantization and equatorial states on the surface of a nanosphere

The Landau quantization for the electron gas on the surface of a sphere is considered. It is shown that in the regime of strong fields the lowest energy states are those with magnetic quantum numbers m of order of Φ /Φ₀, the number of magnetic flux quanta piercing the sphere. For an electron gas of low density (semiconducting situation) it leads to the formation of an electronic stripe on the equator of the sphere in high fields. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 6, 405–409 (25 September 1999) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Diamagnetic susceptibility of the electron gas in the cylindrical nanolayer

Diamagnetic properties of the electron gas in cylindrical nanolayer have been investigated. The dependence of mean energy, mean magnetization and mean magnetic susceptibility on the values of magnetic field is obtained. Comparison of these dependencies with the case, when the electron gas is localized in the cylindrical quantum dot, is carried out. In a nanolayer, the character of an effect of size quantization on the magnetic properties of the electron gas has been revealed.     

二维电子体系在高密度下的稳定性

本文计算了高密度的二维电子体系的边缘能(将二维体系沿某一直线解离成两片时,形成单位长度新边缘所需要的能量)。结果发现,当r_ss^(c)(约0.415)时,边缘能变负,从而表明在高密度下,二维电子气的基态有可能发生不稳。我们分别讨论了二维非束缚的电子气和束缚的电子气基态的稳定性,并在一个简化的模型下给出了束缚的电子气基态稳定性的判据。 关键词：     

An Effective Mass Theorem for the Bidimensional Electron Gas in a Strong Magnetic Field

We study the limiting behavior of a singularly perturbed Schr?dinger-Poisson system describing a 3-dimensional electron gas strongly confined in the vicinity of a plane (x, y) and subject to a strong uniform magnetic field in the plane of the gas. The coupled effects of the confinement and of the magnetic field induce fast oscillations in time that need to be averaged out. We obtain at the limit a system of 2-dimensional Schr?dinger equations in the plane (x, y), coupled through an effective selfconsistent electrical potential. In the direction perpendicular to the magnetic field, the electron mass is modified by the field, as the result of an averaging of the cyclotron motion. The main tools of the analysis are the adaptation of the second order long-time averaging theory of ODEs to our PDEs context, and the use of a Sobolev scale adapted to the confinement operator.     

Quantization of Magnetic Flux Through the Orbits of the Hydrogen Atom

The quantization of magnetic flux through the orbits of the hydrogen atom is investigated on the basis of the Rutherford-Bohr model of the atom. In contrast to earlier studies based on magnetic fields originating from the magnetic moment of the proton, here the origin of the magnetic flux is taken to be the orbiting electron itself. The effect of the magnetic moment of the proton on the magnetic flux through the orbit is studied in more detail. The energy difference due to opposite directions of the magnetic moment of the proton is shown to result in a fractional amount of 3/8 of the hyperfine level splitting of the lowest Bohr orbit. This ratio was also observed for the fine structure energy level splitting when the spin of the electron is neglected.     

Topological Quantization of the Magnetic Flux

The quantization of the magnetic flux in superconducting rings is studied in the frame of a topological model of electromagnetism that gives a topological formulation of electric charge quantization. It turns out that the model also embodies a topological mechanism for the quantization of the magnetic flux with the same relation between the fundamental units of magnetic charge and flux as there is between the Dirac monopole and the fluxoid.     

On the velocity of a 4π kink moving under the action of current

The dependence of bias current density through a junction on the velocity of a uniformly moving vortex carrying two magnetic flux quanta is established in the approximation of weakly nonlocal Josephson electrodynamics. It is shown that the velocity quantization of free motion of the vortex, which is induced by the Cherenkov interaction with Swihart waves, leads to the emergence of a discrete family of curves on the velocity-current plane.     

Thermodynamic functions of electron gas on the semiconductor nanotube surface in a magnetic field

Thermodynamic functions have been calculated in the effective mass approximation for degenerate and nondegenerate electron gases on the semiconductor cylindrical nanotube surface in a longitudinal magnetic field. The Laplace transform linking the density of states and the statistical sum has been used. The thermodynamic quantities of degenerate electron gas undergo the de Haas-van Alphen oscillations with the electron Fermi energy change and the Aharonov-Bohm oscillations with the magnetic flux change within the semiconductor tube cross section. The quantities related to nondegenerate gas oscillate only with the change of magnetic flux. A peak has been found in the nondegenerate gas heat capacity-temperature diagram. A limiting process to 2D electron gas on plane has been carried out.     

Influence of retardation effects on a 2D magnetoplasmon spectrum

Within a dissipationless limit, the magnetic field dependence of the magnetoplasmon spectrum for an unbounded two-dimensional electron gas (2DEG) system was found to intersect the cyclotron resonance line and, then, approach the frequency given by light dispersion relation. Recent experiments done for macroscopic disc-shaped 2DEG systems confirm theoretical expectations.     

Is a Fermi-Dirac distribution function for a non-equilibrium electron gas in high crossed electric and magnetic fields possible?

We generalize our investigation of the electron distribution function of anelectron gas interacting with phonons and moving in high crossed electric and magnetic fields. We consider the case of a degenerate gas: we look for conditions under which the distribution function is of a Fermi-Dirac type with an electric and magnetic field dependent temperature.     

Quantized Magnetic Flux in the Bohr–Sommerfeld Model

Based on the Bohr–Sommerfeld model, we investigate the quantization of magnetic flux through the electronic orbits together with its dependence on additional sources of magnetic fields. The additional magnetic field causes changes of the angular momentum and hence shifts of the energy of the atomic levels. We study this effect for the cases of the Zeeman effect, where the source is an external homogeneous magnetic field, and the hyperfine interaction, where the source is the field of the magnetic moment of the nucleus. We discuss a model for the handling of the different angular momentum contributions for which the energy shifts due to the Zeeman effect and the magnetic dipole contribution to the hyperfine interaction can be reproduced quite well. The meaning of “spin,” however, changes within this approach drastically. The unusual Landé g-factor of the electron is discussed to be the result of a reduced ground-state angular momentum of the electron in combination with the field of the magnetic moment of the electron rather than an intrinsic property of the electron.     

Zero bias conductance peak in InAs nanowire coupled to superconducting electrodes

We report the occurrence of the zero-bias conductance peak (ZBCP) in an InAs nanowire coupled to PbIn superconductors with varying temperature, bias voltage, and magnetic field. The ZBCP is suppressed with increasing temperature and bias voltage above the Thouless energy of the nanowire. Applying a magnetic field also diminishes the ZBCP when the resultant magnetic flux reaches the magnetic flux quantum h/2e. Our observations are consistent with theoretical expectations of reflectionless tunneling, in which the phase coherence between an electron and its Andreev-reflected hole induces the ZBCP as long as time-reversal symmetry is preserved.     

超导电子的角动量和磁通量子化

本文指出,磁通量子化应和超导电子的角动量量子化一致。分数角动量的存在必然导致分数磁通量子化,而分数磁通量子化和超导理论以及迄今为止的实验结果不相矛盾。我们提出和分析的一个新实验可以检测任意子和分数磁通量子。 关键词：