An analytically solvable model of confined electrons in a magnetic field and its relation to Landau diamagnetism

Here we present analytic results for the Slater sum and the magnetic moment for arbitrary magnetic field strengths for an assembly of harmonically confined, but initially free, electrons. The relevance of the results to the generalized Landau diamagnetism of such confined electrons is emphasized.     

Focusing of electrons by a transverse magnetic field

The foundations of the focusing of electrons by a transverse magnetic field proposed by V.S. Tsoi in 1974 have been reviewed. The kinetics of electrons in condensed media and interactions of conduction electrons with interfaces has been studied by means of the focusing of electrons. Various applications of the focusing of charge carriers in low-dimensional, including two-dimensional, electron systems have been demonstrated.     

Bloch electrons in a magnetic field

A complete set of basis functions for the expansion of the wavefunction of a Bloch electron in a uniform magnetic field is derived. In the empty lattice limit this set gives the appropriate Landau free-electron wavefunctions, contrary to the Roth functions which in that limit are plane waves.     

Observation of centrifugally driven interchange instabilities in a plasma confined by a magnetic dipole

Centrifugally driven interchange instabilities are observed in a laboratory plasma confined by a dipole magnetic field. The instabilities appear when an equatorial mesh is biased to drive a radial current that causes rapid axisymmetric plasma rotation. The observed instabilities are quasicoherent in the laboratory frame of reference; they have global radial mode structures and low azimuthal mode numbers, and they are modified by the presence of energetic, magnetically confined electrons. Results from a self-consistent nonlinear simulation reproduce the measured mode structures.     

Bloch electrons in a magnetic field: Topology of quantum states and transport

Quantum states and Hall conductances of electrons in n-type heterojunctions and holes in p-type heterojunctions in a field of a lateral superlattice and a perpendicular magnetic field were studied. It is shown that the energy spectrum of magnetic subbands in a periodic potential without inversion center is not symmetric about the reversal of the quasi-momentum sign. The properties of wave functions and the related topological invariants determining the Hall conductance were examined. The method of calculating the magnetic Bloch states of holes was developed on the basis of the Luttinger Hamiltonian, allowing the spin and spin-orbit interactions to be taken into account in this problem. The Hall conductance quantization law was determined for 2D holes in a periodic superlattice potential.     

Excitation of oscillations in a hemispherical dielectric resonator by a radial magnetic dipole

Forced oscillations excited by a radial magnetic dipole in a dielectric hemisphere (resonator) placed on a perfectly conducting plane are studied. It is shown that the dipole excites H modes. When the dipole radiation frequency equals the eigenfrequency of the resonator, an amplitude resonance is observed in the spectrum. The excitation efficiency is high when the magnetic dipole is placed at the maximum of the radial field component of the resonator’s eigenmode.     

The Green's function of confined electrons in an external magnetic field: Analytical formulation

We derive the analytical form of the Green's function of 2-dimensional electrons with lateral confinement in a perpendicular magnetic field. The confinement potentials considered are infinite barriers at radius R (quantum dot) and at r and R (quantum ring).     

Scattering of electrons by a potential step in a magnetic field

The scattering of two-dimensional electrons drifting in crossed electric and magnetic fields by an abrupt step in the external potential is discussed. The problem is reduced to solving a system of ordinary differential equations. It is shown that for moderate electric fields scattering with a change of Landau level numbers becomes appreciable. Zh. éksp. Teor. Fiz. 112, 1756–1762 (November 1997)     

Crystallization of electrons confined to a lattice

A necessary condition for electron crystallization is the dominance of the electronic Coulomb repulsion as compared with the kinetic energy. We show that 4f systems are good candidates for electron or hole crystallization to occur since the small radius of the 4f shell leads to small hybridizations and hence kinetic energy of the f electrons. Crystallization may take place in lattices with several equivalent 4f sites per unit cell when the electron or hole number is less than the number of sites. We give evidence that charge ordering in Yb₄As₃ is an example of the mechanism considered here. We also compare it with those considered by Wigner, Verwey, Mott and Hubbard.     

An exact form for the magnetic field density of states for a dipole

We present an analytical form for the density of states for a magnetic dipole in the center of a spherical voxel. This analytic form is then used to evaluate the signal decay as a function of echo time for different volume fractions and susceptibilities. The decay can be considered exponential only in a limited interval of time. Otherwise, it has a quadratic dependence on time for short echo times and an oscillatory decaying behavior for long echo times.     

Inelastic tunnel transport of electrons through an anisotropic magnetic structure in an external magnetic field

Quantum transport of electrons through a magnetic impurity located in an external magnetic field and affected by a substrate is considered using the Keldysh diagram technique for the Fermi and Hubbard operators. It is shown that in a strongly nonequilibrium state induced by multiple reflections of electrons from the impurity, the current-voltage (I–V) characteristic of the system contains segments with a negative conductivity. This effect can be controlled by varying the anisotropy parameter of the impurity center as well as the parameters of coupling between the magnetic impurity and metal contacts. The application of the magnetic field is accompanied by an increase in the number of Coulomb steps in the I–V curve of the impurity. The effect of appreciable magnetoresistance appears in this case. We demonstrate the possibility of switching between magnetic impurity states with different total spin projection values in the regime of asymmetric coupling of this impurity with the contacts.     

Correlation function of electrons in a magnetic field

The influence of a magnetic field on the correlation function of conduction electrons in metals at zero temperature is examined.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 91–94, August, 1972.     

Electromagnetic wave generation in a cylindrical resonator by electrons orbiting in a radial electrostatic field

The mechanisms leading to the generation of microwaves by electrons orbiting in a radial electrostatic field produced by a positively charged filament on the axis of a cylindrical resonator are investigated theoretically. The dispersion relations describing the interaction of the waves with the electrons are obtained. It is shown that the generation of electromagnetic fields is possible on account of both Cherenkov and plasma resonances. The frequencies and growth rates of waves under Cherenkov resonance conditions and also plasma resonance conditions in uniform and nonuniform electron layers are found. The advantages and disadvantages of different generation mechanisms are determined. Zh. Tekh. Fiz. 68, 91–94 (August 1998)