E.M. Kazaryan

Interband transitions in a spherical quantum layer in the presence of an electric field: Spherical rotator model

The interband transitions in a spherical GaAs quantum layer in the presence of an arbitrarily directed electric field are studied theoretically within the framework of the rigid spherical rotator model. The problem is solved under the assumption that the external field is a perturbation. Within the framework of the dipole approximation an expression for the interband absorption coefficient is obtained, and the absorption threshold frequency is determined. The corresponding selection rules are derived. A comparison with the case of quantum transitions in a spherical quantum layer in the presence of a radial electric field is performed.

Impurity states in a cylindrical quantum dot with the modified Pöschl-Teller potential

We study impurity states in a cylindrical quantum dot with two confining potentials: in the direction of cylinder axis modified Pöschl-Teller potential and in radial direction parabolic potential. Studies of impurity states are performed in the frames of variational method and by using numerical methods, the dependences of the particle energy on the geometrical parameters of the cylindrical quantum dot are derived. Dependences of the electron binding energy on the half-width and depth of the potential wall are revealed.

On the possibility of implementation of Kohn’s theorem in the case of ellipsoidal quantum dots

An electron gas in a strongly oblated ellipsoidal quantum dot with impenetrable walls is considered. Influence of the walls of the quantum dot is assumed to be so strong in the direction of the minor axis (the OZ axis) that the Coulomb interaction between electrons in this direction can be neglected and considered as two-dimensional, coupled. On the basis of geometric adiabaticity we show that in the case of a few-particle gas a powerful repulsive potential of the quantum dot walls has a parabolic form and localizes the dot in the geometric center of the structure. Due to this fact, conditions occur to implement the generalized Kohn theorem for this system.

Quasi-Conical Quantum Dot: Electron States and Quantum Transitions

The exactly solvable model of quasi-conical quantum dot, having a form of spherical sector is proposed. Due to the specific symmetry of the problem the separation of variables in spherical coordinates is possible in the one-electron Schrodinger equation. Analytical expressions for wave function and energy spectrum are obtained. It is shown that at small values of the stretch angle of spherical sector the problem reduced to the conical QD problem. The comparison with previously performed works showed good agreement of results. As an application of the obtained results, the quantum transitions in the system are considered.

Spin Magnetic Moment and Persistent Orbital Currents in Cylindrical Nanolayer

Abstract Densities of persistent orbital and spin magnetic moment currents of an electron in a cylindrical nanolayer in the presence of external axial magnetic field are considered. For the mentioned current densities analytical expressions are obtained. The conditions when in the system only spin magnetic moment current is present are defined. Dependencies of orbital and spin magnetic moment currents on geometrical parameters of nanolayer are derived. It is shown that in the case of layered geometry the dependence of spin magnetic moment current on radial coordinate has a non-monotonic behavior and changes the sign. This is the peculiarity of layered geometry of nanostructure and it is due to the behavior of wave function of the system along the radial direction. Dependent on the directions of the field and orbital rotation of the electron there are defined values of radial coordinates when the orbital current disappears. The transition to the case of cylindrical quantum dot is discussed as well.

Tunability of absorption threshold frequencies and Stark shift in the InSb narrow gap spherical quantum layer

In this work the interband optical absorption and Stark shift in the ensemble of InSb spherical quantum layers are investigated. Calculations are carried out both for the cases of parabolic and Kanes dispersion laws. The distribution of layers by their inner radii is taken into account. The effect of weak electric field on the energy levels coupling is investigated as well. It is found out that the energy spectrum 1s1p1d2s1f2p… for spherical quantum dot turns to the spectrum 1s1p1d1f2s2p… for spherical quantum layer with enough large value of inner radius. It is also shown that in the spherical quantum layer, where the coupling between neighboring states is not negligible, there is no square low dependence of Stark shift on electric field strength in contrast to the rotator model.

DIRECT INTERBAND LIGHT ABSORPTION IN A SPHERICAL QUANTUM DOT WITH THE MODIFIED PÖSCHEL-TELLER POTENTIAL

The energy levels and direct interband absorption of light in a spherical quantum dot with a modified Poschel-Teller confining potential are studied. Analytical expressions for the particle energy spectrum and absorption threshold frequencies in the regime of strong size quantization are obtained. Selection rules for quantum transitions are revealed. Red shift and blue shift of absorption threshold has been observed depending on the values of half-width and depth of confining potential, correspondingly.

Two electronic states in a quantum ring: Mathieu equation approach

The problem of two-electronic states is considered for the case of thin GaAs quantum ring in the framework of adiabatic approximation. It is assumed that electrons are localized on a circle, and the Coulomb interaction between the electrons depends only on angular coordinates. The real Coulomb interaction is replaced by function which makes it possible the separation of relative motion and the motion of the center of mass. The Mathieu equation is obtained for the relative motion of electrons. The harmonic, anharmonic and the libration regimes of oscillations are discussed.

Quantum model of the prolate spheroidal Thomson hydrogen atom

In a uniformly charged prolate spheroidal Thomson hydrogen atom the electron states have been investigated. It has been shown from the mathematical point of view that the problem is equivalent to a spheroidal hydrogen atom in a parabolic potential with the cylindrical symmetry. In the framework of adiabatic approximation, the energy of ground state has been calculated. Comparison with the case of uncharged spheroidal quantum dot has been made, and the analytical form of wave function of electron has been also obtained.

Dipole and quadrupole moments of electron in spherical nanolayer

In this paper for one electron states dipole and quadrupole moments are studied in spherical impenetrable quantum nanolayer. It is shown that dipole moment is zero for the considered system. An analytical formula for quadrupole moment is derived. Quadrupole moment dependence upon one radius of the nanolayer, when the other one is fixed, is obtained.