F. Dujardin

The order parameters of a spin-1 Ising film in a transverse field

Using the effective-field theory with a probability distribution technique that accounts for the self-spin-correlation functions, the layer longitudinal magnetizations and quadrupolar moments of a spin-1 Ising film and their averages are examined. These quantities as functions of the temperature, the ratio of the surface exchange interactions to the bulk ones, the strength of the transverse field and the film thickness are calculated numerically and some interesting results are obtained.

Landau levels of two-dimensional negatively charged three-particle Coulomb states

We study the influence of a low external uniform magnetic field on the energy levels of three-particle Coulomb states in a strictly two-dimensional medium. We show that at low magnetic fields, when the coupling between the relative motion and the motion of the centre of mass may be neglected, additional Landau levels appear. We compute the ground state energy corresponding to the relative motion as a function of the strength of the magnetic field for different values of the mass ratio of the negatively and positively charged particles. We compare our results with those we obtained previously in the three-dimensional limit.

On the anomalous Stark effect in a thin disc-shaped quantum dot

The effect of a lateral external electric field F on an exciton ground state in an InAs disc-shaped quantum dot has been studied using a variational method within the effective mass approximation. We consider that the radial dimension of the disc is very large compared to its height. This situation leads to separating the excitonic Hamiltonian into two independent parts: the lateral confinement which corresponds to a two-dimensional harmonic oscillator and an infinite square well in the growth direction. Our calculations show that the complete description of the lateral Stark shift requires both the linear and quadratic terms in F which explains that the exciton possess nonzero lateral dipolar moment and polarizability. The fit of the calculated Stark shift permits us to estimate the lateral permanent dipole moment and the polarizability according to the disc size. Our results are compared to those existing in the literature. In addition the behavior of the optical integral shows that the exciton lifetime is greater than that under zero field which is due to the field-induced polarization.

Effect of a lateral electric field on an off-center single dopant confined in a thin quantum disk

The effect of a lateral electric field on a donor impurity confined in a thin quantum disk is studied theoretically in the framework of mass approximation and using the Ritz variational approach. We show that the binding energy depends on several parameters: the dot size, the position of the donor impurity, the lateral field strength, and its orientation relative to the axis containing the impurity. When the impurity is located at one edge and the electric field is oriented in the opposite direction, the binding energy is considerably reinforced due to the simultaneous additive effects of coulombic potential and electrostatic force. The competition between these effects modifies considerably the probability densities and allows a better comprehension of the binding energy variations. This interesting behavior can contribute to an better understanding of the experimental optical response.

Binding energy of excitons in inhomogeneous quantum dots under uniform electric field

Abstract Excitons in inhomogenous quantum nanospheres have been theoretically studied within the effective mass approximation. An infinite deep potential has been used to describe the effects of quantum confinement. The binding energy with or without an applied electric field is determined by the Ritz variational method taking into account the correlation between the electron and the hole in the trial wave function. It appears that the binding energy strongly depends on the core and shell radii. The existence of a radius ratio critical value has been shown: it may be used to distinguish between tridimensional and spherical surface confinement. The influence of a uniform electric field is analyzed. It has been found that the Stark effect appears even for very small sizes and that the energy shift is more significant when the exciton is near the spherical surface.

THE FERROMAGNET SPIN-1/2 ISING SUPERLATTICE IN A TRANSVERSE FIELD

The phase transitions of a ferromagnet spin-1/2 Ising superlattice consisting of two different materials are examined using the effective field theory. The critical temperature of the system is studied as a function of the thickness of the constituents in a unit cell, exchange interactions in each material and transverse field. A critical value of the interface exchange interaction above which the interface magnetism appears is found.

Size dependence of the polarizability and Haynes rule for an exciton bound to an ionized donor in a single spherical quantum dot

We study the effect of an external electric field on an exciton bound to an ionized donor (D+, X) confined in a spherical quantum dot using a perturbative-variational method where the wave function and energy are developed in series of powers of the electric field strength. After testing this new approach in the determination of the band gap for some semiconductor materials, we generalize it to the case of (D+, X) in the presence of the electric field and for several materials ZnO, PbSe, and InAs, with significant values of the mass ratio. Three interesting results can be deduced: First, we show that the present method allows to determine the ground state energy in the presence of a weak electric field in a simple way (E = E0 − αf2) using the energy without electric field E0 and the polarizability α. The second point is that our theoretical predictions show that the polarizability of (D+, X) varies proportionally to R3.5 and follows an ordering αD0

The site-diluted spin-12 Ising film

The phase transitions of a diluted spin-12 Ising film are examined using the framework of the effective field theory with a probability distribution technique that accounts for the single-site spin correlations. The critical temperature Tc/J of the system is calculated as a function of the thickness of the film, the concentration c of magnetic atoms and the ratio R=Js/J of the surface constant couplings to the bulk ones. It is shown that for R=Js/J less than a critical value Rc, the critical temperature of the film Tc/J is smaller than the bulk critical temperature TcB/J and for R⩾Rc, Tc/J is larger than the bulk TcB/J and surface TcS/J critical temperatures of the corresponding semi-infinite system and as the film thickness L is increased further, for R⩽Rc (R⩾Rc), Tc/J increases (decreases) and approaches asymptotically for large values of L the bulk critical temperature TcB/J (the surface critical temperature TcS/J) of the corresponding semi-infinite system.

Photoionization cross section and binding energy of single dopant in hollow cylindrical core/shell quantum dot

In this study, we have investigated the confined donor impurity in a hollow cylindrical-shell quantum dot. The charges are assumed to be completely confined to the interior of the shell with rigid walls. Within the framework of the effective-mass approximation and by using a simple variational approach, we have computed the donor binding energy as a function of the shell sizes in order to study the behavior of the electron-impurity attraction for a very small thickness. Our results show that the binding energy of a donor impurity placed at the center of cylindrical core/shell dots depends strongly on the shell size. The binding energy increases when the shell-wideness becomes smaller and shows the same behavior as in a simple cylindrical quantum dot. A special case has been studied, which corresponds to the ratio between the inner and outer radii near to one (a/b → 1) for which our model gives a non-significant behavior of the impurity binding energy. This fact implies the existence of a critical value (a...

The transverse spin-1 Ising film

Within the framework of the effective-field theory, we examine the phase transitions of a transverse spin-1 Ising film. We discuss an L -layer film of simple cubic symmetry with nearest-neighbour exchange interactions in which the exchange interaction strengths in surface layers are assumed to be different from the bulk values, and we derive and illustrate expressions for the phase diagrams and order parameter profiles. It is found that for a ratio of the surface exchange interactions to the bulk ones R = Js /J less than a critical value Rc , the critical temperature Tc /J of the film is smaller than the bulk critical temperature Tc B /J and, as L is increased further, Tc /J increases. However, for R >Rc , Tc /J is greater than the bulk critical temperature Tc B /J and, as L is increased further, Tc /J decreases.