Ahmet Erdinç

The photoionization cross section of a hydrogenic impurity in a multi-layered spherical quantum dot

In this study, we have investigated the photoionization cross section of an on-center hydrogenic impurity in a multi-layered spherical quantum dot. The electronic energy levels and their wave functions have been determined fully numerically by shooting method. Also, we have calculated the binding energy of the impurity by using these energy values. The photoionization cross section has also been computed as a function of the layer thickness and normalized photon energies. We have discussed in detail the possible physical reasons behind the changes in the binding energies and photoionization cross section. It is observed that both the binding energies and the photoionization cross sections depend strongly on the layer thickness and photon energies.

A detailed investigation of electronic and optical properties of the exciton, the biexciton and charged excitons in a multi-shell quantum dot nanocrystal

In the present study, the electronic and optical properties of the exciton (X), the biexciton (XX) and charged excitons (X− and X+) in a multi-shell quantum dot nanocrystal have been systematically explored in detail. The electronic properties have been determined in the framework of the single-band effective mass approximation. For this purpose, the Poisson–Schrodinger equations have been solved self-consistently in the Hartree approximation. In the electronic structure calculations for XX, X− and X+, the quantum mechanical exchange–correlation potentials between particles of the same type have been taken into account in the local density approximation. Some optical parameters, such as the overlap integrals, recombination oscillator strengths, radiative lifetimes, etc, have been determined by using the single-particle energy levels and wavefunctions obtained. A different approximation, reported in Sahin and Koc 2013 Appl. Phys. Lett. 102 183103, has been used in the recombination oscillator strength calculations. The results have been presented comparatively as a function of the shell thicknesses, and the well widths and probable physical reasons underlying them have been discussed in detail.

Equilibrium and nonequilibrium behavior of the spin-1 Ising model in the quadrupolar phase

Equilibrium properties of the spin-1 Ising model with the arbitrary bilinear (J) and biquadratic (K) pair interactions are studied on a body centered cubic lattice by using the pair approximation of the cluster variation method, which is identical to the Bethe approximation, in the quadrupolar phase. First, the thermal variation of the metastable and unstable dipole and quadrupolar moment order parameters is investigated and the metastable and unstable branches of them are found besides the stable branch of the quadrupolar moment order. In addition, it is found that when the values of α=J/K decreases, transition temperatures also decrease and some of metastable and unstable branches of order parameters disappear. On the other hand, nonequilibrium behavior of the model in the quadrupolar phase is studied by using the path probability method and the set of nonlinear differential equations, which is also called the dynamic or rate equations, is obtained. The solutions of the dynamic equations are expressed by means of flow diagrams near the transition temperatures. The stable, metastable and unstable solutions are shown and the “overshooting” phenomenon is seen in the flow diagrams, explicitly. The role of the unstable points, as separators between the stable and the metastable points, is described and how a system freezes in a metastable state is also investigated, extensively.

EQUILIBRIUM AND NONEQUILIBRIUM BEHAVIOR OF THE BLUME–EMERY–GRIFFITHS MODEL USING THE PAIR APPROXIMATION AND PATH PROBABILITY METHOD WITH THE PAIR DISTRIBUTION

Equilibrium properties of Blume–Emery–Griffiths (BEG) model with the arbitrary bilinear (J), biquadratic (K) and crystal field interaction (D) are studied on a body centered cubic lattice by using the pair approximation of the cluster variation method, which is identical to the Bethe approximation. The thermal variation of the stable, metastable and unstable dipole and quadrupolar moment order parameters are found for various values of the two different coupling parameters J/K and D/K. The phase transitions of the stable, metastable and unstable branches of the order parameters are investigated extensively. The critical temperatures in the case of a second-order phase transition are obtained for different values of J/K and D/K by the Hessian determinant. The first-order phase transition temperature is determined by matching the values of the two branches of the free energy values. On the other hand, nonequilibrium behavior of the model is studied by using the path probability method with the pair distribu...

APPLICATION OF THE GENETIC ALGORITHM TO BLUME–EMERY–GRIFFITHS MODEL: TEST CASES

The equilibrium properties of the Blume–Emery–Griffiths (BEG) model Hamiltonian with the arbitrary bilinear (J), biquadratic (K) and crystal field interaction (D) are studied using the genetic algorithm technique. Results are compared with lowest approximation of the cluster variation method (CVM), which is identical to the mean field approximation. We found the genetic algorithm to be very efficient for fast search at the average fraction of the spins, especially in the early stages as the system is far from the equilibrium state. A combination of the genetic algorithm followed by one of the well-tested simulation techniques seems to be an optimal approach. The curvature of the inverse magnetic susceptibility is also presented for the stable state of the BEG model.

THE GROUND-STATE PHASE DIAGRAMS OF THE SPIN-2 ISING MODEL

The ground-state phase diagrams are obtained for the spin-2 Ising model Hamiltonian with bilinear and biquadratic exchange interactions and a single-ion crystal field. The interactions are assumed to be only between nearest-neighbors. Obtained phase diagrams are presented in the (Δ,J), (K,J), (Δ/J,K/J), (Δ/|J|,K/|J|), (Δ/|K|,J/|K|), (H/J,Δ/J), (H/|J|,Δ/|J|), (H/J,K/J), and (H/|J|,K/|J|) planes where J, K, Δ, and H are the bilinear, biquadratic exchange interactions, the single-ion crystal field, and the external magnetic field, respectively. The influence of the external magnetic field on the spin configurations is investigated.

THE METASTABLE PHASE DIAGRAM OF THE BLUME–EMERY–GRIFFITHS MODEL IN ADDITION TO THE EQUILIBRIUM PHASE DIAGRAM USING THE PAIR APPROXIMATION

As a continuation of our previously published work, the metastable phase diagram of the Blume–Emery–Griffiths model with the arbitrary bilinear (J), biquadratic (K) and crystal field interaction (D) is presented in addition to the equilibrium phase diagram in (T/K, J/K) and (T/K, D/K) plane by using the pair approximation of the cluster variation method on a body centered cubic lattice. We also calculate the phase transitions for the unstable branches of order parameters. The calculated first- and second-order phase boundaries of the unstable branches of the order parameters are superimposed on the equilibrium phase diagram and metastable phase diagram. It is found that the metastable phase diagram and the first- and second-order phase boundaries for unstable branches of order parameters always exist at low temperatures, which are consistent with the experimental and theoretical works.

THE COUPLED SPIN-1 BLUME-CAPEL SUBLATTICES WITH DIFFERENT BILINEAR INTERACTIONS

The equilibrium properties of the spin-1 Blume-Capel model are studied by the lowest approximation of the cluster-variation method which is identical to the mean-field approximation. The lattice is divided into two sublattices A and B, and different bilinear interaction parameters JAB and JBA between the nearest-neighbor spins are assumed. The temperature variations of the order-parameters are studied, therefore, the phase diagrams are obtained on the (JAB, T) planes for given values of JBA and crystal fields D. It was found that the model yields both second- and first-order phase transitions at higher positive D values and the lines of which combine at tricritical points. Negative values of D lead only second-order phase transitions. The phase diagrams are symmetric under the exchange of JAB with JBA as expected.

Critical Behaviour of the Ferromagnetic Spin-3/2 – Blume-Emery-Griffiths Model with Repulsive Biquadratic Coupling

The critical behaviour of the ferromagnetic spin-3/2 Blume-Emery-Griffiths model with repulsive biquadratic coupling in the absence and presence of an external magnetic field is studied by using the lowest approximation of the cluster variation method, which is identical with the mean-field approximation. Thermal variations of the order parameters are investigated for different values of the interaction parameters and the external magnetic field. The complete phase diagrams of the system are calculated in the (kT/J,K/J), (kT/J,D/J) and (kT /J,H/J) planes. Five new phase diagram topologies are obtained, which are either absent from previous approaches or have gone unnoticed. A detailed discussion and comparison of the phase diagrams is made.