Numerical Diagonalization Of Hamiltonian Matrix Research Articles

Excited-state absorptions of an exciton confined in a quantum dot

The optical absorptions of an exciton with the higher excited states in a disc-like quantum dot are investigated. Calculations are made by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. With typical semiconducting GaAs based materials, the linear, third-order nonlinear, total optical absorption coefficients and refractive index changes have been calculated for the s–p, p–d, and d–f transitions. The results show that as the angular momentum quantum number of transitions increases, the absorption peaks shift towards lower energies and the absorption intensities increase.

A study of nonlinear optical properties of a negative donor quantum dot

In this paper, we studied the nonlinear optical properties of a negative donor center ( D −) in a disk-like quantum dot (QD) with a Gaussian confining potential. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. A detailed investigation of the linear, third-order nonlinear, total optical absorptions and refractive index changes has been carried out for the D − QD and the D 0 QD. The linear, third-order nonlinear, total optical absorptions and refractive indices have been examined for a double-electron QD with and without impurity. Our results show that the optical absorption coefficients and refractive indices in a disk-like QD are much larger than their values for quantum wells and spherical QDs and the nonlinear optical properties of QDs are strongly affected not only with the confinement barrier height, dot radius, the number of electrons but also the electron-impurity interaction.

Nonlinear optical properties of a D− system in a spherical quantum dot

The nonlinear optical properties of a D− system confined in a spherical quantum dot represented by a Gaussian confining potential are studied. The great advantage of our methodology is that the model potential possesses the finite height and range. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. We calculate the linear, third-order nonlinear and total optical absorption coefficients under the density matrix formalism. Numerical results for GaAs−Ga1−xAlxAs QDs are presented. Our results show that the optical absorption coefficients in a spherical QD are much larger than their values for GaAs quantum wells. It is found that optical absorptions are strongly affected not only the confinement barrier height, dot radius, the electron–impurity interaction but also the position of the impurity.

A STUDY OF THE GROUND STATE BEHAVIOR OF A TWO-ELECTRON QUANTUM RING

We study a two-electron system of a quantum ring under the influence of a perpendicular homogeneous magnetic field. Calculations are made by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. A ground-state behavior (spin singlet–triplet transitions) as a function of the strength of a magnetic field is investigated. We find that the ring radius R0 and the ring width W are important for the singlet–triplet transition of the ground-state.

Binding Energies of D− Centers Trapped by a Quantum Dot in a Magnetic Field

A investigation of the properties of the bound states of D− centers confined in a parabolic quantum dot has been performed for the case with the presence of a perpendicular magnetic field. Calculations are carried out by using the method of numerical diagonalization of Hamiltonian matrix within the effective-mass approximation. The binding energies of the ground and some bound-excited states are obtained as a function of the applied magnetic field strength. Detailed calculations of the binding energies for a number of low-lying states show that for field strength less than B = 2.1 T, the D− center confined in a quantum dot possesses two bound states, for 2.1 ≤ B < 2.4 T, there exist three bound states, etc. Further relevant characteristics of the D− center quantum dots in magnetic fields are provided.

Singlet-Triplet Transitions of a Pöschl–Teller QuantumDot

We study the energy spectra of a two-dimensional two-electron quantum dot(QD) with Pöschl–Teller confining potential under the influence ofperpendicular homogeneous magnetic field. Calculations are made by using themethod of numerical diagonalization of Hamiltonian matrix within theeffective-mass approximation. A ground-state behavior (spin singlet-triplettransitions) as a function of the strength of a magnetic field isfound. We find that the dot radius R of a Pöschl–Teller potential isimportant for the ground-state transition and the feature of ground-statefor a Pöschl–Teller QD and a parabolic QD is similar when R is larger.The larger the well depth, the higher the magnetic field for thesinglet-triplet transition of the ground-state of two interacting electronsin a Pöschl–Teller QD.

Ground State of a Two-Electron Quantum Dot with a GaussianConfining Potential

We investigate the ground-state properties of a two-dimensional two-electronquantum dot with a Gaussian confining potential under the influence ofperpendicular homogeneous magnetic field. Calculations are carried out by using themethod of numerical diagonalization of Hamiltonian matrix within theeffective-mass approximation. A ground-state behaviour(singlet⟶triplet state transitions) as a function of the strength ofa magnetic field has been found. It is found that the dot radius R of theGaussian potential is important for the ground-state transition and thefeature of ground-state for the Gaussian potential quantum dot (QD), and the parabolicpotential QDs are similar when R is larger. The larger the quantum dotradius, the smaller the magnetic field for the singlet-triplet transition ofthe ground-state of two interacting electrons in the Gaussian quantum dot.