GaAs Parabolic Quantum Dot Research Articles

The Analytical Effects of a Hydrostatic Pressure on the Ground State Energy of GaAs Quantum Dot at Low-Temperature: Algebraic Method

This analytical study focused on discussing the collective effects of hydrostatic pressure and temperature on the ground state energy for two electrons trapped in GaAs parabolic quantum dot in the presence of a magnetic field using the effective mass approximation. The electronic interaction was approximated by the Johnson-Payne potential model, where its parameters were carefully chosen to match the Coulomb interaction. It is noted that the ground state energy decreases with an increment in pressure while it increases linearly slightly with increasing temperature. As is customary, it was found that ground state energy decreases with increasing dot size and reach its bulk value as the dot becomes wider. Among the most prominent notes related to this study were as follows: (i) The largest contribution to the total ground state energy is caused by the relative motion since the effect of pressure on this part is more pronounced than the part of the center of mass that often does not feel the presence of pressure. (ii) Ground state energy shows temperature insensitivity while pressure exerts a tangible effect on the ground state energy in the strong magnetic field confinement. (iii) The effect of temperature on the ground state energy is always the opposite of the pressure effect. (iv) With regard to the increase in pressure, it was found that it reduces the electron separation (r), therefore the ground state energy decreases in the presence of the harmonic interaction that is directly proportional to the square of r, but compared to previous works mentioned in the literature, energy showed increased behavior because Coulomb's interaction is inversely proportional to the electron separation. (v) In the region of weak confinement (R>aB*), the effect of pressure on ground state energy becomes neglected, while this effect becomes noticeable in the region of ??strong confinement (R<aB*). Keywords: Quantum Dots, Hydrostatic Pressure, Harmonic e-e Interaction.

The Analytical Effects of a Hydrostatic Pressure on the Ground State Energy of GaAs Quantum Dot at Low-Temperature: Algebraic Method

This analytical study focused on discussing the collective effects of hydrostatic pressure and temperature on the ground state energy for two electrons trapped in GaAs parabolic quantum dot in the presence of a magnetic field using the effective mass approximation. The electronic interaction was approximated by the Johnson--Payne potential model, where its parameters were carefully chosen to match the Coulomb interaction. It is noted that the ground state energy decreases with an increment in pressure while it increases linearly slightly with increasing temperature. As is customary, it was found that ground state energy decreases with increasing dot size and reach its bulk value as the dot becomes wider. Among the most prominent notes related to this study were as follows: (i) The largest contribution to the total ground state energy is caused by the relative motion since the effect of pressure on this part is more pronounced than the part of the center of mass that often does not feel the presence of pressure. (ii) Ground state energy shows temperature insensitivity while pressure exerts a tangible effect on the ground state energy in the strong magnetic field confinement. (iii) The effect of temperature on the ground state energy is always the opposite of the pressure effect. (iv) With regard to the increase in pressure, it was found that it reduces the electron separation (r), therefore the ground state energy decreases in the presence of the harmonic interaction that is directly proportional to the square of r, but compared to previous works mentioned in the literature, energy showed increased behavior because Coulomb's interaction is inversely proportional to the electron separation. (v) In the region of weak confinement (R>a_B*), the effect of pressure on ground state energy becomes neglected, while this effect becomes noticeable in the region of strong confinement (R<a_B*). Keywords: Quantum Dots, Hydrostatic Pressure, Harmonic e-e Interaction.

Exact calculations of the thermal properties of two-electron GaAs quantum dots with inverse-square interactions

In this study, we theoretically scrutinize the effect of the inverse-square interaction on the thermal properties of two electrons trapped in a parabolic GaAs quantum dot. The analytical energy spectrum was used to calculate the thermal properties of the system using the canonical ensemble formalism. It was found that the thermal energy increased with the increase in temperature, while it remained almost constant for sufficiently low temperatures; it was also demonstrated that the inverse-square interaction increased the thermal mean energy. Moreover, the heat capacity increased sharply within a low-temperature window and saturated to the value of 2kB in the high-temperature limit. As expected, entropy increased linearly with increasing temperature. It was also shown that both entropy and heat capacity decreased rapidly when the confinement strength increased (or the dot size decreased) in the low-temperature limit, regardless of the influence of the interaction between the electrons. We also show that the number of allowed states of the system decreased as the interaction strength increased (Z(λ = 0) > Z(λ ≠ 0)). Finally, the stability of the system was investigated through F–T curves. The three-dimensional surface for the temperature-dependent mean energy and heat capacity was also plotted. It should be noted that, for the thermal mean energy, partition function, and Helmholtz free energy, the normal physical behavior of the two-oscillator system with Fermi statistics is recovered for λ → 0. However, heat capacity and entropy show exact two-fermion oscillator system behavior. The most impressive result found in this work is that the inverse-square interaction does not affect the heat capacity and entropy at all despite its noticeable effects on the thermal mean energy. This, in turn, facilitates theoretical studies related to finding the distinctive parameters of quantum dots without going into the heavy calculations resulting from the effects of interactions.

Solvable Model of the Thermal Persistent Current at Low Temperatures of Two-Electron Parabolic GaAs Quantum Dot

Solvable Model of the Thermal Persistent Current at Low Temperatures of Two-Electron Parabolic GaAs Quantum Dot

Rashba spin-orbit interaction effects on thermal and magnetic properties of parabolic GaAs quantum dot in the presence of donor impurity under external electric and magnetic fields

Based on the effective mass approximation, the magnetic and thermal properties of parabolic GaAs quantum dot have been investigated in the presence of Rashba Spin-Orbit interaction (RSOI), donor impurity and applied magnetic and electric fields. The exact diagonalization method has been used to solve the Hamiltonian of an electron confined in a quantum dot (QD) and obtain the eigenenergies and the binding energy of the donor impurity as a function of various QD physical parameters. We have shown the dependence of the average statistical energy, magnetization, magnetic susceptibility and heat capacity of the donor impurity in the QD on: the Rashba interaction parameter, the magnetic and electric fields, confining frequency, and temperature. The results reveal that these parameters can tune the magnetic properties of the GaAs quantum dot and flip the sign of magnetic susceptibility from negative (diamagnetic) to positive (paramagnetic) type material.

Analytical Ground-State of an Exciton Trapped in a Circular Parabolic Quantum Dot in the Presence of a Magnetic Field

The quasi-exact properties of an exciton are investigated theoretically in the presence of an external magnetic field using the effective-mass approach in GaAs parabolic quantum dot. The energy spectrum is obtained analytically as a function of the dot radius, interaction strength and magnetic field. It is established that, a steady bound state of an exciton in the ground state exists under the effect of a strong magnetic field; also I noticed that the exciton binding energy decreases by increasing both the radius of the dot and the magnetic field strength and the reduction becomes pronounced for larger dots. As expected, it has been found that the exciton total energy decreases with increasing the size of the dot and it enhances by increasing the magnetic field. It appears that the exciton total energy strongly depends on the magnetic field for dots with big size. The magnetic field effect on the exciton size also has been studied. It is shown that the increase in the magnetic field leads to a reduction in the exciton size; due to magnetic field confinement, while the size of an exciton reach its bulk limit as the dot size increases. Moreover, it is shown that, if the dot radius is sufficiently large the oscillator strength saturates and it becomes insensitive to the magnetic field while the increase in the magnetic field gradually weakened the oscillator strength. I have calculated the ground-state distribution for both the electron and the hole. It is found that the localization of the electron/hole increases in the presence of a magnetic field. Moreover, the ground-state optical-absorption intensity is investigated. Finally, the dependence of the lowest five states of an exciton on both the dot radius and the magnetic field are discussed.

The magnetic properties of GaAs parabolic quantum dot in the presence of donor impurity, magnetic and electric fields

The magnetization and the magnetic susceptibility quantities of a single electron moving in a two-dimensional (2D) parabolic quantum dot are studied under the influence of external uniform electric and magnetic fields, in the presence of a donor impurity. The Hamiltonian was solved using shifted 1/N expansion method within the effective mass approximation. The results have been displayed as a function of physical parameters: confinement strength ω0, magnetic field strength ωc, temperature T and electric field strength F.

A Comprehensive Study of the Thermal and Magnetic Properties of Two-Harmonically Interacting Electrons Confined in a Parabolic GaAs Quantum Dot in a Magnetic Field

The thermal and magnetic properties of a parabolic GaAs quantum dot for two-Harmonically interacting electrons when it exposed to an external magnetic field, taking into account the spin-Zeeman energy are investigated using the canonical ensemble approach. The effect of spin on these properties is also investigated. With the possibility of a basic and physically sensible model of electron-electron interaction, the issue is precisely soluble. We found a Schottky-like anomaly in the heat capacity at low temperature, while it saturates to the 4kB value as the temperature increases. Also it is noted that entropy enhances with temperature as expected. However as a function of a magnetic field, a peak structure is observed in heat capacity at very low values of magnetic field, while it saturates to the 2kB value as magnetic field increases. Also we noticed that these peaks are not presented in the spinless case. Moreover magnetic field does not show a significant effect on the entropy at high temperatures, but at relatively lower temperatures, the entropy shows a monotonic increase with magnetic field. As a function of the Lande g* factor, we found a local minima and a double peak-structure in the susceptibility and in the heat capacity at g*=0. It is demonstrated that the favored state for both magnetization and susceptibility is the diamagnetic state. The significant effect of the spin on the magnetic properties of quantum dot is seen at low values of temperature and magnetic field. Moreover, our results showed a very good agreement with reported previous works.

Magnetic properties of GaAs parabolic quantum dot in the presence of donor impurity under the influence of external tilted electric and magnetic fields

The dependence of the magnetization and magnetic susceptibility of donor impurity in parabolic GaAs (Gallium Arsenide) quantum dot has been investigated, at finite temperature under the influence of external tilted electric and magnetic fields. Based on the effective mass approximation, the Hamiltonian of an electron confined in a parabolic quantum dot in the presence of donor impurity which is presented in electric and magnetic fields has been solved by employing the numerical diagonalization method of the Hamiltonian matrix. All the energy matrix elements have been obtained in analytical form. We have shown the variations of the statistical energy and binding energy of donor impurity with the electric and magnetic field strengths and tilt electric field angle. The computed results show that the electrical field can tune the magnetic properties of the QD GaAs medium by flipping the sign of its magnetic susceptibility from diamagnetic (χ < 0) to paramagnetic (χ > 0).

THE EFFECTS OF PRESSURE AND TEMPERATURE ON THE MAGNETIZATION OF A PARABOLIC QUANTUM DOT IN A MAGNETIC FIELD

In this work , we present a theoretical study of the magnetization of two-electron GaAs parabolic quantum dot (QD) under the combined effects of external pressure, temperature and magnetic field. First, we obtain the eigenenergies by solving the two electron quantum dot Hamiltonian using the exact diagonalization method. The obtained results show that the energy levels of the quantum dot depend strongly on the pressure and temperature. Next, we investigate the dependence of magnetization of a quantum dot as a function of external pressure, temperature, confining frequency and magnetic field. The singlet-triplet transitions in the ground state of the quantum dot spectra and the corresponding jumps in the magnetization curves have been shown .The comparison shows that our results are in very good agreement with the reported works. PACS: 73.21.La, 65.80.-g Keywords: Pressure; temperature; magnetization; quantum dot; magnetic field; exact diagonalization.

Heat capacity and entropy of two electrons quantum dot in a magnetic field with parabolic interaction

The thermodynamic properties of two electrons in two dimensional parabolic GaAs quantum dot are studied where both the magnetic field and the e–e interaction are fully considered. The e–e interaction has been treated by a model potential which makes the Hamiltonian exactly solvable. The energy spectrum is used to calculate the canonical partition function, and then we obtain the thermodynamic properties; mean energy, heat capacity and entropy as a function of temperature (T) and magnetic field (B).A steep transition from zero to 4kB is observed in the heat capacity as a function of temperature for small values of magnetic field and saturates within a small temperature range, also the heat capacity has a peak-like structure at low temperature, while for high magnetic field heat capacity develops a shoulder at 2kB then it approaches the saturation value with further increase in temperature. The entropy increases with increasing temperature, but at higher temperature, it remains almost independent of the magnetic field. It is shown that, at low magnetic field values, the effect of magnetic field on heat capacity is tangible and it attains a constant value with further increase in magnetic field. Entropy is almost linearly proportional with increasing magnetic field strength.

The effects of pressure and temperature on the exchange energy of a parabolic quantum dot under a magnetic field

The combined effects of pressure and temperature on the energy levels of a parabolic GaAs quantum dot under a magnetic field have been studied. The exact diagonalization method was used to solve the two-electron quantum dot Hamiltonian and to obtain the eigenenergies. In addition, we investigated the effects of pressure and temperature on the singlet-triplet exchange energy (J=ET−Es) of the quantum dot as a function of a magnetic field. The magnetic field-parabolic confinement (ωc−ω0) phase diagram of the quantum dot was calculated. The comparisons show that our results are in very good agreement with the previously published works.

The effects of pressure and temperature on the energy levels of a parabolic two-electron quantum dot in a magnetic field

In the present work, we have calculated the energy levels of GaAs parabolic quantum dot under the combined effects of external pressure, temperature and magnetic field. The eigenenergies have been obtained by solving the two electron quantum dot Hamiltonian using the exact diagonalization method. The obtained results show that the energy levels of the quantum dot depend strongly on the pressure and temperature. We have found that the energy levels enhance as the pressure increases for fixed temperature and magnetic field while the quantum dot energy levels decrease as the temperature increases for fixed pressure and magnetic field. The comparisons show that our results are in very good agreement with the reported works.

The Effects of Pressure and Temperature on the Magnetic Susceptibility of Semiconductor Quantum Dot in A Magnetic Field

In this work, we present a theoretical study of the magnetic susceptibility (x of two-electron GaAs parabolic quantum dot (QD) under the combined effects of external pressure, temperature and magnetic field. We used the exact diagonalization method to obtain the eigenenergies by solving the two electron quantum dot Hamiltonian taking into account the dependence of the effective mass and dielectric constant on the hydrostatic pressure and temperature. The pressure and temperature show significant effects on the calculated QD spectra. Next, we investigate the behavior of the magnetization of a quantum dot as a function of external pressure, temperature, confining frequency and magnetic field. The singlet-triplet transitions in the ground state of the quantum dot spectra and the corresponding jumps in the magnetic susceptibility spectra have been shown. The comparison shows that our results are in very good agreement with the reported works.

Effect of Rashba and Dresselhaus interactions on the energy spectrum, chemical potential, addition energy and spin-splitting in a many-electron parabolic GaAs quantum dot in a magnetic field

The effect of electron–electron interaction and the Rashba and Dresselhaus spin–orbit interactions on the electronic properties of a many-electron system in a parabolically confined quantum dot placed in an external magnetic field is studied. With a simple and physically reasonable model potential for electron–electron interaction term, the problem is solved exactly to second-order in the spin–orbit coupling constants to obtain the energy spectrum, the chemical potential, addition energy and the spin-splitting energy.

Effect of electron–electron interaction on the magnetic moment and susceptibility of a parabolic GaAs quantum dot

The problem of a parabolically confined two-dimensional semiconductor GaAs quantum dot with two interacting electrons in the presence of an external magnetic field and the spin-Zeeman interaction is studied using a method of numerical diagonalization. The energy spectrum is calculated as a function of the magnetic field. The magnetic moment (M) and the magnetic susceptibility (χ) show zero temperature diamagnetic peaks due to the exchange induced singlet–triplet transitions. The position and the number of these peaks depend both on the confinement strength of the quantum dot and the strength of the electron–electron interaction (β).

Magnetization of GaAs Parabolic Quantum Dot by Variation Method

Magnetization of GaAs Parabolic Quantum Dot by Variation Method

Optical Absorptions of Impurity-Bound Polaron in a GaAs Quantum Dot with Parabolic Potential

The linear and nonlinear optical properties considering polaron and Coulomb impurity effect in a GaAs parabolic quantum dot are investigated theoretically. Calculations have been performed by using the compact density-matrix approach and the Lee-Low-Pines-Huybrecht variational technique for all electron–LO–phonon coupling strengths. The dependence of the optical absorption coefficients on the incident photon energy, the Coulomb potential and incident optical intensity is also studied.

Temperature Dependence of Polaronic Correction to the Ground State Energy in a GaAs Parabolic Quantum Dot

Within the framework of second-order Rayleigh-Schrodinger perturbation theory (RSPT), the polaronic corrections to the ground state (GS) energy of an electron in both two-dimensional (2D) and three-dimensional (3D) parabolic quantum dots (QDs) are presented at finite temperature. We apply our calculations to GaAs. It is found that the polaronic corrections to the GS energy of an electron in both 2D and 3D QDs increase with temperature increasing and size of the QD decreasing. Furthermore, this trend is much more pronounced with dimensionality decreasing.

Thermodynamic properties of two-dimensional few-electrons quantum dot using the static fluctuation approximation (SFA)

The two-dimensional GaAs parabolic quantum dot (QD) is investigated in the static fluctuation approximation (SFA) where both the magnetic field and the electron–electron interaction are fully taken into account. The thermodynamic properties of the system are computed as functions of the temperature and magnetic field for different numbers of electrons ( N). It is noted that the mean internal energy increases with increasing number of electrons and magnetic field. This increase is not smooth, and a sudden change in slope is observed at a certain value of magnetic field for N≥4. It is found that the magnetization has sharp jumps for N≥4; for N≤3 a smooth monotonic diamagnetism is exhibited. A sharp peak is observed in the specific heat when the magnetic field is increased. It is found that the lowest-state transitions occur at a critical value of magnetic field. These transitions appear in the mean internal energy and magnetization.