Hydrogen-like Impurity Research Articles

The effects of magnetic field and hydrogen-like impurity on RbCl quantum pseudodot qubit

By using a variational method of Pekar type, we investigate the effects of the hydrogen-like impurity and magnetic field on the electron’s probability density (PD) and oscillating frequency (OF) of a RbCl quantum pseudodot qubit. Numerical results indicate that (1) the PD oscillates periodically; (2) the crest of the PD will decrease with increasing the cyclotron frequencies and the Coulombic impurity potential strength; (3) as the cyclotron frequency of the magnetic field and the strength of the Coulombic impurity potential increases, PD’s peaks will occur more frequently; (4) besides, Figs. 1b and 2b clearly show that in a single period the PD will decrease with increasing the cyclotron frequency and the Coulombic impurity potential strength when \( t > 1.8\;\text{fs} \); whereas the changing law is just the opposite when \( t < 1.8\;\text{fs} \); (5) the OF is an aggrandizing function of the strength of the Coulombic impurity potential, whereas it is a decaying one of the cyclotron frequencies of the magnetic field. The coherence of qubit is crucial to the investigations of quantum information and quantum computation, where the electron’s PD, the OF and the coherence time are the physical quantities representing the properties of coherence. Our research results fine that by changing the cyclotron frequency of the magnetic field and the strength of the Coulombic impurity potential one can adjust the electron’s PD and the OF. Open image in new window Fig. 1 The PD \( \text{Q}\left( {r,t} \right) \) versus the time \( t \) and the cyclotron frequency of the magnetic field \( \omega_{c} \) with \( \text{V}_{0} = 10.0\,\text{meV, r}_{0} = 1.0\,\text{nm, }\beta \text{ = 1.0}\,\text{meV} \cdot \text{nm} \) and \( x = y = z = 1.0\,\text{nm} \) Open image in new window Fig. 2 The PD \( \text{Q}\left( {r,t} \right) \) versus the time \( t \) and strength of the Coulombic impurity potential \( \beta \) with \( \text{V}_{0} = 10.0\,\text{meV, r}_{0} = 1.0\,\text{nm,} \, \omega_{c} \text{ = 2.0}\, \times \text{10}^{13}\,\text{Hz} \) and \( x = y = z = 1.0\,\text{nm} \)

Influence of image charge effect on impurity-related optical absorption coefficients and refractive index changes in a spherical quantum dot

We have investigated the influence of an image charge effect (ICE) on the energies of the ground and first few excited states of a hydrogen-like impurity in a spherical quantum dot (QD) in the presence of an external electric field. The oscillator strengths of transitions from the 1s-like state to excited states of 2px and 2pz symmetries are calculated as the functions of the strengths of the confinement potential and the electric field. Also, we have studied the effect of image charges on linear and third-order nonlinear optical absorption coefficients and refractive index changes (RICs). The results show that image charges lead to the decrease of energies for all the hydrogen-like states, to the significant enhancement of the oscillator strengths of transitions between the impurity states, and to comparatively large blue shifts in linear, nonlinear, and total absorption coefficients and refractive index changes. Our results indicate that the total optical characteristics can be controlled by the strength of the confinement and the electric field.

Temperature and hydrogen-like impurity effects on the excited state of the strong coupling bound polaron in a CsI quantum pseudodot**Project supported by the National Natural Science Foundation of China (Grant No. 11464033).

With hydrogen-like impurity (HLI) located in the center of CsI quantum pseudodot (QPD) and by using the variational method of Pekar type (VMPT), we investigate the first-excited state energy (FESE), excitation energy and transition frequency of the strongly-coupled bound polaron in the present paper. Temperature effects on bound polaron properties are calculated by employing the quantum statistical theory (QST). According to the present work’s numerical results, the FESE, excitation energy and transition frequency decay (amplify) with raising temperature in the regime of lower (higher) temperature. They are decreasing functions of Coulomb impurity potential strength.

Effects of hydrostatic pressure on the donor impurity in a cylindrical quantum dot with Morse confining potential

ABSTRACTThe effects of hydrostatic pressure and size quantization on the binding energies of a hydrogen-like donor impurity in cylindrical GaAs quantum dot (QD) with Morse confining potential are studied using the variational method and effective-mass approximation. In the cylindrical QD, the effect of hydrostatic pressure on the binding energy of electron has been investigated and it has been found that the application of the hydrostatic pressure leads to the blue shift. The dependence of the absorption edge on geometrical parameters of cylindrical QD is obtained. Selection rules are revealed for transitions between levels with different quantum numbers. It is shown that for the radial quantum number, transitions are allowed between the levels with the same quantum numbers, and any transitions between different levels are allowed for the principal quantum number.

Electric field and image charge effects on impurity-bound polarons in a CdS colloidal quantum dot embedded in organic matrices

An adiabatic variational approach is used to study the ground and first excited states of a hydrogen-like impurity bound polaron in a colloidal quantum dot (QD) under an external electric field, including image charge effect (ICE). The binding energy (BE) of donor impurity is calculated by taking into account the interaction of an electron with both bulk-type longitudinal optical (LO) phonons and interface optical phonons. Calculations have been carried out for CdS colloidal quantum dots embedded in thiophenol and oleic acid. Both parabolic confinement and electric field effects on the binding energy and its polaronic shift for 1s and 2s hydrogen-like states with and without ICE are investigated in detail.

Temperature Effect of Hydrogen-Like Impurity on the Ground State Energy of Strong Coupling Polaron in a RbCl Quantum Pseudodot

We study the ground state energy and the mean number of LO phonons of the strong-coupling polaron in a RbCl quantum pseudodot (QPD) with hydrogen-like impurity at the center. The variations of the ground state energy and the mean number of LO phonons with the temperature and the strength of the Coulombic impurity potential are obtained by employing the variational method of Pekar type and the quantum statistical theory (VMPTQST). Our numerical results have displayed that Open image in new window the absolute value of the ground state energy increases (decreases) when the temperature increases at lower (higher) temperature regime, Open image in new window the mean number of the LO phonons increases with increasing temperature, Open image in new window the absolute value of ground state energy and the mean number of LO phonons are increasing functions of the strength of the Coulombic impurity potential.

Energies and wave functions of an off-centre donor in hemispherical quantum dot: Two-dimensional finite difference approach and ritz variational principle

Eigenvalues equation solutions of a hydrogen-like donor impurity, confined in a hemispherical quantum dot deposited on a wetting layer and capped by an insulating matrix, are determined in the framework of the effective mass approximation. Conduction band alignments at interfaces between quantum dot and surrounding materials are described by infinite height barriers. Ground and excited states energies and wave functions are determined analytically and via one-dimensional finite difference approach in case of an on-center donor. Donor impurity is then moved from center to pole of hemispherical quantum dot and eigenvalues equation is solved via Ritz variational principle, using a trial wave function where Coulomb attraction between electron and ionized donor is taken into account, and by two-dimensional finite difference approach. Numerical codes developed enable access to variations of donor total energy, binding energy, Coulomb correlation parameter, spatial extension and radial probability density with respect to hemisphere radius and impurity position inside the quantum dot.

Effects of Temperature and Hydrogen-Like Impurity on the Vibrational Frequency of the Polaron in RbCl Parabolic Quantum Dots

The properties of an electron strongly coupled to longitudinal optical (LO) phonon in RbCl parabolic quantum dot (PQD) with a hydrogen-like impurity at the center were investigated at a finite temperature. We have obtained the vibrational frequency of a strong-coupling polaron in RbCl PQD by using linear combination operator method. We then calculate the effects of temperature, the Coulombic impurity potential and the effective confinement strength on the vibrational frequency by using unitary transformation and the quantum statistics theory methods. The influences of the temperature, the Coulombic impurity potential and the effective confinement strength on the ground state energy and the ground state binding energy are also analyzed. The strengths of these quantities increase with raising temperature. The vibrational frequency is an increasing function of the Coulombic impurity potential and the effective confinement strength. The ground state energy is an increasing function of the effective confinement strength, whereas it is a decreasing one of the Coulombic impurity potential. The ground state binding energy is an increasing function of the Coulombic impurity potential, whereas it is a decayed one of the effective confinement strength.

Effects of temperature and hydrogen-like impurity on the coherence time of RbCl parabolic quantum dot qubit

By using a variational method of Pekar type, the Fermi Golden Rule and the quantum statistics theory (VMPTFGRQST), we investigate the effects of the hydrogen-like impurity and temperature on the coherence time of a parabolic quantum dot (PQD) qubit with a hydrogen-like impurity at the center. We then derive the ground and the first excited states' (GFES) eigenenergies and the eigenfunctions in a PQD. A single qubit can be realized in this two-level quantum system. The phonon spontaneous emission causes the decoherence of the qubit. The numerical results show that the coherence time is a decreasing function of the temperature, the strength of the Coulombic impurity potential (CIP) and the polaron radius (PR).

Effect of impurities on the properties of bound polarons in an asymmetric Gaussian confinement potential quantum well

The effects of hydrogen-like impurities and the range of the asymmetrical Gaussian confinement potential (AGCP) on the vibrational frequency, the ground-state energy and the ground-state binding energy of weak-coupling bound polarons in an asymmetrical Gaussian confinement potential quantum well (AGCPQW) are studied by using the linear combination operator and the unitary transformation methods. Numerical results demonstrate that the vibrational frequency, and the absolute values of the ground-state energy and the ground-state binding energy will increase with increasing strength of the Coulombic impurity potential. The vibrational frequency is a decreasing function of the range of the AGCP in the growth direction of the AGCPQW whereas the absolute values of the ground state energy and the ground state binding energy are increasing functions.

The effect of hydrogen-like impurity on RbCl asymmetric quantum dot qubit

We study the eigenenergies and eigenfunctions of the ground and the first excited states of an electron, which is strongly coupled to longintudinal-optical phonon in an asymmetric quantum dot with a hydrogen-like impurity by using variational method of Pekar type. A single qubit can be realized in this two-level quantum system. The electron probability density oscillates in the asymmetric quantum dot with a certain period of T 0 = 10.958 fs when the electron is in the superposition state of the ground and the first excited states. Moreover, due to the presence of the different harmonic potentials, the dependence way of the probability density of the electron on the coordinate of z is different from that on the coordinates of x and y. It is found that the oscillating period increases with decreasing Coulombic impurity potential and the polaron radius.

Coulomb Impurity Potential RbCl Quantum Pseudodot Qubit

By employing a variational method of Pekar type, we study the eigenenergies and the corresponding eigenfunctions of the ground and the first-excited states of an electron strongly coupled to electron-LO in a RbCl quantum pseudodot (QPD) with a hydrogen-like impurity at the center. This QPD system may be used as a two-level quantum qubit. The expressions of electron’s probability density versus time and the coordinates, and the oscillating period versus the Coulombic impurity potential and the polaron radius have been derived. The investigated results indicate ① that the probability density of the electron oscillates in the QPD with a certain oscillating period of \(T_0 =7.817\mathrm{fs}\), ② that due to the presence of the asymmetrical potential in the z direction of the RbCl QPD, the electron probability density shows double-peak configuration, whereas there is only one peak if the confinement is a two-dimensional symmetric structure in the xy plane of the QPD, ③ that the oscillation period is a decreasing function of the Coulombic impurity potential, whereas it is an increasing one of the polaron radius.

Impurity Effect of Asymmetric Gaussian Potential Quantum Well Qubit

On the condition of strong electron-LO phonon coupling in an asymmetrical Gaussian potential quantum well (AGPQW) with a hydrogen-like impurity at the origin of the coordinate, we calculate the eigenenergies and the eigenfunctions of the ground and the first excited states (GFES) by using a variational method of Pekar type. A single qubit can be realized in this two-level quantum system. We calculate the time evolution and the change of the coordinate of the electron’s probability density. When the electron is in the superposition state of the GFES, the electron’s probability density oscillates in the AGPQW with a certain period \(T_0 =20.716\) fs. It turns out that due to the presence of the asymmetrical Gaussian potential in the growth direction of the QW, the electron probability density shows a single peak configuration in the coordinate range of \(z>0\), whereas it equals to zero in the range of \(z 0.24\) nm. It has a minimum when \(R=0.24\) nm.

Hydrogen-Like Impurities in novel potential barriers: Theoretical development

A systematic theoretical study of the binding energy of the ground state of a hydrogenic off-axis donor in a cylindrical quantum wire containing two quantum wells in a section of the tube layer is calculated in the presence of a uniform magnetic field applied parallel. We express the wave function as a product of free electron wave functions and an envelope function that depends only on the electronion separation. By using the variational principle we derive a differential equation for the envelope function, which we solve numerically.

Conductivity of granular structures based on wide band gap ZnO semiconductors

The experimental studies of granular structures based on ZnO films that are randomly arranged small areas, granules or crystallites, which have different conductivity and are in direct contact, were carried out. The influence of donor complex, consisting of an oxygen vacancy and interstitial zinc atom, the donor impurity Ga, and acceptor impurity Li on the structural conductivity of the films is considered. The specifics of the conductivity in lightly doped wide band gap semiconductors with hydrogen-like impurities are investigated. The influence of grain size and crystallite structure on the conductivity kinetics is discussed. A new method for current density determination as a function of the coordinates for thin conductive films is developed. The experimental data are interpreted on the basis of the percolation theory.

Impurity binding energies in quantum dots with parabolic confinement

We present an effective numerical procedure to calculate the binding energies and wave functions of the hydrogen-like impurity states in a quantum dot (QD) with parabolic confinement. The unknown wave function was expressed as an expansion over one-dimensional harmonic oscillator states, which describes the electron's movement along the defined z-axis. Green's function technique used to obtain the solution of Schredinger equation for electronic states in a transverse plane. Binding energy of impurity states is defined as poles of the wave function. The dependences of the binding energy on the position of an impurity, the size of the QD and the magnetic field strength are presented and discussed.

Spin magnetic moment current of impurity electron in a spherical quantum dot

Current of the spin magnetic moment of an electron coupled with hydrogen-like impurity, placed in the center of a spherical quantum dot, is studied. Confinement potential of the quantum dot is approximated by rectangular infinitely high walls. S-states of electron for both positive and negative values of total energy are considered. Dependences of spin magnetic moment current of electron on the radial variable for different values of dot radius are obtained. It is shown that for quantum dots with large radius, due to weakening of size-quantization effect, corresponding curves approach each other.

The influence of absolute minimum (l1–δ1) type inversion on the ionization energy of the ground state of shallow donors in n-Ge single crystals

Based on the Ritz variational method and perturbation theory, ionization energy of shallow donors for the cases of L 1 and Δ 1 model of the conduction band of germanium single crystals was calculated. It was shown that the absolute minimum (L 1 –Δ 1 ) type inversion in n-Ge leads to a significant increase in ionization energy of shallow donors. Using the Ritz variational method allows more accurately describe the experimental results with respect to the calculation based on perturbation theory. Comparison of theoretical calculations with experimental data shows that the hydrogenlike impurity model is approximate and may be used only for Sb impurity in germanium. For impurities, such as, P and As chemical shift, that is personality of the ion field potential of each impurity, which is not Coulomb must be considered.

Ground state energy and wave function of an off-centre donor in spherical core/shell nanostructures: Dielectric mismatch and impurity position effects

Ground state energy and wave function of a hydrogen-like off-centre donor impurity, confined anywhere in a ZnS/CdSe spherical core/shell nanostructure are determined in the framework of the envelope function approximation. Conduction band-edge alignment between core and shell of nanostructure is described by a finite height barrier. Dielectric constant mismatch at the surface where core and shell materials meet is taken into account. Electron effective mass mismatch at the inner surface between core and shell is considered. A trial wave function where coulomb attraction between electron and off-centre ionized donor is used to calculate ground state energy via the Ritz variational principle. The numerical approach developed enables access to the dependence of binding energy, coulomb correlation parameter, spatial extension and radial probability density with respect to core radius, shell radius and impurity position inside ZnS/CdSe core/shell nanostructure.

Influences of temperature and impurity on excited state of bound polaron in the parabolic quantum dots

On the condition of strong electron-LO phonon coupling in parabolic quantum dot (QD), the first excited state energy, the excitation energy and the transition frequency between the first excited and the ground states of the bound polaron are calculated by using the linear combination operator and the unitary transformation methods. The variation of the above quantities with the temperature, the Coulombic impurity potential and the QD confinement strength are studied in detail. We find that (1) These physical quantities will increase with increasing temperature. (2) They are increasing functions of the confinement strength due to the existence of the Coulombic impurity potential between the electron and the hydrogen-like impurity. (3) We obtain three ways of tuning them via controlling the temperature, the Coulombic impurity potential and the confinement strength.