Gaussian Confinement Research Articles

Effect of magnetic and electric field on the ground state properties of weak coupling piezoelectric polaron in a quantum well with asymmetric Gaussian confinement

In this study, we employed the linear combination operation and a modified Lee-Low-Pines unitary transformation method to explore the ground state properties of an interacting electron coupled with piezo-acoustic phonons within a quantum well featuring asymmetric Gaussian confinement potential well under the influence of magnetic and electric fields. We calculated various properties, including the ground state energy, ground state binding energy, magnetic moment, magnetic susceptibility, and polarizability of the weakly coupled piezoelectric polaron. The effects of the magnetic and electric fields, electron-phonon weak coupling strength, Debye cut-off wavenumber, and confinement depth and range on these properties were thoroughly analyzed. Our findings reveal that the ground state energy decreases with increasing the Debye wavenumber, confinement range, and electron-phonon weak coupling strength. In contrast, the ground state binding energy shows the opposite trend, increasing with these parameters. Furthermore, the magnetic and electric fields, confinement depth and range, electron-phonon coupling strength, and Debye wavenumber are critical factors that significantly impact the magnetic and optical properties of the piezoelectric polaron.

Magnetic field modulation of polaron relaxation coherence effects in III-V semiconductor Gaussian quantum wells

We have theoretically investigated the effects of the cyclotron frequency of magnetic field, the initial depth and the range of the asymmetrical Gaussian confinement potential on the vibrational frequency, ground state energy, excited state energy and coherence time of polaron in III-V semiconductors by using a linear combination operator and unitary transformations methods. Through numerical calculations, we find some interesting phenomena that the polaron decreases the energy level and releases the energy of a phonon to jump. From the point of view of the energy level of the polaron, which is αℏωLO energy lower than that of the electron, and the transition of the polaron to the ground state will have a change in lattice position, and the lattice relaxation phenomenon will appear. The theoretical study of the quantum coherence effect of polaron energy levels will provide guidance for the development of optoelectronic devices and the transmission of quantum information.

Spin-orbit interaction effects on electronic, magnetic, and optical properties of [formula omitted]- center in a quantum dot with Gaussian confinement

In this paper, we study the binding energy, transition energy, and oscillator strength of a D0 impurity positioned at the center of a two-dimensional quantum dot. The QD is subject to a Gaussian confining potential, magnetic field, Rashba, and Dresselhaus spin-orbit interactions (SOI). The ground state and first exited state energies, and corresponding binding energies are calculated. Using the variational method with simple wave functions, transition energy, magnetic moment, and susceptibilities are obtained as a function of QD parameters, magnetic field, and SOI coupling strengths. The energies and binding energies increase with Dresselhaus SOI strength but decrease with Rashba SOI strength in a magnetic field. The magnetic moment and susceptibility of both states of a (D0) impurity show diamagnetic behaviour with both SOI strengths. Finally, we studied oscillator strength and compared the available literature, which did not consider all these effects.

Polaron level spectrum in double-potential quantum wells

The description of macroscopic systems of quasi-particles is a bright spot in quantum physics, providing an accurate description of the physics development. The current study presents a theoretical study of the energy level spectrum of weakly coupled polarons in polar crystals (GaAs, PbSe, PbTe) in double potential quantum wells (parabolic and asymmetric Gaussian confinement potentials) using the linear combination operator and two simple unitary transformations. Rigorous electron-phonon coupling interaction results are obtained under the weak coupling limitation. The results indicate that the polaron energy is relatively lower than that of the electron and the coupling strength affects the energy difference between polaron and electron. The influence of quantum wells’ confinement potential on energy is also discussed. These findings provide the possibility for potential application of polaron.

Asymmetrical Gaussian Potential Effects on Strongly Coupled Magnetopolaron Properties in Triangular Confinement Potential Quantum Wells

In this research, the existence of an asymmetrical Gaussian confinement potential (AGCP) along the quantum well (QW) growth direction and of a parabolic potential perpendicular to the polar coordinate direction were considered. The magnetic field and temperature properties of the longitudinal optical (LO)-phonon mean number, ground-state energy (GSE), ground-state binding energy (GSBE) and vibrational frequency (VF) of strongly coupled magnetopolarons in triangular confinement potential QWs (TCPQWs) were investigated according to the quantum statistical theory as well as the linear combination operator and unitary transformation methods. We obtained analytical expressions for the GSE, GSBE, VF and LO-phonon mean number as functions of the applied magnetic field, temperature, AGCP barrier height, AGCP range, polar coordinate system’s polar angle and polar coordinate system’s confinement strength. It was demonstrated by the calculated numerical results that the GSE, GSBE, VF and LO-phonon mean number varied with the related physical quantities. The obtained theoretical results are expected to provide a reference for future research on polarons.

Few electron systems confined in Gaussian potential wells and connection to Hooke atoms

AbstractIn this work, we have computed and implemented one‐body integrals concerning Gaussian confinement potentials over Gaussian basis functions. Then, we have set an equivalence between Gaussian and Hooke atoms and we have observed that, according to singlet and triplet state energies, both systems are equivalent for large confinement depth for a series of even number of electrons n = 2, 4, 6, 8 and 10. Unlike with harmonic potentials, Gaussian confinement potentials are dissociative for small enough depth parameter; this feature is crucial in order to model phenomena such as ionization. In this case, in addition to corresponding Taylor‐series expansions, the first diagonal and sub‐diagonal Padé approximant were also obtained, useful to compute the upper and lower limits for the dissociation depth. Hence, this method introduces new advantages compared to others.

Electromagnetic field effect on weak-coupling piezoelectric polaron in an asymmetrical Gaussian confinement potential quantum well

The properties of an electron weakly coupled to piezo-acoustic phonon in asymmetrical Gaussian confinement potential quantum well (AGCPQW) subject to external electric field (EF) and magnetic field (MF) has been investigated using the Lee-Low-Pines unitary transformation and linear combination operation methods. We have obtained the ground state energy (GSE) and the ground state binding energy (GSBE) of piezoelectric polaron. The effects of the EF, the MF, the range of the asymmetrical Gaussian confinement potential (RAGCP), Debye cut-off wavenumber (DCOW) and the electron–phonon coupling strength on the GSE and the GSBE are also analyzed. It is found that the GSE is an increasing function of the EF and the cyclotron frequency (CF), whereas it is a decreasing one of the RAGCP, the DCOW and electron–phonon coupling strength. The GSBE is an increasing function of the DCOW and the electron–phonon coupling strength. It is also an aggrandizing function with decreasing of the RAGCP, whereas it is a decayed one of the EF and CF. It is shown that the EF, the RAGCP, the MF, the DCOW and electron–phonon coupling strength are important factors that have great influence on the properties of the piezoelectric polaron in AGCPQW.

Electronic and optical properties of a $$D_2^+$$ complex in two-dimensional quantum dots with Gaussian confinement potential

Electronic and optical properties of a $$D_2^+$$ complex in two-dimensional quantum dots with Gaussian confinement potential

Influence of the LO Phonon Effect on the Transition Rate and the Spontaneous Emission Rate in Donor-Center Quantum Dot with Spherical Gaussian Confinement Potential

Influence of the LO Phonon Effect on the Transition Rate and the Spontaneous Emission Rate in Donor-Center Quantum Dot with Spherical Gaussian Confinement Potential

The influences of parabolic potential and magnetism on strongly coupled polaron characteristics within asymmetric Gaussian quantum wells

In this research, the effects of magnetism and parabolic potential on strongly coupled polaron characteristics within asymmetric Gaussian quantum wells (AGQWs) were investigated. To do so, the following six parameters were studied, temperature, AGQW barrier height, Gaussian confinement potential (GCP) width, confinement strengths along the directions of [Formula: see text] and [Formula: see text], as well as magnetic field cyclotron frequency. The relationships among frequency oscillation, AGQW parameters and polaron ground state energy in RbCl crystal were studied based on linear combination operator and Lee–Low–Pines unitary transformation. It was concluded that ground state energy absolute value was decreased by increasing GCP width and temperature, and increased with the increase of confinement strength along [Formula: see text] and [Formula: see text] directions, cyclotron frequency of magnetic field and barrier height of AGQW. It was also found that vibrational frequency was increased by enhancing confinement strengths along the directions of [Formula: see text] and [Formula: see text], magnetic field cyclotron frequencies, barrier height AGQW and temperature and decreased with the increase of GCP width.

The effect of parabolic potential on ground state energy and vibration frequency of magnetopolaron in asymmetric Gaussian potential quantum wells

Anisotropy parabolic potential (APP) effects on ground state (GS) energy [Formula: see text] and the vibration frequency (VF) [Formula: see text] of weak-coupled magnetopolaron (MP) in asymmetric Gaussian quantum wells (AGQWs) were investigated using the linear combination operator and unitary transformation method. The obtained results showed that [Formula: see text] and [Formula: see text] were increased by increasing the barrier height [Formula: see text] of AGQWs as well as transverse and longitudinal confined strengths [Formula: see text] and [Formula: see text] of APP and decreased with increase in the asymmetric Gaussian confinement potential (AGCP) range [Formula: see text] and transverse and longitudinal effective confined lengths [Formula: see text] and [Formula: see text] of APP. Thus, the GS energy and VF of MP could be changed by adjusting the confinement parameters of the APP and AGCP. The study of quantum wells’ semiconductor materials has broad potential applications in semiconductor lasers, optoelectronic devices and quantum information.

The Energy Spectra and Heat Capacity of GaAs Gaussian Quantum Dot in an External Magnetic Field

In this paper, a theoretical study of the energy spectra and the heat capacity of one electron quantum dot with Gaussian Confinement in an external magnetic field are presented. Using the exact diagonalization technique, the Hamiltonian of the Gaussian Quantum Dot (GQD) including the electron spin is solved. All the elements in the energy matrix are found in closed form. The eigenenergies of the electron were displayed as a function of magnetic field, Gaussian confinement potential depth and quantum dot size. Explanations to the behavior of the quantum dot heat capacity curve, as a function of external applied magnetic field and temperature, are presented.

Effect of Magnetic Field on the Energy Spectrum, Binding Energy and Magnetic Susceptibility of an Impurity in a 2D Gaussian Quantum Dot

The problem of on-center acceptor and donor impurities in a two-dimensional (2D) GaAs quantum dot in the presence of an externally applied magnetic field now modelled with Gaussian confinement and examined with the exact matrix diagonalization technic. Magnetic moment, susceptibilities are calculated after obtaining the energy spectrum of these impurities. I have compared the results of these impurities with parabolic confinement. I found an interesting phenomenon in the attendance of spin-Zeeman term, the ground state magnetic (GSM) moment and the GSM susceptibility of one electron system, donor and acceptor impurity systems demonstrate zero-temperature diamagnetic spikes owing to transitions in the orbital angular momentum (OAM). The number of spikes and the position of these spikes depend on the radius of the quantum dot and depth of the potential also. The low-lying binding energy levels have been studied by computing state away from the energies of donor impurity and an electron.

Effect of the anisotropic parabolic potential on the polaron’s properties in asymmetric Gaussian quantum wells

In the current study, the linear combination operator (LCO) and Lee–Low–Pines unitary transformation (LLPUT) are adopted to verify the effect of the anisotropic parabolic potential (APP) on the polaron’s properties in the asymmetric Gaussian quantum well (AGQW). Relations of the vibrational frequency (VF) and the ground state energy (GSE) of weak coupling polaron in the AGQW for GaAs crystal varying with the effective confinement strengths of the APP, the barrier height, and range of the asymmetric Gaussian confinement potential (AGCP) are derived. The numerical calculated results illustrate that the GSE and VF of the weak coupling polaron in the AGQW can increase according to the effective confinement strengths’ growth for given values of the barrier height and range of the AGCP. They will increase by increasing the barrier height of the AGCP. However, they are decreasing functions of the range of the AGCP for the determined values of the effective confinement strengths and the barrier height of the AGCP.

Optical response of plasma processed quantum dot under the external fields

AbstractWe investigate theoretically the total refractive index changes (TRICs) and the total absorption coefficients (TACs) of two‐electron Gaussian quantum dot (TEGQD) including Gaussian potential confinement generated by GaAs/GaAlAs heterostructure, embedded in Debye and quantum plasma environments modeled by the more general exponential cosine screened Coulomb (MGECSC) potential, under the influence of the external electric and magnetic field. The wave equation is solved within the effective mass approach framework by using Runge–Kutta–Fehlberg method in order to obtain the subband spectra and the electronic wave functions of TEGQD. Nonlinear optical response of TEGQD is obtained through the compact‐density‐matrix formalism within the iterative method. The effects of both Debye and quantum plasma environments in the strong and weak regimes of the external fields are considered and compared throughout the study. The potents of the external electric field, the external magnetic field, the quantum dot width, the barrier height, and the plasma screening on TRICs and TACs resonant frequencies and amplitudes are analyzed. In addition to these analyses, the alternatives to each parameter effects of the model are also elucidated. TRICs and TACs analyze are carried out in a plasma‐free environment, and thus the function of environments with plasma compared to that without plasma is better explained. Thanks to all these reviews, it is elucidated how to and at what ranges perform in terms of the incident photon energy of TEGQD's optimum for TRICs and TACs characters by using plasma, and in which cases it will be an alternative to the external field and geometrical encompassing.

Qubit coherence effects in a RbCl quantum well with asymmetric Gaussian confinement potential and applied electric field

We theoretically investigate the coherent time of a single qubit in a RbCl quantum well (QW) with asymmetric Gaussian confinement potential (AGCP) using the Pekar-type variational method. Additionally, we utilize Fermi’s golden rule to consider strong coupling between electrons and longitudinal optical phonons in the QW with an electric field applied. The results show that the coherence time changes with AGCP QW’s height, height of the QW, polaron radius and electric field. Moreover, we also show that the coherence time is minimized to $$ \tau = 412.0\;{\text{ps}} $$ in a confinement potential range $$ R = 0.19\;{\text{nm}} $$ . Thus we conclude that these tunable parameters of the QW are vital for adjusting the coherence time and deciding the stability of the qubit.

Temperature and resultant dipole moment of an off-center D- impurity in a Gaussian quantum dot

Abstract The present study investigates the variation of energy ( E ), binding energy ( E B ) and the resultant dipole moment ( D p ) of a negative donor impurity ( D − ) with on-center and off-center locations ( d ) in a GaAs three-dimensional quantum dot (3D-QD) modelled with a Gaussian confinement potential. I have performed Ritz-variational method (RVM) with a very simple wave function which contains just three-variational parameters and a Jastrow-like factor. For on-center ( D − ) impurity, it is true from [47,50] and present results that the E B is always positive and maximum at a particular size of the QD ( R c ). For off-center ( D − ) impurity especially for a large value of locations ( d ) the ( E B ) can be negative. These situations imply that the stability and instability of the system for a given range of the quantum dot size ( R ), respectively. I have obtained the temperatures of D 0 , D − impurities at which these impurities are more stable in a 3D-QD. The confinement length ( R ) and the confinement strength ( V 0 ) effects, on the resultant dipole moment ( D p ) are also investigated for various values of the impurity locations ( d ).

Asymmetric Gaussian confinement potential and decoherence effect on polaron in quantum disk with electromagnetic field

Selecting the asymmetric Gaussian potential to describe the electron that is confined in a quantum dot, the ground and first excited state energy and wave function of the system are derived by using the Pekar-type variational method, and the two-level structure required for a qubit is constructed. The influence of the electron–phonon (EP) coupling constant on the probability density of the electron in the superposition state and the period of the oscillation of a qubit with electromagnetic field are investigated. By studying the effect of the dispersion coefficient, the EP coupling constant and the electromagnetic field on the spontaneous emission rate of the LO phonon, the influence of material parameters and the electromagnetic field on the decoherence of the qubit in quantum dots is revealed, and the theoretical scheme of suppressing the decoherence of qubit in quantum dots by phonon effect is enriched and perfected.

Influence of Dispersion and Polarization on the Two-Parameter Asymmetric Gaussian Confinement Potential Two-Level System with Electric Field

In this paper, the influence of dispersion and polarization on the electronic probability density, the transition frequency and the longitudinal optical (LO) phonon spontaneous emission rate in the two-parameter asymmetric Gaussian confinement (AGC) potential two-level system with the electric field are studied by using the Pekar-type variational method. Numerical results show that the selecting the two-parameter AGC potential to describe the restricted effects of electron in quantum dot can more accurately reveal the quantization characteristics of of the wave property of electronic states, the statistical regularity of electron motion and LO phonons spontaneous emission rate. The influence of the electric field, dispersion and electron -phonon coupling of materials on the probability distribution, transition frequency and LO spontaneous emission rate in the two-level system cannot be ignored.

Modulation of the spin-orbit interaction and the transition probability of polaron in disk quantum dot under electromagnetic field

This work presents the important role played by the spin-orbit interaction in nanostructures such as disk quantum dot when subjected to an external field. Here by using the LLP variational method, the Rashba effect on polaron in this nanostructure with Gaussian confinement potential under electromagnetic field is investigated. The polaron ground, first excited state energy and the electron transition probability are derived. Results show that the external electromagnetic field highly modulates the spin-orbit coupling strength αr, the polaron energies and transition probability. The polaron transition probability splits in two branches due to the splitting of the eigenstates energies. Our study also reveals that DQD properties can be adjusted by the external field. Therefore, the transport and the optical properties of the quantum dot can be controlled by turning the spin-orbit coupling.