Position-dependent Effective Mass Research Articles

The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass

We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute the Wigner distribution function exactly for such a semiconfinement quantum system. This method suppresses the divergence of the integrand in the definition of the quantum distribution function and leads to the computation of its analytical expressions for the stationary states of the semiconfined oscillator model. For this quantum system, both the presence and absence of the applied external homogenous field are studied. Obtained exact expressions of the Wigner distribution function are expressed through the Bessel function of the first kind and Laguerre polynomials. Furthermore, some of the special cases and limits are discussed in detail.

Position-Dependent Effective Mass and Asymmetry Effects on the Electronic and Optical Properties of Quantum Wells with Improved Rosen–Morse Potential

In this study, we investigated, for the first time, the effects of the spatially varying effective mass, asymmetry parameter, and well width on the electronic and optical properties of a quantum well which has an improved Rosen–Morse potential. Calculations were made within the framework of the effective mass and parabolic band approximations. We have used the diagonalization method by choosing a wave function based on the trigonometric orthonormal functions to find eigenvalues and eigenfunctions of the electron confined within the improved Rosen–Morse potential. Our results show that the position dependence mass, asymmetry, and confinement parameters cause significant changes in the electronic and optical properties of the structure we focus on since these effects create a significant increase in electron energies and a blue shift in the absorption spectrum. The increase in energy levels enables the development of optoelectronic devices that can operate at wider wavelengths and absorb higher-energy photons. Through an appropriate choice of parameters, the Rosen–Morse potential offers, among many advantages, the possibility of simulating heterostructures close to surfaces exposed to air or vacuum, thus giving the possibility of substantially enriching the allowed optical transitions given the breaking of the system´s symmetries. Similarly, the one-dimensional Rosen–Morse potential model proposed here can be extended to one- and zero-dimensional structures such as core/shell quantum well wires and quantum dots. This offers potential advancements in fields such as optical communication, imaging technology, and solar cells.

Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass

Dynamical symmetry of a semiconfined harmonic oscillator model with a position-dependent effective mass

Modeling of electronic spectra and optical responses of a laser-affected double GaAsSb/GaAs parabolic quantum well using COMSOL multiphysics: the role of position-dependent effective mass and the static electric field

Modeling of electronic spectra and optical responses of a laser-affected double GaAsSb/GaAs parabolic quantum well using COMSOL multiphysics: the role of position-dependent effective mass and the static electric field

The effect of position-dependent effective mass on the optical properties of a spherical quantum dot confined in inverse square root truncated and deformed exponential potential

The effect of position-dependent effective mass on the optical properties of a spherical quantum dot confined in inverse square root truncated and deformed exponential potential

Transmission of a position-dependent mass system through a soft Coulomb potential

This research delves into the fascinating transmission characteristics of a system with variable mass, confined by a Coulomb-like potential. By utilizing an analytic approach to transmission probability, we were able to unveil the intriguing features that are observed experimentally in a specially designed two-dimensional lattice. This lattice was engineered to manipulate itinerant electrons through entanglement, resulting in variable masses as they traverse the lattice. To build our model system, we utilized the displacement operator approach to the position-dependent effective mass theory. This allowed us to investigate the effects of different configurations of leads, system geometries and lattice deformations on the transmission characteristics of the system. The resulting data showed that the model system was highly sensitive to these parameters, which led to various interesting features. First, we observed Andreev-like reflections, which occur when a particle is reflected as a hole, resulting in the transfer of both energy and charge. Another feature was reflectionless transmission, in which the transmission probability of a particle is close to unity, and almost no reflection occurs. We also observed complete localization of charge carriers, where the transmission probability is effectively zero, indicating that the charge carriers are completely confined within the lattice. Our findings demonstrate the remarkable versatility of the effective mass approach in the modeling of physical systems. By unraveling the intricate relationships between system parameters and transmission probability, we have gained new insights into the behavior of itinerant charge carriers in lattice structures. These insights may guide the design and development of novel electronic devices with enhanced performance and functionality.

Schrödinger equation with singular position dependent mass

We consider the Schrödinger equation with singular position dependent effective mass and prove that it is very weakly well posed. A uniqueness result is proved in an appropriate sense; moreover, we prove the consistency with the classical theory. In particular, this allows one to consider $\delta$-like or more singular masses.

Optical response of position dependent hybrid optomechanical system

AbstractOptomechanics is a growing field of research, studies the interaction between optical field and mechanical oscillator. In this study, we theoretically analyze a hybrid system which consists of Fabry Perot cavity containing two‐level N‐ Number of atoms. The cavity having two mirrors one is fixed, and other is oscillating. The oscillating mirror has a position dependent mass, considered as effective mass. The mechanical resonator generates a nonlinear effect because it is position dependent. Dynamics of the system's operators, steady‐state solutions, and optical response of the hybrid optomechanical system are analytically calculated. Optical response in the regime of position dependent effective mass (PDEM) are the main result in this article. We deduced that position dependent parameter of the resonator not only effect the dynamics but also the optical response of the optomechanical system.

Optical Properties of Cylindrical Quantum Dots with Hyperbolic-Type Axial Potential under Applied Electric Field.

In this paper, we have researched the electronic and optical properties of cylindrical quantum dot structures by selecting four different hyperbolic-type potentials in the axial direction under an axially-applied electric field. We have considered a position-dependent effective mass model in which both the smooth variation of the effective mass in the axial direction adjusted to the way the confining potentials change and its abrupt change in the radial direction have been considered in solving the eigenvalue differential equation. The calculations of the eigenvalue equation have been implemented considering both the Dirichlet conditions (zero flux) and the open boundary conditions (non-zero flux) in the planes perpendicular to the direction of the applied electric field, which guarantees the validity of the results presented in this study for quasi-steady states with extremely high lifetimes. We have used the diagonalization method combined with the finite element method to find the eigenvalues and eigenfunction of the confined electron in the cylindrical quantum dots. The numerical strategies that have been used for the solution of the differential equations allowed us to overcome the multiple problems that the boundary conditions present in the region of intersection of the flat and cylindrical faces that form the boundary of the heterostructure. To calculate the linear and third-order nonlinear optical absorption coefficients and relative changes in the refractive index, a two-level approach in the density matrix expansion is used. Our results show that the electronic and, therefore, optical properties of the structures focused on can be adjusted to obtain a suitable response for specific studies or goals by changing structural parameters such as the widths and depths of the potentials in the axial direction, as well as the electric field intensity.

Study of photoionization cross section and binding energy of shallow donor impurity in multilayered spherical quantum dot

In the framework of the effective mass approximation and by using the finite element method , we have studied the simultaneous effects of position dependent effective mass (PDEM) and dielectric function on the shallow donor impurity binding energy and photoionization cross section in a multilayered spherical quantum dot . We have also investigated the influence of conduction band nonparabolicity and polaronic mass on the both binding energy and photoionization cross section (PCS). The obtained results have shown that the nonparabolicity and polaronic mass effects enhance the binding energy and photoionization cross section. Furthermore, it can be concluded from this research that the binding energy and the PCS are strongly dependent on the geometrical parameters, and PDEM. Changes in binding energy and photoionization cross section have physical reasons, which are discussed in details. • The photoionization cross section (PCS) and the binding energy are strongly dependent on the width of the structure layers. • The conduction band nonparabolicity and the polaronic mass effects enhance the binding energy and reduce the PCS peak magnitude. • The dependence of the dielectric function ε ( r ) on the electron coordinates makes the amplitude peak of the PCS take high values.

Quantum mechanics solvable systems with position-dependent effective mass

Considering the position-dependent effective mass in the study of quantum mechanical systems, a wide range of solvable potentials has been obtained. These potentials are obtained by applying canonical transformations to the Schrödinger equation. In this method, the internal functions introduced by Levai for solvable potentials with constant mass have been used, and the eigenfunctions and eigenvalues have been fully obtained. The eigenfunction of these solvable potentials can be obtained based on specific known functions (Jacobian, generalized Laguerre, and Hermit polynomials). Some of these potentials are Scarf-II, Pöschl-Teller, Rosen-Mörse-II and Eckart, whose applications have been described in physical systems. Finally, all the results are placed in a table and the figures of the desired functions is drawn for specific values

The Husimi function of a semiconfined harmonic oscillator model with a position-dependent effective mass

In this paper, the phase space representation for a semiconfined harmonic oscillator model with a position-dependent effective mass is constructed. We have found the Husimi distribution function for the stationary states of the oscillator model under consideration for both cases without and with the applied external homogeneous field. The obtained function is expressed through the double sum of the parabolic cylinder function. Different special cases and the limit relations are discussed, too.

Classification of quantum systems with position-dependent effective mass based on lie algebra and special functions

Classification of quantum systems with position-dependent effective mass based on lie algebra and special functions

Schrödinger Equation with Geometric Constraints and Position-Dependent Mass: Linked Fractional Calculus Models

We investigate the solutions of a two-dimensional Schrödinger equation in the presence of geometric constraints, represented by a backbone structure with branches, by taking a position-dependent effective mass for each direction into account. We use Green’s function approach to obtain the solutions, which are given in terms of stretched exponential functions. The results can be linked to the properties of the system and show anomalous spreading for the wave packet. We also analyze the interplay between the backbone structure with branches constraining the different directions and the effective mass. In particular, we show how a fractional Schrödinger equation emerges from this scenario.

Investigating the valence-band bound states in GaAs/GaAsSb/GaAs V-shaped quantum wells: The role of intense laser fields and position-dependent effective mass

This theoretical study investigated the valence-band electronic features in GaAs/GaAsSb/GaAs V-shaped quantum wells. Accordingly, an analytical relation has been extended on the position-dependent effective mass in GaAsSb well region as a function of well geometry. The Finite Element Method and the effective mass approximation have been used to investigate the combined effects due to a non-resonant high-frequency intense laser field and an applied electric field. This study considered the effects of geometric and structural parameters on the laser-dressed confining potential profile, bound states, and the corresponding wave functions. The performed studies have shown that the laser-dressing could convert a V-shaped potential profile to a parabolic-like potential and also a single-well to a double-well. The combined effects of intense laser and electric fields have caused a conversion from a symmetric well to a larger and shallower asymmetric structure. It has been found from the valence-band energy levels that pronounced blueshifts and redshifts were obtained in the electromagnetic energy spectrum with increasing the strength of the intense laser and applied electric fields, respectively. The numerical results have indicated that the electronic properties in valence-band quantum wells were modulated according to the purpose through varying the well half-width and the antimony concentration. Such adjustable valence-band-based features can be beneficial in the design and fabrication of the next generation equipment used in the optoelectronic domain.

On the exactly-solvable semi-infinite quantum well of the non-rectangular step-harmonic profile

An exactly-solvable model of the non-relativistic harmonic oscillator with a position-dependent effective mass is constructed. The model behaves itself as a semi-infinite quantum well of the non-rectangular profile. Such a form of the profile looks like a step-harmonic potential as a consequence of the certain analytical dependence of the effective mass from the position and semiconfinement parameter $a$. Both states of the discrete and continuous spectrum are studied. In the case of the discrete spectrum, wavefunctions of the oscillator model are expressed through the Bessel polynomials. The discrete energy spectrum is non-equidistant and finite as a consequence of its dependence on parameter $a$, too. In the case of the continuous spectrum, wavefunctions of the oscillator model are expressed through the $_1F_1$ hypergeometric functions. At the limit, when the parameter $a$ goes to infinity, both wavefunctions, and the energy spectrum of the model under construction correctly reduce to corresponding results of the usual non-relativistic harmonic oscillator with a constant effective mass. Namely, wavefunctions of the discrete spectrum recover wavefunctions in terms of the Hermite polynomials, and wavefunctions of the continuous spectrum simply vanish. We also present a new limit relation that reduces Bessel polynomials directly to Hermite polynomials and prove its correctness using the mathematical induction technique.

Investigating the effect of position-dependent effective mass on the valence-band electronic states of GaAs/GaAsSb/GaAs parabolic quantum wells modulated by intense laser fields

This article has theoretically investigated the valence-band electronic properties of GaAs/GaAsSb/GaAs parabolic quantum well structures. To this end, an analytical expression has been developed to describe the position-dependent effective mass in the GaAsSb parabolic well region as a function of well geometry. Simultaneous effects of a non-resonant high-frequency intense laser field and an applied electric field have been studied using the Finite Element Method within the framework of the effective mass approximation. The laser-dressed confinement potential profile, bound states, and the corresponding wave functions have been examined as a function of geometric and structural parameters of GaAsSb well. The obtained numerical findings have shown that the well geometry was modulated to achieve a Gaussian-like profile from a parabolic shape and a double-well structure from a single-well one under intense laser irradiations. Simultaneous effects of intense laser and electric fields have indicated the formation of asymmetric geometric profiles from symmetric quantum well structures. The analysis of valence-band energy states has revealed pronounced blueshifts and redshifts in the electromagnetic energy spectrum, increasing the strength of the intense laser and applied electric fields. Studies have demonstrated that the valence-band electronic features were adjusted to alter the well half-width and the antimony concentration. These tunable valence-band-based properties can be profitable in designing and applying new devices operating in the optoelectronic field.

Optical properties of Al x Ga1−x As/GaAs Woods–Saxon quantum well in the presence of hydrostatic pressure and applied electric field

The third harmonic generation (THG), linear and nonlinear optical absorption coefficients (OACs), and refractive index changes (RICs) are investigated in a Woods–Saxon quantum well (QW) modulated by the hydrostatic pressure and applied electric field. The effect of non-uniform aluminum doping (position-dependent effective mass (PDEM)) on the mass of the system is discussed, and further to explore the influence of PDEM on the nonlinear THG, OACs, and RICs of the Woods–Saxon QW. These nonlinear optical properties above are obtained using the compact-density matrix formalism. The electron states in a Woods–Saxon QW under the constant effective mass (CEM) and PDEM are calculated by solving the Schrödinger equation via the finite difference technique. The contributions from competing effects of the hydrostatic pressure and applied electric field to the nonlinear optical properties with CEM and PDEM are reported, as well as the comparison with each other. The observations reveal that the regulation of external fields and the influence of PDEM play an important role in the photoelectric properties of QW.

Effect of position-dependent effective mass on donor impurity- and exciton-related electronic and optical properties of 2D Gaussian quantum dots

Effect of position-dependent effective mass on donor impurity- and exciton-related electronic and optical properties of 2D Gaussian quantum dots

Application of Morse potential and improved deformed exponential-type potential (IDEP) model to predict thermodynamics properties of diatomic molecules

The thermal properties of three diatomic molecules such as hydrogen (H2), carbon monoxide (CO) and iodine (I2) are theoretically predicted. To this end, two different potential models are considered, Morse potential and improved deformed exponential-type potential (IDEP). The Schrödinger equation is analytically solved to obtain energy levels. For the Morse and IDEP potential models, the Laplace transformation and the Greene–Aldrich approximation and appropriate coordinate transformation are employed, respectively. In the former potential model, we have obtained energy eigenvalues by considering position-dependent effective mass. Using the energy levels of two models, the partition function is first determined. Second, thermal functions of the molecules such as heat capacity, enthalpy and entropy are obtained and compared with the available results. The calculated enthalpy using the two models for CO and I2 molecules is in excellent agreement in comparison with the available data in a wide temperature range. But, the obtained enthalpy of H2 molecule using the Morse potential at high temperatures does not agree excellently with the experimental data. The entropy of H2, CO and I2 using the two models is tin good agreement in comparison with the available data in a wide temperature range whereas the entropy of H2 at low temperatures does not agree excellently with the experimental data. Our theoretical results using the two potential models do not show a suitable prediction about the heat capacity at a constant pressure of H2, CO and I2 molecules, But the IDEP shows more agreement compared to the Morse potential.