Rectangular Potential Well Research Articles

Floquet Transmission in Weyl/Multi‐Weyl and Nodal‐Line Semimetals through a Time‐Periodic Potential Well

AbstractA quantum pumping protocol through which the quasiparticles of Weyl/multi‐Weyl and nodal‐line semimetals are subjected to a time‐periodic rectangular potential well is considered. The presence of an oscillating potential of frequency ω creates equispaced Floquet side‐bands with spacing . As a result, a Fano resonance is observed when the difference in the Fermi energy (i.e., the energy of the incident quasiparticle), and the energy of one of the (quasi)bound state levels of the well, coincides with the energy of an integer number of photons (each carrying energy quantum ). Using the Floquet theory and the scattering matrix approach in the zero‐temperature non‐adiabatic pumping limit, characteristic Fano resonance patterns are found in the transmission coefficients. The inflection points in the pumped shot noise spectra also serve as a proxy for the corresponding Fano resonances. Therefore, the pumped shot noise is also numerically evaluated. Finally, the existence of the Fano resonance points is correlated to the (quasi)bound states of the well, by explicitly calculating the bound states of the static well (which are a subset of the bound states of the driven system). Since semimetals with anisotropic dispersions are considered, all the features observed depend on the orientation of the potential well.

Coherent control and creation of population gratings for a pair of attosecond pulses in a resonant medium based on one-dimensional rectangular quantum wells

Attosecond pulses can be used to create and control coherence in resonant media, since their duration is shorter than the population relaxation times T1 and medium polarization T2. Previously, the possibility of creating and ultrafast control of electromagnetically induced gratings (EMIG) of atomic populations in a resonant medium was shown using a sequence of extremely short light pulses, when the pulses coherently interact with the medium and do not simultaneously overlap in the medium. These studies were carried out in various approximations, when a finite number of energy levels of the medium is taken into account, or when the pulse amplitude is small. In this paper, based on a direct numerical solution of the time dependent Schredinger equation without the indicated approximations, we study the possibility of ultrafast coherent control of populations and the creation of an EMIG by a pair of attosecond pulses in a multilevel resonant medium with a low density of particles. The medium is modeled using a one-dimensional rectangular potential well with infinitely high walls. The studies performed show the possibility of ultrafast coherent control of the properties of resonant media based on quantum wells using attosecond pulses. Keywords: electromagnetically induced gratings, coherent interaction, extremely short pulses, unipolar pulses, attosecond pulses, medium coherence.

Когерентное управление и создание решеток населенностей парой аттосекундных импульсов в резонансной среде на основе одномерных прямоугольных квантовых ям

Attosecond pulses can be used to create and control coherence in resonant media, since their duration is shorter than the population relaxation times T_1 and medium polarization T_2. Previously, the possibility of creating and ultrafast control of electromagnetically induced gratings (EMIG) of atomic populations in a resonant medium was shown using a sequence of extremely short light pulses, when the pulses coherently interact with the medium and do not simultaneously overlap in the medium. These studies were carried out in various approximations, when a finite number of energy levels of the medium is taken into account, or when the pulse amplitude is small. In this paper, based on a direct numerical solution of the time dependent Schrödinger equation without the indicated approximations, we study the possibility of ultrafast coherent control of populations and the creation of an EMIG by a pair of attosecond pulses in a multilevel resonant medium with a low density of particles. The medium is modeled using a one-dimensional rectangular potential well with infinitely high walls. The studies performed show the possibility of ultrafast coherent control of the properties of resonant media based on quantum wells using attosecond pulses.

Comparison of the magneto-optical properties of the semi-parabolic well with those of the parabolic and rectangular wells under the combined influences of aluminum concentration and hydrostatic pressure

In this paper, we report the comparison of the magneto-optical transport properties of the semi-parabolic potential quantum well with those of the parabolic and rectangular potential quantum wells under the combined influences of the aluminum concentration, the temperature, the hydrostatic pressure, and the Landau levels by using the methods of the quantum field theory for many-particle systems in statistical physics and the profile to calculate analytically the conductivity tensor expression, the magneto-optical absorption power expression of the optically detected magneto-phonon resonance (ODMPR) oscillation, and the full width at half maximum (FWHM) of the ODMPR peak, respectively, in quantum wells with three above different confining potential shapes for typical GaAs/AlxGa1−xAs material. The results obtained from the present study show that (i) the ODMPR peak position undergoes a red-shift as the aluminum concentration and the hydrostatic pressure increase while it experiences a blue-shift as the temperature augments for all three above confining potential shapes; (ii) the FWHM as functions of the barrier's Al-concentration, the system's temperature, and the hydrostatic pressure for all three confining potential shapes is presented to compare; (iii) the dependence of the FWHM on the barrier's Al-concentration and the hydrostatic pressure for the Landau levels for three confining potential shapes also is taken into account in detail; (iv) our present theoretical calculations are found to be consistent with previous experimental calculations.

НЕКОТОРЫЕ СВОЙСТВА РЕЗОНАНСНЫХ ПИКОВ ПРОЗРАЧНОСТИ ПРИ ОБРАЗОВАНИИ ЦЕПОЧКИ БАРЬЕРОВ

Some features of the energy spectrum and wave functions of microparticles in the chain of potential barriers are considered. The structure under consideration is a sequence of rectangular potential wells and barriers through which the particle moves. As is known, when such a chain is formed, resonant levels arise in the link, for which the transparency of the system is equal to one. As the number of links increases, these levels and the corresponding wave functions undergo a significant rearrangement. These levels are split into close sublevels, the energy of which depends on the parameters of the barriers and the number of links in the chain. The q-factor of the resulting levels and its dependence on the characteristics of the chain are determined. The dependence of the wave function on the chain parameters is investigated. It is shown that there is a certain analogy between quantum tunneling of particles through a system of barriers and propagation of electromagnetic waves through electric filters. The features of resonant phenomena in these systems are discussed. The developed concepts can be used in nanoelectronics in the development and construction of new devices based on quantum tunneling effects, as well as in the study of relevant sections of the physics course in higher Education institutions.

Analytical Calculation of the Composition of Thermal Dusty Plasma with Metal Particles

For a thermal dusty plasma with metal particles, the relations of the particle charge to the temperature of the system and the particle size have been obtained using a two-plasma model and the approximation of a rectangular potential well. The number densities of electrons and ions in the plasma have been determined for various temperatures and particle sizes of the system. It has been shown that in the case of metal particles, the ionization of the buffer gas leads to underestimation of the charge in comparison with the case when the ionization of the gas is negligible.

Energy partition for anharmonic, undamped, classical oscillators

Using stochastic methods, general formulas for average kinetic and potential energies for anharmonic, undamped (frictionless), classical oscillators are derived. It is demonstrated that for potentials of |x|ν, (ν > 0) type energies are equipartitioned for the harmonic potential only. For potential wells weaker than parabolic potential energy dominates, while for potentials stronger than parabolic kinetic energy prevails. Due to energy conservation, the variances of kinetic and potential energies are equal. In the limiting case of the infinite rectangular potential well (ν → ∞) the whole energy is stored in the form of the kinetic energy and variances of energy distributions vanish.

Quantum Faraday excitations in degenerate electron-ion plasma

A hydrodynamic two-fluid model encompassing inertialess electrons of arbitrary degree of degeneracy and cold ions using the quasineutrality assumption are reduced to an effective nonlinear Schrödinger equation (NLSE) which is used to investigate driven electrostatic plasma-phonon excitations. The quantized frequency spectrum of these plasma-phonon excitations in a one-dimensional quasineutral electron-ion plasma confined in rectangular potential well is calculated. The spectrum shows a quadratic energy level increase quite similar to that of a single electron confined in a hard box, with much reduced level spacings proportional to the electron-to-ion mass ratio. The parametrically driven NLSE is also used to study the quantum Faraday excitations in both weakly and fully nonlinear regimes by employing the pseudo-potential technique. The quantization criterion for fully nonlinear driven quantum Faraday excitations in an arbitrary degenerate plasma confined in a hard box of length l is derived, and it is shown that these excitations constitute a full frequency spectrum level starting with those of small amplitude, high frequency sinusoidal plasma-phonon up to the topmost zero-frequency level solitary plasma-phonon excitations (plasma-soliton level).

Times of Execution of the CCNOT and CCCNOT Quantum Gates in a Quantum Computer based on a Quantum Dots Technology

It is considered a quantum computer consisting of a system of quantum dots (electrons) which are described by a Hamiltonian having rotation, inversion, and exchange symmetries. We consider exclusively the cases of both n = 3 and n = 4 quantum dots. In order to neglect their mutual Coulomb-like interactions, the electron dots are allocated very far way one of each other. In quantum dot technologies the figure of merit is the structure of the confinement potential. Thus, a realistic confinement potential of an electron dot which is composed of a very high rectangular potential well of width approximately equal to three orders of magnitude of the electron dot Compton wavelength (one nanometer) is proposed here. In order to verify the consistence of the present approach, the times of execution of the CCNOT and CCCNOT gates are calculated. It is found that in the case of a soft tunneling through the walls of the potential, the times of execution of such a gates are drastically small.

Partial time delays in elastic electron scattering by rectangular potential well with arising discrete levels

We have studied the times delay of slow electrons scattered by a spherically symmetric rectangular potential well as functions of the well parameters. We have shown that the electron interaction with the scattering center qualitatively depends on the presence of discrete levels in the well. While electron retention dominates for the potential well with no discrete levels, the appearance of a level leads to the opposite situation where the incident electron hardly enters the scatterer. Such a behavior of the time delay is universal since we found it not only for the first s-level but also for the following arising s-, p-, and d-levels.

Terahertz conductivity and coupling between geometrical and plasmonic resonances in nanostructures

Terahertz conductivity spectra of charges moving ballistically in one-, two-, and three-dimensional infinitely deep rectangular potential wells were investigated theoretically using semiclassical and quantum Kubo formulas. The conductivity spectrum of a degenerate electron gas in these nanostructures exhibits a series of geometrical resonances. These further couple with plasmon resonances occurring in isolated structures: qualitatively different interaction regimes are found in one-, two-, and three-dimensional nanostructures. In contrast, the response of a nondegenerate electron gas smears into a single broad band due to the excessive spectral broadening caused by the wide distribution of charge velocities.

The chemical potential and the work function of a metal film on a dielectric substrate

ABSTRACTThe chemical potential and the work function of an aluminium metal film which is in the vacuum (1) and on a dielectric substrate (2) are obtained using the model of non-interacting electrons confined by an asymmetric rectangular potential well. For the first time, these two characteristics are calculated with correct taking into account the electroneutrality condition. As a result, the values of the chemical potential and the work function tend to their bulk values upon increasing the film thickness. The presence of a dielectric substrate leads to a small shift in the values of these characteristics.

Jellium Edge and Size Effect of Chemical Potential and Surface Energy in Metal Slabs

Although free electron models have been established in order to capture the essential physics of interfacial and bulk properties in metals, some issues still remain regarding the application of free electron models to thin metal films. One of the issues relates to whether the geometric edge coincides with the potential edge in order to satisfy the charge neutrality condition when the potential profile is modeled as a rectangular potential well. We show that they coincide by rigorously taking into account the quantization effect arising from electron confinement in a thin metal slab. As a result, the overall behaviors of the chemical potential and surface energy show an increasing trend by decreasing the thickness of the slab. The chemical potential and surface energy show an oscillatory thickness dependence by further taking into account the discreteness of the total number of free electrons.

Low-dimensional systems on the base of PbSnAgTe (LATT) compounds for thermoelectric application

In the paper the p-type of conductivity polycrystalline thin films were received on the basis of PbSnAgTe (LATT) materials deposited on the mica-muscovite substrate. The temperature and thickness dependences of conductivity, current carriers mobility and specific thermoelectric power were investigated for these films. It is shown that scattering on acoustic phonons is the dominant mechanism at above room temperature. The presence of oscillations in profiles of thermoelectric parameters of specific electrical conductivity and Seebeck coefficients is experimentally obtained. The theoretical explanation of oscillations is explained within the framework of model of rectangular potential well with infinitely high walls. The estimation of the efficiency of thermoelectric materials, namely, the dimensionless thermoelectric figure of merit is ZT ∼ (1.2–1.5).

Exceptional points in the Riesz-Feller Hamiltonian with an impenetrable rectangular potential

The number of bound states in a standard rectangular potential well depends on the potential depth and width. In an impenetrable one-dimensional rectangular potential well, there are infinite bound states. In this work we study a non-Hermitian Riesz-Feller kinetic energy; i.e., the second-order derivative of the standard kinetic energy operator is replaced by a fractional, $\ensuremath{\alpha}\mathrm{th}$-order derivative. We show that for $\ensuremath{\alpha}<2$ a particle in an impenetrable one-dimensional rectangular potential well contains a finite number of bound states and an infinite number of metastable decaying states. The transitions from bound states to metastable decaying states occur at $\ensuremath{\alpha}$ values that correspond to exceptional points, for which two bound states coalesce. Our findings indicate that one can describe a transition of highly excited bound states to metastable decaying states, for example due to the interactions of atoms and molecules with the environment, by using the Riesz-Feller kinetic energy operator rather than the standard one.

Effect of Coulomb interaction on chemical potential of metal film

The chemical potential of a metal film within the jellium model taking into account the Coulomb interaction between electrons is calculated. The surface potential is modelled as the infinite rectangular potential well. The behaviour of the chemical potential as a function of the film thickness is studied, the quantum size effect for this quantity is analysed. It is shown that taking into account the Coulomb interaction leads to a significant decrease of the chemical potential and to an enhancement of the quantum size effect.

Optical properties of GaAs/Al_{x}Ga_{1-x}As/GaAs quantum dot with off-central impurity driven by electric field

The effect of a constant electric field and donor impurity on the energies and oscillator strengths of electron intraband quantum transitions in double-well spherical quantum dot GaAs/Al$_{x}$Ga$_{1-x}$As/GaAs is researched. The problem is solved in the framework of the effective mass approximation and rectangular potential wells and barriers model using the method of wave function expansion over a complete set of electron wave functions in nanostructure without electric field. It is shown that under the effect of electric field, the electron in the ground state tunnels from the inner potential well into the outer one. It also influences on the oscillator strengths of intraband quantum transition. The binding energy of an electron with ion impurity is obtained as a function of electric field intensity at a different location of impurity.

LIGHT ABSORPTION of SMALL CdS QUANTUM DOTS

The aim of article is to analyze the conditions of the interface states arise which caused by the polarization trap, and determine the impact of these conditions on the light absorption. Therefore, it was determined the energy of interface states caused by polarization charges arising on heteroboundaries. For calculations we took into account two models: the transition layer on the interface and his absence. In both cases, we shown that polarization traps exist, which can capture the electrons in the case of the small size of quantum dots. The energy spectrum of surface states was calculated by the Ritz variational method. A comparison of these energy states with energy internal states was made.The internal states are defined accurately using the effective masses approximation and the model of rectangular potential wells and barriers. This made it possible to conclude that for the real quantum dot size, the ground state of an electron is always in the internal states of quantum dot. Excited state is not affected. The dependence of the surface states energy on the quantum dot size was obtained. The corresponding energy of these states increases with decreasing of the quantum dot size. This is due to the polarization dependence of the depth of the trap sizes.We calculated matrix elements of the dipole moment of interlrvel transitions into surface states. The light absorption coefficient caused by the interlrvel transitions was defined as a function of the electromagnetic wave frequency. In the final formula of absorption coefficient, we take into account the quantum dots size distribution. It is shown that absorption bands which corresponds to electron transitions into surface states is much smaller than the absorption bands caused by transitions between inner states.

On the motion control of microparticles by means of an electromagnetic field increasing with time for spectroscopic applications

The possibility of controlling the motion of microparticles by means of external electromagnetic fields (nonresonance laser radiation, in particular) that induce potential wells for such particles, which are characterized by fixed spatial distribution but deepen over time to a certain level, are analyzed. It is assumed that the particles are located in high vacuum and are affected by nondissipative external forces. Slowing down of relatively fast particles when they pass through the discussed potential wells is shown. Such slowing down of particles is demonstrated using a nonresonance laser beam with intensity increasing over time as an example. Specific features of particle dynamics in the electromagnetic fields under consideration in the case of a one-dimensional rectangular potential well are studied in detail based on simple analytical relations derived from the fundamental equations of classical mechanics. The methods of particle cooling and localization demonstrated in the present work can substantially increase spectroscopy resolution of various microparticles, including, under certain conditions, atoms and molecules.

To the Theory of Electron Passage in a Semiconductor Structure Consisting of Alternating Asymmetric Rectangular Potential Wells and Barriers

Propagation of electron waves in a medium, whose properties vary only along a certain direction, is theoretically studied. The approach is based on the use of the single-electron stationary Schrodinger equation for the description of elastic scattering processes, including tunneling, of non-interacting spinless particles while maintaining their total energy.