Quantum Harmonic Oscillators with Nonlinear Effective Masses in the weak density approximation

2022 ◽  
Author(s):  
Jen-Hsu Chang ◽  
Chun-Yan Lin ◽  
Ray-Kuang Lee
Keyword(s):  
Effective Mass ◽  
Discrete Dynamical System ◽  
Stationary Solutions ◽  
Harmonic Oscillators ◽  
Density Approximation ◽  
Quantum Harmonic Oscillator ◽  
Effective Masses ◽  
Quantum Particles ◽  
Weak Density ◽  
Unexplored Area

Abstract We study the eigen-energy and eigen-function of a quantum particle acquiring the probability density-dependent effective mass (DDEM) in harmonic oscillators. Instead of discrete eigen-energies, continuous energy spectra are revealed due to the introduction of a nonlinear effective mass. Analytically, we map this problem into an infinite discrete dynamical system and obtain the stationary solutions in the weak density approximation, along with the proof on the monotonicity in the perturbed eigen-energies. Numerical results not only give agreement to the asymptotic solutions stemmed from the expansion of Hermite-Gaussian functions, but also unveil a family of peakon-like solutions without linear counterparts. As nonlinear Schr ¨odinger wave equation has served as an important model equation in various sub-fields in physics, our proposed generalized quantum harmonic oscillator opens an unexplored area for quantum particles with nonlinear effective masses.

scholarly journals Ab InitioStudy of Strain Effects on the Quasiparticle Bands and Effective Masses in Silicon

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Mohammed Bouhassoune ◽  
Arno Schindlmayr
Keyword(s):  
Electronic Properties ◽  
Effective Mass ◽  
Local Density Approximation ◽  
Field Effect Transistors ◽  
Local Density ◽  
Energy Splitting ◽  
Density Approximation ◽  
Self Energy ◽  
Effective Masses ◽  
Structural And Electronic Properties

Usingab initiocomputational methods, we study the structural and electronic properties of strained silicon, which has emerged as a promising technology to improve the performance of silicon-based metal-oxide-semiconductor field-effect transistors. In particular, higher electron mobilities are observed inn-doped samples with monoclinic strain along the [110] direction, and experimental evidence relates this to changes in the effective mass as well as the scattering rates. To assess the relative importance of these two factors, we combine density-functional theory in the local-density approximation with theGWapproximation for the electronic self-energy and investigate the effect of uniaxial and biaxial strains along the [110] direction on the structural and electronic properties of Si. Longitudinal and transverse components of the electron effective mass as a function of the strain are derived from fits to the quasiparticle band structure and a diagonalization of the full effective-mass tensor. The changes in the effective masses and the energy splitting of the conduction-band valleys for uniaxial and biaxial strains as well as their impact on the electron mobility are analyzed. The self-energy corrections withinGWlead to band gaps in excellent agreement with experimental measurements and slightly larger effective masses than in the local-density approximation.

Effective masses in a dense fermion background — Applied to neutrinos, dark matter and dark energy

2014 ◽  
Vol 29 (21) ◽  
pp. 1444010
Author(s):  
Bruce H. J. McKellar ◽  
T. J. Goldman ◽  
G. J. Stephenson
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Scalar Field ◽  
Effective Mass ◽  
Negative Pressure ◽  
Expectation Value ◽  
Effective Masses ◽  
Neutrino Astrophysics

If fermions interact with a scalar field, and there are many fermions present the scalar field may develop an expectation value and generate an effective mass for the fermions. This can lead to the formation of fermion clusters, which could be relevant for neutrino astrophysics and for dark matter astrophysics. Because this system may exhibit negative pressure, it also leads to a model of dark energy.

Direct evaluation of hole effective mass of SnS–SnSe solid solutions with ARPES measurement

2021 ◽  
Author(s):  
Issei Suzuki ◽  
Zexin Lin ◽  
Sakiko Kawanishi ◽  
Kiyohisa Tanaka ◽  
Yoshitaro Nose ◽  
...  
Keyword(s):  
Effective Mass ◽  
Valence Band ◽  
Thermoelectric Properties ◽  
Solid Solutions ◽  
Photoemission Spectroscopy ◽  
Direct Evaluation ◽  
Hole Effective Mass ◽  
Single Crystalline ◽  
Angle Resolved Photoemission Spectroscopy ◽  
Effective Masses

Valence band dispersions of single-crystalline SnS1-xSex solid solutions were observed by angle-resolved photoemission spectroscopy (ARPES). The hole effective masses, crucial factors in determining thermoelectric properties, were directly evaluated. They decrease...

Electronic Structure of Si/InAs Composite Channels

2007 ◽  
Vol 995 ◽  
Author(s):  
Marta Prada ◽  
Neerav Kharche ◽  
Gerhard Klimeck
Keyword(s):  
Electronic Structure ◽  
Quantum Well ◽  
Effective Mass ◽  
Tight Binding ◽  
Localized States ◽  
Equivalent Thickness ◽  
Binding Model ◽  
Direct Bandgap ◽  
Effective Masses ◽  
Composite Channels

AbstractElectronic structure calculations on composite channels, consisting of indium arsenide grown on the technologically relevant (001), (011) and (112)-orientated silicon surfaces are reported. The calculations are performed with NEMO 3-D, where atoms are represented explicitly in the sp3d5s* tight-binding model. The Valence Force Field (VFF) method is employed to minimize the strain. NEMO 3-D enables the calculation of localized states in the quantum well (QW) and their dispersion in the quantum well plane. From this dispersion, the bandgap, its direct or indirect in character, and the associated effective masses of the valence and conduction band can be determined. Such composite bandstructure calculations are demonstrated here for the first time. The numerical results presented here can then be included in empirical device models to estimate device performance. Pure InAs QWs create a direct bandgap material, with a relatively small gap and effective masses of about one order of magnitude smaller than for pure Si QW of equivalent thickness. Si, on the other hand, has a larger bandgap, superior thermal and mechanical properties, and a heavily invested industry. Thus heteroepitaxy of both components is expected to yield a highly optimized overall system. For samples grown along the (001) direction, Si is a direct bandgap material, and deposition of an InAs 3nm layer reduces substantially the hole effective mass and slightly the electronic mass, decreasing the magnitude of the gap. Along the (011) and (112)-growth direction, Si QWs are indirect bandgap material, and deposition of a few InAs layers suffies to make the new material a direct-bandgap heterostructure, decreasing significantly the electronic effective mass. (011) and (112) are the experimentally most relevant growth directions since they prevent heterointerface dipoles.

Design of Heterostructures for High Efficiency Thermionic Emission

2005 ◽  
Vol 886 ◽  
Author(s):  
Zhixi Bian ◽  
Ali Shakouri
Keyword(s):  
Effective Mass ◽  
High Efficiency ◽  
Thermionic Emission ◽  
Vertical Direction ◽  
Mean Free Path ◽  
Energy Conversion Efficiency ◽  
Potential Barriers ◽  
Effective Masses ◽  
Barrier Region ◽  
Electron Mean Free Path

ABSTRACTWe use two heterostructure designs to improve the energy conversion efficiency of solid-state thermionic devices. The first method is to use a non-planar heterostructure with roughness in order of electron mean free path. This has some combined benefits of increased effective interface area, and reduced total internal reflection for the electron trajectories arriving at the interface. Monte Carlo simulations of various geometries show that the electrical conductivity and thermoelectric figure of merit can be improved for non-planar barrier compared to the planar counterpart. The second method is to use planar high barrier heterostructures with different effective masses for charge carriers in emitter and barrier regions. When an electron passes from a lower effective mass emitter and arrives at a barrier with higher effective mass, since both the lateral momentum and total energy are conserved, part of the lateral energy is coupled to the vertical direction and the electron gains momentum in the direction perpendicular to the interface to enter the barrier region. For high potential barriers, the improvement of thermionic current is about the same as the ratio of the effective masses of the two materials, which can be a factor of 5-10 for typical heterostructure material systems.

EFFECTIVE MASSES FOR DONOR BINDING ENERGIES IN QUANTUM WELL SYSTEMS

2006 ◽  
Vol 20 (24) ◽  
pp. 1529-1541 ◽  
Author(s):  
S. RAJASHABALA ◽  
K. NAVANEETHAKRISHNAN
Keyword(s):  
Quantum Well ◽  
Effective Mass ◽  
Binding Energies ◽  
Bohr Radius ◽  
Mass Variation ◽  
Effective Masses ◽  
Approximate Form ◽  
Finite Barrier ◽  
Infinite Barrier ◽  
Barrier Model

The donor ionization energies in a quantum well and quantum dot with finite and infinite barriers are estimated for different well dimensions. Using the effective mass (EM) approximation, calculations are presented with constant effective mass and position dependent effective masses that are different for finite and infinite cases. Our results reduce to an approximate form used by X. H. Qi et al., Phys. Rev. B58 (1998) 10578 in the finite barrier model and that of L. E. Oliveira and L. M. Falicov, Phys. Rev. B34 (1986) 8676 in the infinite barrier case. Results are presented by taking the GaAs quantum well as an example. The use of constant effective mass of 0.067m0 is justified for well dimensions ≥a* where a* is an effective Bohr radius which is about 100 Å. While Qi et al. found a maximum of 22% variation in the binding energies due to mass variation, we obtained nearly 100% variation when mass variations are included correctly.

scholarly journals Электронный спектр капсулированных монослоев: аналитические результаты

2021 ◽  
Vol 47 (13) ◽  
pp. 52
Author(s):  
С.Ю. Давыдов
Keyword(s):  
Green’S Function ◽  
Effective Mass ◽  
Strong Coupling ◽  
Green's Function ◽  
Function Method ◽  
Energy Gap ◽  
Green’S Function Method ◽  
Effective Masses ◽  
Analytical Expressions

Green’s function method is used to find the dispersion low for a monolayer (ML) placed be-tween two crystalline slabs. Weak- and strong-coupling regimes are considered in details. For the systems graphene, hBN – metallic ML – SiC polytypes analytical expressions for the ML electron effective masses are obtained. It is shown that the effective mass decreases with the increase of the SiC polytype energy gap.

scholarly journals Determination of the exciton binding energy and effective masses for methylammonium and formamidinium lead tri-halide perovskite semiconductors

2016 ◽  
Vol 9 (3) ◽  
pp. 962-970 ◽  
Author(s):  
Krzysztof Galkowski ◽  
Anatolie Mitioglu ◽  
Atsuhiko Miyata ◽  
Paulina Plochocka ◽  
Oliver Portugall ◽  
...  
Keyword(s):  
Binding Energy ◽  
Effective Mass ◽  
Exciton Binding Energy ◽  
Effective Masses ◽  
Halide Perovskite

The reduced effective mass (μ) and excitonic Rydberg (R*) are measured by magneto-optics for new perovskite semiconductors.

scholarly journals NEUTRINO ENERGIES IN A NEUTRINOSPHERE

2013 ◽  
Vol 28 (34) ◽  
pp. 1350153 ◽  
Author(s):  
LEONARD S. KISSLINGER
Keyword(s):  
Effective Mass ◽  
Gravitational Collapse ◽  
Massive Star ◽  
Dense Matter ◽  
Energy Eigenvalues ◽  
Effective Masses

The energies of neutrinos in a neutrinosphere, the dense matter created after the gravitational collapse of a massive star are estimated. Cubic equations for energy eigenvalues of neutrinos are used with the effective masses found by taking the neutrinos at rest in neutrinosphere matter. Large differences in the effective mass of some neutrino species in a neutrinosphere compared to vacuum are found.

Sign in / Sign up

Export Citation Format

Share Document