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Free electron model

About: Free electron model is a research topic. Over the lifetime, 4678 publications have been published within this topic receiving 103535 citations.


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TL;DR: In this article, it was shown that nearly free nearly-relativistic nearly-free electrons in solids should experience a trembling motion (Zitterbewegung, ZB) in the absence of external fields, similarly to relativistic electrons in a vacuum.
Abstract: We show theoretically that non-relativistic nearly-free electrons in solids should experience a trembling motion (Zitterbewegung, ZB) in the absence of external fields, similarly to relativistic electrons in a vacuum The ZB is directly related to the influence of the periodic potential on the free electron motion The frequency of the ZB is , where Eg is the energy gap The amplitude of the ZB is determined by the strength of periodic potential and the lattice period, and it can be of the order of nanometres We show that the amplitude of the ZB does not depend much on the width of the wavepacket representing an electron in real space An analogue of the Foldy–Wouthuysen transformation, known from relativistic quantum mechanics, is introduced in order to decouple electron states in various bands We demonstrate that after the bands are decoupled electrons should be treated as particles of a finite size In contrast to nearly-free electrons we consider a two-band model of tightly-bound electrons We show that in this case also the electrons should experience the trembling motion It is concluded that the phenomenon of ZB of electrons in crystalline solids is the rule rather than the exception

22 citations

Journal ArticleDOI
TL;DR: In this paper, the width of the free electron cyclotron resonance in InSb has been studied as a function of resonant magnetic field, by means of laser spectrometers operating at seven different wavelengths.

22 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the quantum dynamics of the electron-electron scattering process on an attosecond time scale and investigated the interaction of an incoming keV-range electron wavepacket by the bound electron of an aligned H 2 + 2 + 1 molecule, using a one-dimensional model.
Abstract: Ultrafast diffraction with free attosecond electron pulses promises insight into the four-dimensional motion of charge density in atoms, molecules and condensed matter. Here we consider the quantum dynamics of the electron-electron scattering process on an attosecond time scale. By numerically solving the time-dependent two-electron Schrodinger equation, we investigate the interaction of an incoming keV-range electron wavepacket by the bound electron of an aligned H 2 + molecule, using a one-dimensional model. Our findings reveal the ratio of elastic to inelastic contributions, the role of exchange interaction, and the influence of the molecular electron density to diffraction. Momentum transfer during the scattering process, from the incoming to the bound electron mediated by the nuclei, leaves the bound electron in a state of coherent oscillation with attosecond recurrences. Entanglement causes related state-selective oscillations in the phase shift of the scattered electron. Two scenarios of distinguishable and indistinguishable free and bound electrons yield equivalent results, irrespective of the electronic spins. This suggests to employ the scenario of distinguishable electrons, which is computationally less demanding. Our findings support the possibility of using electron diffraction for imaging the motion of charge density, but also suggest the application of free electron pulses for inducing attosecond dynamics.

22 citations

Journal ArticleDOI
TL;DR: In this paper, the electron temperature in a low-pressure argon plasma diffusing from a magnetically expanding radiofrequency plasma containing a current-free double layer (DL) over the argon gas pressure of 0.3-3 mTorr was characterized.
Abstract: Electron temperature is characterized in a low-pressure argon plasma diffusing from a magnetically expanding radiofrequency plasma containing a current-free double layer (DL) over the argon gas pressure of 0.3–3 mTorr. The measured electron energy probability function (EEPF) is Maxwellian at the downstream side of the DL, while the upstream EEPF shows a depleted tail corresponding to free electrons, which can overcome the potential drop of the DL and diffuse into the downstream side. The free electrons relating to the amplitude of the DL electrically neutralize a supersonic ion beam accelerated by the DL. The electron temperature measured at the downstream plasma is found to be in good agreement with that of the free electrons in the upstream source tube and agrees with the numerical result given from low-pressure diffusion theory.

22 citations

Journal ArticleDOI
TL;DR: The electronic structure of three rare earth metals has been studied by measuring the angular correlations of the photons emitted when positrons annihilate with the electrons in the metal as mentioned in this paper, and it was deduced that gadolinium and cerium at room temperature each has approximately three conduction electrons per atom, while ytterbium has approximately two as expected from the localized f -electron model.

22 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202340
202290
2021132
2020122
2019114
2018112