Friedel oscillations for temperatures T≠0

Friedel oscillations (FO) of electron density caused by a delta-like neutral impurity in twodimensional (2D) systems in a magnetic field are calculated. Three 2D cases are considered: free electron gas, monolayer graphene and group-VI dichalcogenides. An exact form of the renormalized Green's function is used in the calculations, as obtained by a summation of the infinite Dyson series and regularization procedure. Final results are valid for large ranges of potential strengths V0, electron densities ne, magnetic fields B and distances from the impurity r. Realistic models for the impurities are used. The first FO of induced density in WS2 are described by the relation ∆n(r) ∝ sin(2πr/TF O)/r 2 , where TF O ∝ 1/ √ EF . For weak impurity potentials, the amplitudes of FO are proportional to V0. For attractive potentials and high fields the total electron density remains positive for all r. On the other hand, for low fields, repulsive potentials and small r, the total electron density may become negative, so that many-body effects should be taken into account.

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“…7b and in Eqs. (55) and (56) are extensions of the predictions of Refs. [9,12] concerning 2D electron gas in materials with honeycomb lattice.…”

Section: Fig 3 A) Position Of the Fermi Level For Ws2 In A Magneticsupporting

confidence: 58%

“…As shown in Figs. 6 and 7, equations (55) and (56) are valid for the ideal 2D electron gas and for that in group-VI dichalogenides in the parabolic approximation of energy band for typical material parameters. Our calculations for monolayer graphene and WS 2 in the nonparabolic bands model suggest that Eq.…”

Section: Discussionmentioning

confidence: 99%

Theory of Friedel oscillations in monolayer graphene and group-VI dichalcogenides in a magnetic field

Rusin

Zawadzki

2018

Phys. Rev. B

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“…Therefore, the nature of the complicated spot structures should originate from an electronic effect rather than a simple relief modulation. These observations lead to the hypothesis that the observed interference features do not relate to oscillations of charge density 13,14 of surface states in the vicinity of a scattering center, but they are likely the result of electron interference due to the presence of a subsurface nanoinclusion reflecting bulk electrons. It is expected that the magnitude of the dI / dV signal as well as its specific spatial distribution reflects somehow the size, shape, and depth of location of the nanoinclusion.…”

Section: Resultsmentioning

confidence: 96%

Probing quantum wells induced above a subsurface nanocavity in copper

et al. 2008

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Argon-filled nanocavities embedded in a single crystal of copper near the surface reflect electrons and induce a quantum well ͑QW͒ between the nanocavity and the atomically flat Cu͑001͒ surface. The spatial variation of conductance at the surface above the nanocavity was studied by scanning tunnelling microscopy and/or spectroscopy. Interference features were observed over several nanometers at some locations on the surface. In the ͓100͔ and ͓010͔ directions, the interference fringes propagate over longer distances up to tens of nanometers. In addition to these spatially resolved features, the conductance reveals an oscillatory behavior as a function of energy of injected electrons. A model taking into account the specific shape of the nanocavity, as well as the band structure of copper, allows us to simulate the spatial variation of the conductance in close agreement with the experiment. The modeling demonstrates that not only the specific shape of the subsurface nanocavity reflecting electrons is crucial to explain the observed pattern, but also the anisotropy of the band structure and the phenomenon of focusing of hot electrons connected to it. Our approach opens up opportunities to examine buried nano-objects with scanning tunneling microscopy, and also to study how the anisotropy of a crystal influences the spatial variation of QW properties.

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“…This is apparent because in the high-temperature limit the theory of Friedel oscillations [11] predicts only a small temperature dependence: i) for high temperatures (300 K) significant deviations from the expected r −3 decay of the oscillation amplitude are expected only for relatively large distances from the scatterer. ii) the ratio r of the oscillation amplitude at 8 K and 300 K is near unity (r ∼ 0.8) for distances between 5 nm and 10 nm from the scattering center.…”

mentioning

confidence: 99%

Erythrocyte Deformability and its Hemorheological Consideration

Shin¹,

Ku²,

Park³

et al. 2004

Jpn. J. Appl. Phys.

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PACS. 61.16Ch -Scanning probe microscopy: scanning tunneling, atomic force, scanning optical, magnetic force, etc. PACS. 73.20Dx -Electron states in low-dimensional structures (superlattices, quantum well structures and multilayers). PACS. 71.55Eq -III-V semiconductors.Abstract. -In situ cleaved (110) surfaces of n-doped GaAs have been investigated by scanning tunneling microscopy (STM) and spectroscopy (STS) at temperatures from 8 K to 300 K. At low temperatures oscillatory features in the topography around individual donor atoms embedded in the GaAs matrix and peaks in the differential conductivity (dI/dU) curves are seen. Both vanish with increasing temperature. The experimental results are described consistently in the framework of quantized subbands of a low-dimensional electron gas within the band-bending region which is induced by the STM tip. The quantization occurs at unpinned semiconductors surfaces and is also relevant for a quantitative understanding of STM data at room temperature.

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Friedel oscillations for temperatures T≠0

Cited by 11 publications

References 3 publications

Theory of Friedel oscillations in monolayer graphene and group-VI dichalcogenides in a magnetic field

Theory of Friedel oscillations in monolayer graphene and group-VI dichalcogenides in a magnetic field

Probing quantum wells induced above a subsurface nanocavity in copper

Erythrocyte Deformability and its Hemorheological Consideration

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