Modern nanotechnology allows one to scale down various important devices (sensors, chips, fibers, etc.) and thus opens up new horizons for their applications. The efficiency of most of them is based on fundamental physical phenomena, such as transport of wave excitations and resonances. Short propagation distances make phase-coherent processes of waves important. Often the scattering of waves involves propagation along different paths and, as a consequence, results in interference phenomena, where constructive interference corresponds to resonant enhancement and destructive interference to resonant suppression of the transmission. Recently, a variety of experimental and theoretical work has revealed such patterns in different physical settings. The purpose of this review is to relate resonant scattering to Fano resonances, known from atomic physics. One of the main features of the Fano resonance is its asymmetric line profile. The asymmetry originates from a close coexistence of resonant transmission and resonant reflection and can be reduced to the interaction of a discrete (localized) state with a continuum of propagation modes. The basic concepts of Fano resonances are introduced, their geometrical and/or dynamical origin are explained, and theoretical and experimental studies of light propagation in photonic devices, charge transport through quantum dots, plasmon scattering in Josephson-junction networks, and matter-wave scattering in ultracold atom systems, among others are reviewed.

/pdf/fano-resonances-in-nanoscale-structures-2c8qeas3bm.pdf

Fano resonances in nanoscale structures

Spin-polarized electron tunneling

We present a method for calculating the core-level x-ray photoemission (XPS), the $3d\ensuremath{\rightarrow}4f$ x-ray absorption (XAS), the valence photoemission, and the bremsstrahlung isochromat spectra in a slightly modified Anderson impurity model of a Ce compound at zero temperature. Both the spin and orbital degeneracies of the $f$ level are included and the Coulomb interaction between the $f$ electrons is taken into account. The spectra are expressed in terms of a resolvent operator. A many-electron basis set is introduced, and the resolvent is obtained from a matrix inversion. The particular form of the Anderson model allows us to find a small but sufficiently complete basis set, if the degeneracy ${N}_{f}$ of the $f$ level is large. In particular, we consider the limit ${N}_{f}\ensuremath{\rightarrow}\ensuremath{\infty}$, and show that the method is exact for the XPS, XAS, and valence photoemission spectra in this limit. It is also demonstrated that for ${N}_{f}\ensuremath{\gtrsim}6$, the method provides accurate spectra. Analytical results are obtained for the valence photoemission spectrum ${\ensuremath{\rho}}_{v}(\ensuremath{\epsilon})$. The spectrum has a sharp rise close to the Fermi energy ${\ensuremath{\epsilon}}_{F}$, which goes over to a "Kondo peak" in the spin-fluctuation limit. An exact relation between ${\ensuremath{\rho}}_{v}({\ensuremath{\epsilon}}_{F})$ and the $f$-level occupancy ${n}_{f}$ is shown to be satisfied to within 10% for ${N}_{f}\ensuremath{\ge}6$. We discuss how core-level XPS spectra can be used to estimate the $f$-level occupancy ${n}_{f}$ and the coupling $\ensuremath{\Delta}$ between the $f$ level and the conduction states. We find that the values of ${n}_{f}$ and $\ensuremath{\Delta}$ obtained from core-level XPS are basically consistent with the other spectroscopies and the static, $T=0$ susceptibility. It is, therefore, possible to describe these experiments in the Anderson model, using essentially the same set of parameters for all the experiments. Typically, we find ${n}_{f}g0.7$ and $\ensuremath{\Delta}\ensuremath{\sim}0.1$ eV.

Electron spectroscopies for Ce compounds in the impurity model

Recently it has been shown that many traditional models used for a description of dilute magnetic alloys are completely integrable and may be solved exactly without any approximation. In this article we summarize the results which have been obtained in this way. The main part of the article is devoted to the consistent and detailed account of the Bethe-Ansatz technique for the s-d exchange (Kondo) model with arbitrary impurity spin, s-d model with anisotropic exchange, degenerate exchange model and for the canonical Anderson model. The thermodynamic properties of a magnetic impurity in a non-magnetic metal host obtained by the Bethe method are considered in detail. Mainly attention is paid to the analysis of singularities associated with the formation of a localized moment, Kondo effect and mixedvalence phenomenon, which can be treated analytically. In the introductory part of the article we discuss the applicability of the models which we study in the paper to the real alloys and consider some m...

Exact results in the theory of magnetic alloys

We have derived the expression of the Ruderman-Kittel-Kasuya-Yosida coupling between two ferromagnetic layers separated by a nonmagnetic spacer, for arbitrary crystal structure and Fermi surface. For the first time, quantitative predictions of the interlayer coupling for Cu, Ag, and Au spacers are given. The results are in good agreement with recent experimental data for fcc Co/Cu and Fe/Cu systems.

Oscillatory coupling between ferromagnetic layers separated by a nonmagnetic metal spacer.

Adawi's calculation of the photoelectric current for noninteracting electrons is extended to the case of a Fano resonance, which involves electron interactions. The method allows the calculation of the Auger current that is produced by the filling of the core hole. With Auger processes included, the primary photocurrent still exhibits a Fano line shape but with a value of the $q$ parameter different (always smaller) than that of the optical-absorption spectrum. The spectrum of the Auger current with respect to incident photon frequency is Lorentzian and centered at the position of the resonance. At a given frequency, the optical-absorption rate equals the sum of the primary and Auger currents.

Photoelectron spectrum, including that of Auger electrons, of Fano resonances in atoms

The inclusion of the shake-up matrix element in the transition amplitude for Auger electrons in Fano resonances changes the intensity profile from Lorentzian to a Fano line shape. Transition elements at the end of the series offer a possibility for the observation of this effect.

Effect of shake-up transitions on the spectrum of Auger electrons in Fano resonances

The wave-number- and frequency-dependent spin susceptibility of a two-band ($s$ and $p$) model with $\ensuremath{\delta}$-function interactions is calculated in the random-phase approximation. The result shows that when the character of the $s$ band changes with temperature, the Korringa product ${({T}_{1}T)}^{\ensuremath{-}1}$ can be temperature dependent even when the Knight shift is not.

Spin Susceptibility and the Korringa Relation in a Two-Band Model

The photoelectron currents emitted from the d valence bands of Ni and Pt metal show strong modulation as the photon energy is scanned through, respectively, the 3p and 4f core-electron resonances. We demonstrate that the emitted electrons can be divided into three parts, a primary part which is coherent with the excitation step, and primary and Auger parts which are incoherent with the initial excitation. We find that effects due to hole-hole interactions in the d bands are weak, and we therefore neglect them. We calculating the energy dependence of the coherent and the Auger parts from previously published parameters obtained from analysis of electron-energy-loss spectroscopy and photoabsorption data, we demonstrate that a sum rule is obeyed in which the coherent and Auger parts add together with the incoherent primary emission to give the energy dependence of photoabsorption.

Sum-rule test for coherent and incoherent contributions to the photoelectron cross section near core-electron resonances in metallic Ni and Pt

Erratum: Dipole-dipole interactions and two-dimensional magnetism [Phys. Rev. B 33, 6519 (1986)]

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Y. Yafet

Author Tools

Chat about Author