ELECTRON–PHONON INTERACTION AND ELECTRONIC STRUCTURE OF SMALL METAL CLUSTERS

1996 ◽  
Vol 03 (01) ◽  
pp. 489-492 ◽  
Author(s):  
JIJUN ZHAO ◽  
XIAOSHUANG CHEN ◽  
FENGQI LIU ◽  
GUANGHOU WANG
Keyword(s):  
Electronic Structures ◽  
Metal Clusters ◽  
Energy Levels ◽  
Iteration Process ◽  
Coupling Constant ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Size Dependent ◽  
Electron Phonon Coupling ◽  
Valence Electrons

The Su–Schrieffer–Heeger (SSH) Hamiltonian has been extended to study the electron–phonon interaction and the electronic structures of the alkali-like metal clusters. The eigen-energy levels of s valence electrons are obtained from a Hückel-like Hamiltonian including the correction of the electron–phonon interaction in the hopping integral, which is proportional to the variable of bond length. The self-consistent equations for electrons and phonons are solved adiabatically through an iteration process. The energy-level structures of an octahedral Cu6 cluster are calculated with variable electron–phonon coupling constant λ to investigate the influence of electron–phonon interaction on the lattice distortion and electronic structures of metal clusters. The size-dependent ionization potential for small Cun clusters are calculated and compared with the experimental results.

ELASTIC PROPERTIES OF THE Zn SUBSTITUTED ErBa2Cu3O7-δ SUPERCONDUCTOR

2003 ◽  
Vol 17 (02) ◽  
pp. 75-82
Author(s):  
T. V. CHONG ◽  
R. ABD-SHUKOR
Keyword(s):  
Longitudinal Velocity ◽  
Shear Velocity ◽  
Spin Correlation ◽  
Coupling Constant ◽  
Phonon Coupling ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling ◽  
Overlap Method ◽  
Pulse Echo

Ultrasonic longitudinal and shear velocity in superconducting ErBa 2( Cu 3-x Zn x) O 7-δ (x = 0, 0.01 and 0.05) have been measured using the pulse-echo-overlap method at frequency 5–10 MHz in the temperature range 80–300 K. Longitudinal velocity hysteresis and elastic anomaly were observed in the x = 0 sample. Similar hysteresis was not observed in the x = 0.01 and 0.05 samples. The characteristic Debye temperature and electron–phonon coupling constant were calculated. The absence of hysteresis for longitudinal velocity in the x = 0.01 and 0.05 samples may be due to the spin correlation at the CuO 2 planes which affects the electron–phonon interaction.

Pseudo-Anomalous Size-Dependent Electron–Phonon Interaction in Graded Energy Band: Solving the Fano Paradox

2021 ◽  
pp. 2044-2051
Author(s):  
Manushree Tanwar ◽  
Devesh K. Pathak ◽  
Anjali Chaudhary ◽  
Alexander S. Krylov ◽  
Herbert Pfnür ◽  
...  
Keyword(s):  
Energy Band ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Size Dependent

scholarly journals ON THE PHONON-INDUCED SUPERCONDUCTIVITY OF DISORDERED ALLOYS

1996 ◽  
Vol 10 (20) ◽  
pp. 2469-2529 ◽  
Author(s):  
A.O. ANOKHIN ◽  
M.I. KATSNELSON
Keyword(s):  
Effective Interaction ◽  
Energy Scale ◽  
Phonon Interaction ◽  
Interaction Kernel ◽  
Generating Functional ◽  
Electron Phonon Interaction ◽  
Self Energy ◽  
Disordered Alloys ◽  
Electron Phonon Coupling ◽  
Alloy Part

A model of alloy is considered which includes both quenched disorder in the electron subsystem (“alloy” subsystem) and electron-phonon interaction. For given approximate solution for the alloy part of the problem, which is assumed to be conserving in Baym’s sense, we construct the generating functional and derive the Eliashberg-type equations which are valid to the lowest order in the adiabatic parameter. The renormalization of bare electron–phonon interaction vertices by disorder is taken into account consistently with the approximation for the alloy self-energy. For the case of exact configurational averaging the same set of equations is established within the usual T-matrix approach. We demonstrate that for any conserving approximation for the alloy part of the self-energy the Anderson’s theorem holds in the case of isotropic singlet pairing provided disorder renormalizations of the electron-phonon interaction vertices are neglected. Taking account of the disorder renormalization of the electron-phonon interaction we analyze general equations qualitatively and present the expressions for Tc for the case of weak and intermediate electron-phonon coupling. Disorder renormalizations of the logarithmic corrections to the effective coupling, which arise when the effective interaction kernel for the Cooper channel has the second energy scale, as well as the renormalization of the dilute paramagnetic impurity suppression are discussed.

INFLUENCE OF ELECTRON–PHONON INTERACTION ON EFFECTIVE MASS IN SOME HEAVY FERMION (HF) SYSTEMS

2008 ◽  
Vol 22 (04) ◽  
pp. 365-379 ◽  
Author(s):  
S. MOHANTY ◽  
B. K. KALTA ◽  
P. NAYAK
Keyword(s):  
Effective Mass ◽  
Coupling Strength ◽  
Heavy Fermion ◽  
Simple Expression ◽  
Model Parameters ◽  
Coupling Mechanism ◽  
Phonon Coupling ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling

It is a fact that for ordinary metals, the electron–phonon interaction increases the quasi-particle mass, which is in contrast to the finding by Fulde et al. that, for some heavy Fermion (HF) systems, it decreases. Some experiments on HF systems suggest that there exists a strong coupling of the elastic degrees of freedom with these at the electronic and magnetic ones. To understand the effect of electron–phonon interaction on effective mass, the electron–phonon coupling mechanism in the framework of the periodic Anderson model is considered, and a simple expression is derived. This involves various model parameters namely, the position of the 4f level; the effective coupling strength, g, temperature, b; and the electron–phonon coupling strength, r. The influence of these parameters on the value of effective mass is studied, and interesting results were found. For simplicity, the numerical calculation is performed in the long wavelength limit.

EFFECTS OF ELECTRON–PHONON INTERACTION IN TUNNELING PROCESSES IN NANOSTRUCTURES

2007 ◽  
Vol 06 (05) ◽  
pp. 411-414
Author(s):  
P. I. ARSEYEV ◽  
N. S. MASLOVA
Keyword(s):  
Phonon Coupling ◽  
Phonon Interaction ◽  
Strong Electron ◽  
Resonant Case ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling ◽  
Tunneling Conductivity ◽  
Nonequilibrium Effects ◽  
Inelastic Tunneling

Tunneling through a system with two discrete electron levels coupled by electron–phonon interaction is considered. The interplay between elastic and inelastic tunneling channels is analyzed for a strong electron–phonon coupling in the resonant case. It is shown that the intensity and the width of peaks in tunneling conductivity are strongly influenced by nonequilibrium effects.

OPTICAL PHASE RELAXATION IN DISORDERED SEMICONDUCTORS DUE TO ELECTRON-PHONON COUPLING

1994 ◽  
Vol 08 (07) ◽  
pp. 935-941 ◽  
Author(s):  
V. HEUCKEROTH ◽  
D. BENNHARDT ◽  
P. THOMAS ◽  
H. VAUPEL
Keyword(s):  
Transport Processes ◽  
Localized States ◽  
Phase Relaxation ◽  
Phonon Interaction ◽  
Static Disorder ◽  
Optical Phase ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling ◽  
Simple Model System ◽  
Dephasing Rate

Optical phase coherence can be destroyed by various interaction mechanisms, including scattering by static disorder, electron-phonon interaction and interaction among the optical excitations. The electron-phonon interaction strongly depends on the nature of the electronic states, which in turn is determined by the static disorder. It also gives rise to hopping and phonon-induced delocalization, i.e. to transport. However, there is no one-to-one correspondence between transport processes and dephasing processes in general. Only for strongly localized states can the dephasing rate be identified with the hopping rate. A general formulation of the problem is given and illustrated in terms of a simple model system.

Electron Tunneling in High Tc Superconductors

MRS Bulletin ◽  
1990 ◽  
Vol 15 (6) ◽  
pp. 44-49 ◽  
Author(s):  
J.M. Valles ◽  
R.C. Dynes
Keyword(s):  
Energy Gap ◽  
Electron Tunneling ◽  
Quantitative Description ◽  
Bcs Theory ◽  
Phonon Interaction ◽  
Microscopic Mechanism ◽  
Electron Phonon Interaction ◽  
Current Voltage ◽  
Superconducting Energy Gap ◽  
Electron Phonon Coupling

Electron tunneling measurements have proven enormously valuable in studies of conventional superconductors. Very early measurements confirmed, in an especially convincing way, the existence of the superconducting energy gap, and more detailed studies demonstrated the spectral form of the gap and its temperature dependence. These measurements were instrumental in confirming in some detail the predictions of the Bardeen, Cooper, Schrieffer (BCS) theory of superconductivity in simple metals. For example, it was shown very clearly that the ratio of the energy gap (2Δ) and critical temperature Tc was close to the BCS value (2Δ/kTc = 3.5). As the sophistication of the technique improved, deviations from this BCS weak coupling limit became apparent (2Δ/kTc was measured to be >4 in materials like Pb, for example), and subtle structure in the current-voltage characteristics of tunnel junctions unearthed a signature of the electron-phonon interaction—the microscopic mechanism responsible for superconductivity in these traditional materials. Through a quantitative analysis of this structure, people were able to extract a function α2(ω)F(ω), which is the phonon density of states F(ω) modulated by the electron-phonon coupling function α2(ω). This function gave a quantitative description of the electron-phonon interaction and confirmed beyond a doubt that the electron-phonon interaction was responsible for superconductivity.

THE TEMPERATURE DEPENDENCE OF THE ENERGY LEVELS OF SHALLOW DONOR IMPURITIES IN SILICON

1967 ◽  
Vol 45 (4) ◽  
pp. 1421-1438 ◽  
Author(s):  
C. Y. Cheung ◽  
Robert Barrie
Keyword(s):  
Temperature Dependence ◽  
Energy Levels ◽  
Electronic States ◽  
Shallow Donor ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Doped Silicon ◽  
Phosphorus Doped

A calculation is made of the temperature dependence of the energy levels of shallow donor impurities in silicon. This temperature dependence arises from the electron–phonon interaction and we consider mixing only of the {1s}, {2s), and {2p0} electronic states. A comparison is made with experiment for the case of phosphorus-doped silicon.

Investigations of the Thermal Shifts and Electron–Phonon Coupling Parameters of R1 and R2 Lines for Cr3+-doped Forsterite

2014 ◽  
Vol 69 (8-9) ◽  
pp. 497-500 ◽  
Author(s):  
Xiao-Xuan Wu ◽  
Wen-Chen Zheng
Keyword(s):  
Thermal Expansion ◽  
Spectral Lines ◽  
Coupling Coefficients ◽  
Phonon Coupling ◽  
Lattice Thermal Expansion ◽  
Phonon Interaction ◽  
Electron Phonon Interaction ◽  
Electron Phonon Coupling ◽  
Coupling Parameters ◽  
Vibrational Contribution

The thermal shifts of R1 and R2 lines in Cr3+-doped forsterite (Mg2SiO4) are studied by considering both the static contribution due to lattice thermal expansion and the vibrational contribution due to electron-phonon interaction. In the studies, the thermal expansion coefficient of the Cr3+ center is assumed reasonably as that of the corresponding cluster in the host crystal. The results suggest that for R1 and R2 lines the static contributions are opposite in sign and in magnitude about 37% and 45%, respectively, of the corresponding vibrational contributions. The true electron-phonon coupling coefficients α' (obtained by considering both contributions) increase by about 58% and 81%, respectively, for R1 and R2 lines in comparison with the corresponding parameters α obtained by considering only the vibrational contribution. It appears that for the reasonable explanation of thermal shift of spectral lines and the exact estimation of electron-phonon coupling coefficient, both the static and vibrational contributions should be taken into account

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