On the dynamics of electrons in an impure metal

The inelastic scattering of the electrons of an impure metal by a screened Coulomb interaction is investigated. It is found that the rate of such an inelastic scattering is increased which can be explained by a loss of momentum conservation which in turn results from loss of translational symmetry introduced by the defects of an impure metal. Eventually, a linearised Boltzmann equation is derived for time and space dependent perturbances of the electronic distribution function. The collision integral takes into account impurity scattering as well as electron-electron and electron-phonon scattering. In an impure metal the terms corresponding to the last two processes are modified as discussed above and in a previous paper on the electron-phonon interaction.     

Role of elastic scattering in electron dynamics at ordered alkali overlayers on Cu(111)

Scanning tunneling spectroscopy of p(2 x 2) Cs and Na ordered overlayers on Cu(111) reveals similar line widths of quasi-two-dimensional quantum well states despite largely different binding energies. Detailed calculations show that 50% of the line widths are due to electron-phonon scattering while inelastic electron-electron scattering is negligible. The mechanism of enhanced elastic scattering due to Brillouin zone backfolding contributes the remaining width.     

To the question on electron-electron scattering in metals

Temperature dependence of the scattering rate in copper and aluminium has been investigated by the radio frequency size effect with the aim of extracting the contribution of electron-electron collisions. The scattering rate is varied by the cubic law on the wide temperature range (1.2–10°K), which is due to the electron-phonon interaction. On the basis of modern representations on the electron-electron interactions, the absence of the quadratic term in the probability of scattering of charge carriers in these metals, close to the transition ones, is discussed.     

Ultrasonic attenuation in copper at low temperatures

Ultrasonic attenuation in copper at low temperatures has been analysed in terms of electron-electron and electron-phonon interactions. The contribution due to electron-electron interactions has been evaluated using a simplified spherical Fermi-surface model with an isotropic Umklapp transition probability. We observe that the contribution to the attenuation constant (α) due to electron-electron scattering in copper at 3 K is about 10% of the electron-phonon contribution. We have also considered the viscous attenuation and the induction attenuation mechanisms simultaneously in copper as suggested by Orlov and find that our results improve the existing theoretical data considerably.     

Theory of electron-electron interaction and superconductivity in dilute magnetic alloys above the Kondo temperature

The effective electron-electron interaction resulting from the virtual polarization of the impurity spin is investigated. Abrikosov's pseudofermion representation of spin operators has been applied. It is pointed out that the effective electron-electron interaction consists of two parts: 1) elastic scattering; 2) inelastic scattering. The second part shows a singularity of new type as (ω-ω′)^?1, whereω-ω′ is the energy transfer between the two electrons. Both parts have been calculated in logarithmic approximation. Inspite of the fact that the second one is found to be lower by one order of the typical logarithmic Kondo terms than the first one, both terms can be of the same order of magnitude. Studying the superconducting transition temperature Abrikosov and Gor'kov's calculation is extended to include these interactions in any order of perturbation theory keeping the leading logarithmic terms. Our results are restricted to the temperature region well above the Kondo temperature. Considering the decrease of the superconducting transition temperature due to the magnetic impurities in the antiferromagnetic case the effect of the elastic scattering can be essentially reduced by the inelastic one.     

Critical dynamics and multifractal exponents at the Anderson transition in 3d disordered systems

We investigate the dynamics of electrons in the vicinity of the Anderson transition in d = 3 dimensions. Using the exact eigenstates from a numerical diagonalization, a number of quantities related to the critical behavior of the diffusion function are obtained. The relation η = d ? D₂ between the correlation dimension D₂ of the multifractal eigenstates and the exponent η which enters into correlation functions is verified. Numerically, we have η ≈? 1.3. Implications of critical dynamics for experiments are predicted. We investigate the long-time behavior of the motion of a wave packet. Furthermore, electron-electron and electron-phonon scattering rates are calculated. For the latter, we predict a change of the temperature dependence for low T due to η. The electron-electron scattering rate is found to be linear in T and depends on the dimensionless conductance at the critical point.     

Dephasing and weak localization in disordered Luttinger liquid

We study the transport properties of interacting electrons in a disordered quantum wire within the framework of the Luttinger liquid model. The conductivity at finite temperature is nonzero only because of inelastic electron-electron scattering. We demonstrate that the notion of weak localization is applicable to the strongly correlated one-dimensional electron system. We calculate the relevant dephasing rate, which for spinless electrons is governed by the interplay of electron-electron interaction and disorder, thus vanishing in the clean limit.     

Q-dependent light scattering by electrons in LaB6

The inelastic light scattering by intraband electronic excitations in metallic lanthanum hexaboride has been studied in the temperature range of 10–300 K. General agreement has been obtained between the measured spectra and the spectra calculated within the band theory taking into account the renormalization of electron energies owing to electron-phonon scattering. The electron-phonon coupling constant λ and electron relaxation frequency Γ have been estimated. The dependence of the electron self-energies on the direction and magnitude of the wave vector has been revealed, implying the anisotropic electron-phonon interaction or the contribution from other electron scattering mechanisms.     

Lifetimes of electronic excitations in unoccupied surface states and the image potential states on Pd(110)

The contribution of inelastic electron-electron scattering to the decay rate of excitations in the surface states and first two image potential states at the ? point on the surface is calculated in the GW approximation, and the quasi-momentum dependence of the corresponding contribution for the surface states is analyzed. The mechanisms of electron scattering in these states are studied, and the temperature dependence of the excitation lifetime is analyzed with allowance for the contribution of the electron-phonon interaction calculated earlier.     

Al0.22Ga0.78N/GaN二维电子气中的弱局域和反弱局域效应

通过磁输运测量研究了Al_0.22Ga_0.78N/GaN二维电子气的电子相干散射中的弱局域和反弱局域化现象.在外加弱磁场的情况下，该系统表现出正-负磁阻的变化，说明在Al_0.22Ga_0.78N/GaN异质结中存在晶体场引起的电子自旋-轨道散射.同时讨论了二维电子气中不同的散射时间对温度的依赖关系，实验得到的非弹性散射时间与温度成反比，表明非弹性散射机理主要来源于小能量转移的电子-电子散射. 关键词： 二维电子气 弱局域 磁阻     

Interband transitions and electronic Raman continuum in systems with strong inelastic scattering: Applications to YBa2Cu3O7-δ

We consider a model for the electronic Raman continuum which takes into account strong inelastic scattering and interband transitions. Calculations are based on four-vertex Raman scattering diagrams (Kawabata formalism) within the RPA for Coulomb interaction and the ladder diagram Bethe-Salpeter equation for the vertex. We apply this method to an analysis of the nature of the electronic Raman continuum in the normal state of the high-T _c superconductor YBa₂Cu₃O₇. In numerical calculations we take into account all the self-energy effects and make simulations for vertex corrections assuming that inelastic scattering is due to electron-phonon interaction. Theab-plane polarized continuum contains a large contribution from interband processes and does not depend strongly on temperature and inelastic scattering strength. The in-plane anisotropy is determined by interband transitions rather than by anisotropy of the Fermi surface. The ZZ continuum contains only weak contribution from interband transitions. It can be crudely described within a single band model with inelastic scattering and is strongly dependent on the relaxation rates of inelastic scattering. The nature of the oxygen-deficiency dependence of the Raman spectra is also commented upon.     

Electron dephasing of a GaAs/AlGaAs quantum well with self-assembled InAs dots

We study the magnetotransport of a GaAs/AlGaAs quantum well with self-assembled InAs quantum dots. Negative magnetoresistance is observed at low field and analysed by weak localization theory. The temperature dependence of the extracted dephasing rate is linear, which shows that the inelastic electron-electron scattering processes with small energy transfer are the dominant contribution in breaking the electron phase coherence. The results are compared with those of a reference sample that contains no quantum dots.     

Effects of absorbed hydrogen on the electronic properties of (Zr2Fe)(1-x)H(x) metallic glasses

The electrical conductivity (σ) of hydrogen doped (Zr(2)Fe)(1-x)H(x) metallic glasses has been measured in the temperature range from 290 down to 5 K. The decrease of the room temperature conductivity and the increase of its temperature coefficient are explained as consequences of increased disorder due to hydrogen doping. σ(T) for (Zr(2)Fe)(1-x)H(x) metallic glasses at low temperatures decreases with the increase of temperature, forming a minimum at T(min), before it starts a monotonic increase with increasing temperature. Both the functional forms and the magnitudes of the observed σ(T) are interpreted in terms of weak localization, electron-electron interaction and spin-fluctuation effects. Our results reveal that the electron-phonon scattering rate varies with the square of temperature from low temperatures up to 100 K and changes behaviour to a linear form at higher temperatures. At low temperatures, the minimum in σ(T) is shifted to higher temperatures, which is ascribed to the increase of the screening parameter of the Coulomb interaction F* associated with the enhancement of the spin fluctuations arising from the increase of the hydrogen doping. The spin-orbit scattering rate and the electron diffusion constant are reduced by hydrogen doping.     

Light scattering by electrons and renormalization of the electron spectrum in osmium

The temperature-dependent inelastic light scattering by electrons in osmium is studied at different values and directions of the wave vector. The frequency dependence for the spectra of electronic light scattering is modeled based on the calculated band structure taking properly into account the effects of inelastic scattering. A comparison of the measured and calculated spectra suggests the dominant role of the electron-phonon scattering in the energy range under study. This allows us to estimate the temperature-dependent renormalization of the electron velocity and the decay rate for the electron states.     

Electromagnetically induced transparency in asymmetric double quantum wells

We show how to compute nonlinear optical absorption spectra of an Asymmetric Double Quantum Well (ADQW) in the region of intersubband electronic transitions. The method uses the microscopic calculation of the dephasing due to electron-electron and electron-phonon scattering rates and the macroscopic real density matrix approach to compute the electromagnetic fields and susceptibilities. The polarization dephasing and the corrections to the Rabi frequencies due to the electron-electron interaction are also taken into account. For a proper choice of the QW widths and of the driving fields we obtain electromagnetically induced transparency. This transparency has a very narrow linewidth when a single driving field is applied resonant to the transition between the second and the third subband. In the case of two resonant driving fields or of a driving field resonant between the first and third subband we obtain a large transparency enhancement over the entire absorption spectrum. Results are given for GaAs/GaAlAs QWs and experiments are proposed. Received 21 June 2001 and Received in final form 21 January 2002     

Temperature dependence of the electrical resistivity and deviations from matthiessen's rule of Pd-Er alloys

Measurements are presented of the electrical resistivity for a series of Pd_1−cEr_c (c = 0, 0.5, 1.0, 1.93, 3.97, 5.20, and 6.63 at.%) alloys in the temperature range from 4 to 1200 K. No Kondo-like anomaly is found in each resistivity curve down to the lowest temperature. The experimental data were interpreted by electron-phonon scattering and electron-electron scattering mechanisms. Finally, the deviations from Matthiessen's rule of this alloy system are discussed in general.     

Weak localization of Dirac fermions in graphene

In the presence of the charged impurities, we study the weak localization effect by evaluating the quantum interference correction to the conductivity of Dirac fermions in graphene. With the inelastic scattering rate due to electron-electron interactions obtained from our previous work, we investigate the dependence of the quantum interference correction on the carrier concentration, the temperature, the magnetic field, and the size of the sample. It is found that weak localization is present in large size samples at finite carrier doping. Its strength becomes weakened or quenched when the sample size is less than a few microns at low temperatures as studied in the experiments. In the region close to zero doping, the system may become delocalized. The minimum conductivity at low temperature for experimental sample sizes is found to be close to the data.     

Optical self-energy in graphene due to correlations

In highly correlated systems one can define an optical self-energy in analogy to its quasiparticle (QP) self-energy counterpart. This quantity provides useful information on the nature of the excitations involved in inelastic scattering processes. Here we calculate the self-energy of the intraband optical transitions in graphene originating in the electron-electron interaction (EEI) as well as electron-phonon interaction (EPI). Although optics involves an average over all momenta (k) of the charge carriers, the structure in the optical self-energy is nevertheless found to mirror mainly that of the corresponding quasiparticles for k equal to or near the Fermi momentum k(F). Consequently, plasmaronic structures which are associated with momenta near the Dirac point at k = 0 are not important in the intraband optical response. While the structure of the electron-phonon interaction (EPI) reflects the sharp peaks of the phonon density of states, the excitation spectrum associated with the electron-electron interaction is in comparison structureless and flat and extends over an energy range which scales linearly with the value of the chemical potential. We introduce a method whereby detailed quantitative information on such excitation spectra can be extracted from optical data. Modulations seen on the edge of the interband optical conductivity as it rises towards its universal background value are traced to structure in the quasiparticle self-energies around k(F) of the lower Dirac cone associated with the occupied states.     

On the relaxation of the order parameter in the BCS model

The relaxation of the nonequilibrium order parameter (wave function of pairs) of a “pure” superconductor is considered for the homogeneous case. The relaxation is due to the electron-phonon interaction. The orderparameter relaxation time is shown to be much longer than the time interval between electron-electron collisions. This relation is explained by the smallness of the superconducting transition temperature compared to both the Fermi energy and the Debye energy in the BCS model.     

Interaction and localization effects in two-dimensional film of superconductor at T > Tc

The magnetic field and temperature dependence of the resistance of thin Al films have been investigated at T > T_c (T_c - superconducting transition temperature). The results are explained on the basis of localization and electron-electron interaction theory in two-dimensional disordered systems. The temperature dependence of inelastic scattering time and interaction constant for such films is found.