Interaction of long wavelength phonons with conduction electrons in impure metals

A formalism is developed to treat the interaction between electrons and the currents set up in a metal by the motion of the ions by many body techniques. As is known from the theories of ultrasonic absorption this interaction is important for the damping of transverse phonons. To write the interaction Hamiltonian in a convenient form we introduce a 4-component quantized electromagnetic field. This allows us to treat longitudinal and transverse phonons in a completely analogous fashion. Impurities, which act as scattering centers for electrons, are included in the theory. The Fourier transformv(p) of the impurity potential is taken to be an arbitrary function of momentump. A set of diagrams in the perturbation expansion of the phonon Green function is discussed that for constantv(p) yields well established expressions for the absorption coefficients of ultrasound.     

Dirac electrons in solids

Electronic band structures in solids sometimes have features similar to Dirac electrons in vacuum. Well-known examples are bismuth and graphite; 4×4 original Dirac matrix in three dimension (3d) in the former with strong spin–orbit interaction, while 2×2 massless Dirac in two dimension (2d) with weak inter-layer coupling described essentially by Weyl equation in the latter. Recently one layer of graphite, graphene, is realized and studied both extensively and intensively. Other recent examples include a molecular solid, α-(BEDT-TTF)₂I₃$\mathrm{\alpha }\mathrm{-}(\mathrm{BEDT}\mathrm{-}\mathrm{TTF}{)}_2{\mathrm{I}}_3$, which has a layered structure with electronic states described by tilted-Weyl equation, and Fe-pnictides. There is also a theoretical proposal that one of inverse perovskites, Ca₃PbO, can be a candidate in 3d with strong spin–orbit interaction similar to bismuth. The particular feature of Dirac electrons in solids is a small, or even vanishing, band gap and then thermodynamic or transport properties are affected by inter-band coupling of electronic states. Typical ones are responses to external magnetic field. Actually, it has long been known that orbital susceptibility of these Dirac electrons has very particular features resulting from inter-band effects of magnetic field. It is of interest to see such inter-band effects on Hall effects to be compared with orbital susceptibility, which will be introduced in this paper, together with possible consequences of mutual interaction between valleys triggered by tilting in molecular solids.     

Interaction of conduction electrons with local excitations. The infrared divergencies

Using the renormalization group method the higher orders of perturbation theory in the interaction of conduction electrons in metals with local paulions (pseudospins), e.g. two-level systems, crystal-field excitations, and bosons, e.g. phonons, are considered. For the paulions, the lowest order logarithmic singularities in the electron self-energy at =E–E _F±, being the splitting, become weaker, at least in the commutative model. It is shown that the singularities of the type ln are absent. This justifies the applicability of the second order perturbation theory resultm ^{* –1} for the electron effective mass even atm ^*m. For the phonons, the singularities at ±₀, ₀ being the phonon frequency, may become stronger or weaker depending on the conduction band filling and the anharmonic contribution to the deformation potential. The singular contributions to the local excitation Green's function are calculated. They result in the change of the line shape of the local level (the orthogonality catastrophe). The singular terms in the ground state energy and average pseudospin are considered.     

Attenuation lengths of low-energy electrons in solids

A compilation is presented of measured attenuation lengths of low-energy electrons in solids in the energy range (40 to 2000 eV) normally employed in X-ray photoelectron and Auger-electron spectroscopy. The techniques used to obtain electron attenuation lengths are summarized, and it is pointed out that the accuracy of measurement needs both to be defined adequately and to be improved for more meaningful intercomparisons of data and theory. An approximate expression is derived to predict attenuation lengths using either dielectric data (derived from optical or electron-energy-loss data) or average excitation energies estimated from electron binding energies for given materials at electron energies greater than about 500 eV. Good agreement is found between the predictions of this formula and some measured attenuation lengths (e.g. for Al, C, Mo, W) but further work is required to validate the formula and to extend it to lower electron energies.     

Inelastic scattering of slow electrons in solids

A theory of the inelastic scattering of slow electrons in solids due to excitation of interband transitions is developed. It is shown that both nondirect and direct transitions occur which can be described by a generalization of the formalism used in solid state optics. Experiments with 30–200 eV electrons scattered from Si (111) surfaces with well defined surface structures as determined by low energy electron diffraction confirm the theoretical predictions. They indicate that the inelastic scattering of slow electrons can be understood in terms of the three-dimensional band structure of solids and suggest the use of inelastic low energy electron scattering as a tool for band structure analysis.     

Hysteresis and memory of the magnetic resonance of conduction electrons in solids. From bistability to stochastic resonance

The magnetic resonance line of conduction electrons in solids may exhibit bistable hysteresis if several conditions are fulfilled. Its mechanism is presented and the manifestation of bistability in the ESR of conduction electrons in single crystal and polycrystalline samples is discussed. The characteristics of the dynamics of the bistability show that bistable resonance can be assimilated to one-dimensional overdamped motion of the spin system in the nuclear field space, driven by a bistable potential. It is shown for the first time that noise acting on this bistable resonance can create order, by the phenomenon of stochastic resonance.     

Spin relaxation of conduction electrons in GaAs

We have used optical spin orientation techniques to measure T₁ of conduction electrons in GaAs (NinA ≈ 10¹⁷ cm^-3) for 4.7 K ? T ? 200 K. From Hall effect measurements we estimated the electron momentum relaxation time τ_p. For 50 K ? T ? 200 K, the product T₁τ_p agrees with our earlier order of magnitude estimate of the D'yakonov-Perel' mechanism, in which band structure induced precession is strongly narrowed by momentum relaxation. The Elliott mechanism is one to two orders of magnitude weaker.     

Spin-orbit symmetries of conduction electrons in silicon

We derive a spin-dependent Hamiltonian that captures the symmetry of the zone edge states in silicon. We present analytical expressions of the spin-dependent states and of spin relaxation due to electron-phonon interactions in the multivalley conduction band. We find excellent agreement with experimental results. Similar to the usage of the Kane Hamiltonian in direct band-gap semiconductors, the new Hamiltonian can be used to study spin properties of electrons in silicon.     

Zeeman splitting of conduction electrons in nickel-doped palladium

The ratio between the Zeeman splitting and the Landau level spacing of the electrons at the Fermi level in palladium is found to be strongly dependent on nickel impurities.     

纳米金属镝的传导电子定域化

研究不同粒径的稀土金属镝(Dy)纳米晶块体材料的电阻率随温度的变化. 电阻率包括剩余电阻率ρ_res=ρ(0)、磁散射电阻率ρ_mag(T)和声子散射电阻率ρ_pho(T). 样品的平均粒径分别为10,30,100和1000 nm. 实验发现磁散射电阻率ρ_mag(T)和声子散射电阻率ρ_{pho 关键词： 镝金属电性 定域化 能带论 无序}     

Kinetics of the conduction electrons in multidomain ferromagnets

The kinetic properties of conduction electrons in ferromagnets with periodical domain structure are studied. The appearance in the problem of the new parameter of length dimension - the period of domain structure 2d allows one to distinguish three groups of electrons whose trajectories qualitatively differ from those in a case of a homogeneous magnetic field. It has been shown that the absorption of high frequency field is of a resonance type. The resonance frequencies are simply connected with a period of the domain structure (ω_res = π (V_F/d), V_F Fermi velocity). The resonance curve shape is obtained.     

Scattering of conduction electrons by vacancies in aluminium

The low-field Hall coefficientR _H ⁰ and transverse magnetoresistance /₀ were measured in high-purity polycrystalline aluminium samples which were quenched from temperatures between 350 and 500°C. The measurements were made at 4.2 K in magnetic fields up to 40 kG. It was found that the low-field Hall coefficientR _H ⁰ of aluminium containing vacancies lies between –1.0 and –2.5×10^–5 cm³ A^–1s^–1, which is in good agreement with the calculation of Pfändner, Böning and Brening.     

Variable range hopping conduction in semiconductor nanocrystal solids

The temperature and electrical field dependent conductivity of n-type CdSe nanocrystal thin films is investigated. In the low electrical field regime, the conductivity follows sigma approximately exp([-(T(*)/T)(1/2)] in the temperature range 10相似文献   

Localization of conduction electrons in the ferromagnetic clusters AuFe

The optical-conductivity spectra of concentrated solutions Au_{1 ? x} Fe _x with x = 17 and 22 at % have been measured in a frequency range of (10–33) × 10³ cm^?1 at room temperature. The results are analyzed together with previous optical data obtained for compounds with x = 4–12 at %. It is found that the magnetic contributions σ_magn = σ_AuFe ? σ_Au to dc and low-frequency(10 cm^?1) conductivities for an Fe concentration below 4 at % are almost equal, while the low-frequency magnetic contribution for larger concentrations is significantly larger than the dc one. An absorption band at frequencies of 1000–3000 cm^?1 has been found for samples with concentrations x = 6–22 at %. The observed phenomena are attributed to the localization of electrons inside clusters containing ferromagnetically ordered iron ions.     

Spin properties of conduction electrons in the noble metals

The g-factors of the conduction electrons have been determined for various orientations of magnetic field in Cu, Ag and Au crystals from de Haas-van Alphen oscillation amplitudes at temperatures high enough to avoid magnetic interaction.     

The spin polarization of conduction electrons in ferromagnetic semiconductors

Within the framework of the s?f exchange model the exact asymptotics of the spin polarization of conduction electrons in the non-degenerate ferromagnetic semiconductor at low temperatures is calculated. It is demonstrated that the temperature dependent corrections to the total density of states are proportional to $\text{T}{}^{\mathrm{<mtext>5</mtext><mtext>2</mtext>}}$.     

Surface properties of a network model of electrons in solids

Surface properties of a network model of electrons in solids are discussed. In the model, electrons are restricted to move along lines connecting node points of a periodic network. Each node point on the network corresponds to an atom. A potential well is introduced for each atom or node point so that as the depth of the potential becomes large, one has the tight binding model and, as the potential vanishes and the number of node points increases, one has the Sommerfeld free electron model. Exact wave functions and energy levels have been obtained elsewhere for the model when periodic boundary conditions are applied.When free boundaries are introduced, a band of surface states develops. Its depth of penetration into the crystal as a function of wave number is investigated. The edges of the surface energy bands are located and their density of states is calculated.     

Attenuation length and escape depth of excited electrons in solids

Escape probability and mean escape depth λ_e of emitted electrons are determined as a function of attenuation length λ_a of excited electrons, their initial energy E_n, and the height of the surface barrier χ. A variable energy loss parameter permits to apply the proposed model to different kinds of electron emission, including the energy loss free Auger and ESCA electrons. An analytical expression was found correlating the internal energy distribution of excited electrons and the external energy distribution of emitted electrons. By means of this excitation energies of secondary electrons and exoelectrons were determined.