Theory of impurity scattering: Interstitial impurities

A framework for studying impurity scattering in dilute, non-magnetic, metal alloys can be developed from a knowledge of the exact electronic eigenstates of a single impurity in an otherwise perfect lattice of muffin tin potentials. Such an approach has been developed for systems in which the impurity occupies a substitutional site of the lattice, as will be discussed by Coleridge, Lee, Harris, and other speakers of this conference. In this paper, motivated by recent experimental studies of Dingle temperature anisotropies induced by hydrogen impurities in copper, we will discuss the analogous treatment of scattering by interstitial impurities. In contrast to a substitutional impurity, an interstitial impurity introduces an additional scattering site into the lattice. Whereas the substitutional impurity wavefunctions can be described in terms of the same structure factors as can the Bloch wavefunctions for the pure host lattice, the interstitial impurity wavefunctions depend upon additional structure factors appropriate to the new scattering geometry. These additional structure factors appear in the transition matrix for impurity-induced scattering between Bloch states of the host lattice, and consequently in the weight factors involved in a partial wave analysis of the Dingle temperature anisotropies.This work was supported by the National Science Foundation through the Materials Research Laboratory at the University of Chicago.     

Theory of inelastic scattering from magnetic impurities

We use the numerical renormalization group method to calculate the single-particle matrix elements T of the many-body T matrix of the conduction electrons scattered by a magnetic impurity at T=0 temperature. Since T determines both the total and the elastic, spin-diagonal scattering cross sections, we are able to compute the full energy, spin, and magnetic field dependence of the inelastic scattering cross section sigma(inel)(omega). We find an almost linear frequency dependence of sigma(inel)(omega) below the Kondo temperature T(K), which crosses over to a omega(2) behavior only at extremely low energies. Our method can be generalized to other quantum impurity models.     

Theory of charged impurity scattering in two-dimensional graphene

We review the physics of charged impurities in the vicinity of graphene. The long-range nature of Coulomb impurities affects both the nature of the ground state density profile and graphene’s transport properties. We discuss the screening of a single Coulomb impurity and the ensemble averaged density profile of graphene in the presence of many randomly distributed impurities. Finally, we discuss graphene’s transport properties due to scattering off charged impurities both at low and high carrier density.     

Theory of resonant inelastic X-ray scattering spectrum for Ni impurities in cuprates

We perform the numerically exact diagonalization calculation for small Cu-O clusters with a Ni impurity site, representing the Ni-substituted cuprate, to examine the single-particle excitation spectra as well as the resonant inelastic X-ray scattering (RIXS) spectra. We clarify relations between low-energy electronic structures near the Ni site and excitations seen in the RIXS spectra.     

Theory of charge-carrier scattering on ionized impurities in anisotropic semiconductors of p-Ge type

The method developed in [10] is used as the basis for a theory of chargecarrier scattering on ionized impurities in anisotropic semiconductors of type p-Ge. A general expression is obtained for the nonequilibrium hole distribution function, and is used to calculate the hole mobility in p-Ge at temperatures 10°KT70°K. The complexity of the band structure and the specific features of the scattering mechanism are taken into account. The results obtained are in good agreement with experimental data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 117–123, January, 1978.The computer calculations were carried out by M. V. Ostapovich to whom thanks are due.     

Neutral impurity scattering in semiconductors

Summary Applying the correlation function technique, a temperature-independent mobility μ_n has been obtained and it is shown that this μ_n remains close to the experimental mobility ofn-type Ge around 10 K.     

Correlated charged impurity scattering in graphene

We study electron transport properties of graphene in the presence of correlated charged impurities via adsorption and thermal annealing of potassium atoms. For the same density of charged scattering centers, the sample mobility sensitively depends on temperature which sets the correlation length between the scatterers. The data are well-understood by a recent theory that allows us to quantitatively extract the temperature dependence of the correlation length. Impurity correlations also offer a self-consistent explanation to the puzzling sublinear carrier-density dependence of conductivity commonly observed in monolayer graphene samples on substrates.     

Host lattice effects in impurity scattering

The problem of separating host lattice and impurity effects is discussed with reference to the interpretation of experimental lifetime anisotropies in dilute alloys.     

Dynamical conductivity of heavy fermion systems: effect of impurity scattering

The influence of impurity scattering on a heavy fermion system is studied within a mean-field approximation of the Anderson Hamiltonian and using a coherent potential approximation for the impurity scattering. Two types of scattering mechanisms are investigated: missingf-ions and potential scatterring centers. The dynamical conductivity shows a nearow peak at low frequencies scaling with the effective mass of the heavy quasi-particles together with a peak at finite frequencies due to interband transitions. These features are also found in experimental results on heavy fermion systems.     

Theory of transport by impurities

The method of the B(t) field is used to analyze conductivity by means of impurities. The case of nonmetallic conductivity with a low degree of compensation is discussed. It is shown that the activation energy in the representation of the B(t) field is equal to the binding energy in the trap. The anomalous dependence on the degree of compensation is also confirmed.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 12, No. 7, pp. 65–69, July, 1969.     

Anisotropic impurity scattering in palladium silver alloys

Measurements have been made of the Hall coefficientR of some alloys of silver in palladium over the temperature range 1°K to 120°K. The alloys contain between ∼1 and ∼10 at.-% silver. Values ofR were also obtained at room temperature and these were in good agreement with earlier published work. The values ofR are negative in all the alloys, and |R| increases both on reducing the temperature and increasing the silver concentration,c. Below ∼10°K, |R| becomes independent of temperature but shows a linear dependence onc, increasing by a factor of 2.5 over the concentration range measured. This increase is too great to be accounted for in terms of band structure changes alone, so we have examined the effects of anisotropic impurity scattering. To a first approximation it can be shown thatR is proportional to an anisotropy parameterA, defined asA=〈τ ²(k)〉/〈τ(k)〉², whereτ(k) represents the relaxation time of an electron in a statek, and 〈〉 is an average over the Fermi surface. In palladium we assume that the majority of the current is carried by the s-electrons. In the presence of silver impurities these electrons can be scattered into s-states or d-states with relaxation times given byτ _ss α1/c(1−c) andτ _sd α1/c ²(1−c) respectively. FollowingPlate we have assumed thatτ _ss is isotropic and thatτ _sd is anisotropic, leading to an overall anisotropic relaxation time for impurity scattering. We then find the parameterA increases approximately linearly with silver content, in accordance with our experimental results.     

Energy and impurity solubility in a crystal containing interstitial impurities

The energy and the impurity solubility are calculated for a crystal containing impurities in octahedral, tetrahedral, and triangular interstitial sites. The energy advantage is derived for distribution of implanted atoms in various types of interstitial sites, along with the accompanying increase in the impurity solubility that accompanies this process.State University, Dnepropetrovsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 31–38, August, 1994.     

Quadrupole scattering: Resistivity anisotropy of rare earth impurities in gadolinium

We report measurements of the resistivity of rare-earth impurities in gadolinium in transverse and longitudinal magnetic fields. The resistivity anisotropy turns out to be mainly induced by the interaction of the conduction electrons with the electric quadrupole of the rare-earth impurities. The interpretation of the experimental data allows us an approximate determination of this interaction.     

Resonant and non-resonant soliton scattering by impurities

The NLSE soliton scattering by impurities is considered in the framework of the one-dimensional model. The scattering intensity is characterized by the reflection coefficient of the soliton is calculated in the Born approximation of the perturbation theory for the following cases: (i) and isolated impurity, (ii) two point impurities, and (iii) a regular or random system of point impurities. An analytical comparison with the scattering of linear waves is carried out. In particular, we analytically describe the nonlinear resonant scattering by two point impurities, and the non-resonant soliton scattering by a random system of point impurities.     

Theory for impurity assisted tunneling

A tunneling formalism is presented which goes beyond the usual Transfer-Hamiltonian model. In order to study many body interactions an expression for the conductance is derived in terms of the one particle scatteringt-matrix.     

Self-consistent calculation of impurity scattering in inversion layers

The local density-functional method has been applied to the calculation of the influence of an ionized impurity on the electrons in an inversion layer on the surface of silicon. Compared to linear screening theories this theory shows improved agreement with experiments on the mobility. The bound state associated with the self-consistent potential has a very small binding energy.     

Skew scattering by rare-earth impurities in silver

We have studied the Hall effect of silver containing rare-earth impurities (Gd, Tb, Dy, Ho, Er, Tm, Nd) between 1.2 and 40° K. It turns out that skew scattering by the rare-earth impurities contributes strongly to the Hall effect. The variation of the skew scattering in the rare-earth series allows us to separate what is due respectively to anisotropic terms of the k-f and of the k-d interactions.