Noninteracting electrons and the metal-insulator transition in two dimensions with correlated impurities

While standard scaling arguments show that a system of noninteracting electrons in two dimensions and in the presence of uncorrelated disorder is insulating, in this paper we discuss the case where interimpurity correlations are included. We find that for pointlike impurities and an infinite interimpurity correlation length, a mobility edge exists in 2D even if the individual impurity potentials are random. In the uncorrelated system we recover the scaling results, while in the intermediate regime for length scales comparable to the correlation length, the system behaves like a metal but with increasing fluctuations, before strong localization eventually takes over for length scales much larger than the correlation length. In the intermediate regime, the relevant length scale is given by the interimpurity correlation length, with important consequences for high mobility systems.     

Low-temperature mobility due to unscreened charged impurities in compensated semiconductors

It is proved that within the Fujita theory, the low-temperature values of mobility of charged carriers in compensated semiconductors due to scattering on charged unscreened impurities result temperature independent. The value of is determined by material parameters including the correlations in space among impurities but it is completely independent of the concentration of the charged impurities.     

Low-temperature mobility due to unscreened charged impurities in compensated semiconductors

For the problem of electron scattering on charged unscreened impurities, the scattering rate is calculated self-consistently. The resulting low-temperature mobility is only, slightly temperature dependent and differs from an analogous result of Fujita et al. (J. Phys. Chem. Sol.37 (1976), 227) and Zubarev et al. (Sol. State Commun.21 (1977), 565) by just a change of a numerical constant.     

Theory of cyclotron resonance halfwidth for electrons scattered by impurities and phonons

A general theory of the cyclotron resonance halfwidth for electrons scattered by impurities and phonons is developed on the basis of the proper connected diagram expansion of the current-correlation-function formula for the dynamic conductivity. The theory is applied to the cases of Ge samples at extremely high magnetic fields and different temperatures. The usual form of Matthiessen's rule Γ = Γ₁ + Γ₂ + …, where Γ and Γ_j are the total and component energy-dependent resonance widths, is valid only if the component widths Γ_j computed separately for each cause of scattering depend linearly on the densities of scatterers. The resonance width Γ_I due to the charged impurities at very low electron densities ($\text{\$}\text{?}$10¹² cm^?3) and at very low temperatures is known to vary in proportion to the square-root of the impurity density. Large deviations from the Matthiessen's rule occur in such a case. The theory is in good quantitative agreement with currently available experimental data. In order to test the generalized form of Matthiessen's rule, however, the high-field resonance experiments around 15 K is desirable where both phonon and impurity scatterings contribute in a comparable manner.     

Spin-polarized ground state for interacting electrons in two dimensions

We study numerically the ground state magnetization for clusters of interacting electrons in two dimensions in the regime where the single particle wave functions are localized by disorder. It is found that the Coulomb interaction leads to a spontaneous ground state magnetization. For a constant electronic density, the total spin increases linearly with the number of particles, suggesting a ferromagnetic ground state in the thermodynamic limit. The magnetization is suppressed when the single particle states become delocalized.     

Transport properties of the disordered charged bose condensate in two dimensions

Analytical results for the frequency-dependent conductivity of a disordered two-dimensional interacting Bose condensate are presented. Charged and uncharged impurities are considered. We find that for weak disorder the condensate is a superfluid while for strong disorder it is an insulator (a Bose glass). At the superfluid-insulator transition point (at the critical boson densityN _c) the condensate exhibits metallic tranport properties. An loffe-Regel criterion for the transition point is derived. The conductivity at the transition point is of ordere ²/h (h is Planck's constant) and depends on the kind of disorder. For charged impurities (with impurity densityN _i) the conductivity (for a condensate of particles with charge 2e and forN _i=2N _c) at the transition point is given by _c =0.26x(2e)²/h. We discuss recent experiments on superconducting ultra-thin films and on high-T _c superconductors.     

Skew scattering of the electrons by Ce impurities in La

Low temperature measurements of the Hall effect in lanthanum containing cerium impurities show, in addition to the ordinary Hall effect, a contribution (nearly) proportional to the magnetization of the cerium magnetic moments. We ascribe this contribution to skew scattering by the cerium impurities. The asymmetry of the scattering can result from the mixing of the conduction band and impurity wave functions for impurities having orbital magnetism.     

Two-dimensional electrons in the presence of spin-orbit scattering by impurities

A two-dimensional disordered system of interacting electrons when the principal source of spin relaxation is the spin-orbit scattering by impurities, is studied. It is shown that in this system conductivity has a very complicated behaviour since there is a focus on the phase plane of the renormalization group equations.     

Scattering of electrons by charged dislocations in InSb-type semiconductors

Electron scattering by parallel arrays of charged dislocations in InSb-type semiconductors is considered. In the theoretical approach the nonparabolic structure of the conduction band of the semiconductors considered is taken into account in the approximation of a simplified Kane's band model. The effect of screening by free electrons of the dislocation charge is also included in the theory. The calculated relaxation time of the electrons is used to derive a formula for the dislocation-limited electron mobility in the semiconductors. Some examples of calculations of the charged dislocation-limited mobility as a function of the electron concentration with the dislocation density as a parameter are given for n-InSb at 77 K and 300 K. The ratio of the magnitudes of the charged dislocation-limited mobility to the ionized impurity-limited mobility in n-type material at low temperatures is also discussed.     

Local-field correction of the charged Bose condensate for two and three dimensions

The local-field correction for the dielectric function of the two-dimensional and of the three-dimensional Bose condensate is calculated within a sum-rule version of the Singwi et al. (Phys. Rev.176, 589 (1968)) approach. We derive analytical expressions for small and large wave numbers and give analytical expressions for the density dependence. We compare the results of the groundstate energy for the three-dimensional system with Monte-Carlo computations. In two dimensions a roton structure in the plasmon dispersion is found at low boson density. The plasmon density of states is calculated. A correlation induced charge-density-wave instability in layered structures of two-dimensional Bose gases is discussed.     

The role of finite hole mass in the negatively charged exciton in two dimensions

The role of finite hole mass on the ground and excited states of the negatively charged exciton in two dimensions is discussed. We present results of configuration-interaction calculation using exact excitonic states and results of a variational calculation of the ground-state energy to elucidate the interplay of finite hole mass and electron–electron interactions.     

Criterion for binding two electrons at a fixed center in three dimensions

We consider the criterion for a donor atom to bind two electrons, as a function of the electron-electron repulsion U and the electron-donor attraction ν, and obtain bounds for the critical curve U_c(ν) in three dimensions. We also correct some statements in our earlier papers on 1D and 2D.     

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.     

Probing disorder and charged impurities in graphene by Raman spectroscopy

Disorder and doping can strongly affect the properties of graphene. Here we analyze these effects on several samples by Raman spectroscopy. In particular, we show that pristine and unprocessed graphene samples deposited on silicon, covered with a thin silicon oxide layer, show strong variations in their Raman spectra, even in absence of disorder. The variation in the Raman parameters is assigned to charged impurities. This shows that as‐deposited graphene is unintentionally doped, reaching charge concentrations up to 10¹³ cm^–2 under ambient conditions. The doping varies from sample to sample and the charges are inhomogeneously distributed on a submicron scale. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A time-of-flight spectrometer for angle-resolved detection of low energy electrons in two dimensions

We have developed a time-of-flight photoelectron spectrometer that simultaneously analyzes low energy electrons photoemitted from solid surfaces in an energy- and angle-resolved manner. To achieve this, a field free drift tube with an acceptance angle of 22° is combined with two-dimensional position-sensitive detection of photoelectrons, which is realized by a microchannel plate stack and a delay-line anode for position encoding. Here, we present the design considerations and principles of operation including analysis of multiple events per light pulse. The performance of the spectrometer is demonstrated by photoemission from a Cu(111) single crystalline surface by UV femtosecond laser pulses at 6.2 eV photon energy. PACS 71.20.-b; 73.20.At; 78.47.J-; 79.60.-i     

Guiding center motion of two interacting n=0 Landau electrons in two dimensions

The properties of a two-electron system in two dimensions subjected to a strong magnetic field are considered. Assuming that the electrons are in the lowest Landau level, all observables are expressed in terms of guiding center variables. In these variables, the hamiltonian can be exactly diagonalized.     

Elastic and inelastic scattering of electrons by vibrating impurities in semiconductors

Elastic and inelastic scattering of conduction electrons by vibrating ionized impurities in valence semiconductors is investigated. For elastic scattering, the modification of the Brooks-Herring formula arising from impurity vibrations is unimportant for all conceivable electron temperatures and donor concentrations. Similarily, for inelastic (one-phonon) processes, the change in electron-phonon relaxation time (or in electron-lattice coupling constant) arising from vibrations of the ionized centres is entirely negligible.