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We present a study on the role of dislocations and impurities for the unintentional n-type conductivity in high-quality InN grown by molecular beam epitaxy. The dislocation densities and H profiles in films with free electron concentrations in the low 10 17 cm - 3 and mid 10 18 cm - 3 range are measured, and analyzed in a comparative manner. It is shown that dislocations alone could not account for the free electron behavior in the InN films. On the other hand, large concentrations of H sufficient to explain, but exceeding substantially, the observed free electron densities are found. Furthermore, enhanced concentrations of H are revealed at the film surfaces, resembling the free electron behavior with surface electron accumulation. The low-conductive film was found to contain C and it is suggested that C passivates the H donors or acts as an acceptor, producing compensated material in this case. Therefore, it is concluded that the unintentional impurities play an important role for the unintentional n-type conductivity in InN. We suggest a scenario of H incorporation in InN that may reconcile the previously reported observations for the different role of impurities and dislocations for the unintentional n-type conductivity in InN.

A method based on focused ion beam milling and analytical electron microscopy to investigate the nature of the tool-chip interface is presented. It is employed to study tool-chip interfaces of the rake face of a (Ti0.83Si0.17)N coated PCBN insert after turning of case-hardened steel. Analytical electron microscopy shows the presence of a smeared adhered layer on the coating, which consists of steel elements from the work-piece, oxygen, and Si and N, most likely originating from the coating. Original Publication:Axel Flink, R M Saoubi, Finn Giuliani, J Sjolen, T Larsson, Per Persson, M P Johansson and Lars Hultman, Microstructural characterization of the tool-chip interface enabled by focused ion beam and analytical electron microscopy, 2009, WEAR, (266), 11-12, 1237-1240.http://dx.doi.org/10.1016/j.wear.2009.03.001Copyright: Elsevier Science B.V., Amsterdam.http://www.elsevier.com/

We show that due to the peculiar structure of the non-interacting energy spectrum, the Coulomb interaction leads for all densities to an in-plane ferromagnetic instability in a two-dimensional electron liquid in the presence of sufficiently strong Rashba spin-orbit coupling. This non perturbative phenomenon is characterized by an interesting anisotropic momentum space repopulation and is in nature quite different from the already identified out-of-plane ferromagnetic instability.

We show that a result equivalent to Overhauser’s famous Hartree-Fock instability theorem can be established for the case of a two-dimensional electron gas in the presence of Rashba spin-obit coupling. In this case it is the spatially homogeneous paramagnetic chiral ground state that is shown to be differentially unstable with respect to a certain class of distortions of the spin-density-wave and charge-density-wave type. The result holds for all densities. Basic properties of these inhomogeneous states are analyzed.

Single-crystal NaCl-structure Al0.68Cr0.32N thin films were deposited onto MgO(0 0 1) substrates. The films exhibit cube-on-cube epitaxial growth with an initial pseudomorphic strained layer before ...

Observations elsewhere have shown that multilayer structures with layers ~10 nm thick can be harder than monolithic ones. Here we see whether these effects can be observed at high temperatures and investigate the effect of temperature on the manner of deformation. The hardness of an AlN/CrN multilayer structure with a range of wavelengths from 6-200 nm has been measured at temperatures from room temperature to 400 oC. The changes in hardness have been related to the deformation behaviour observed by cross-sectional transmission electron microscopy and atomic force microscopy. These observations suggest that the mechanical properties of the coatings are dominated by the refinement in the columnar microstructure rather than directly by an effect of the layer interfaces on dislocation motion.

Examination of cross-sections of nanoindents with the transmission electron microscope has recently become feasible owing to the development of focused ion beam milling of site-specific electron transparent foils. Here, we discuss the development of this technique for the examination of nanoindents and survey the deformation behaviour in a range of single crystal materials with differing resistances to dislocation flow. The principal deformation modes we discuss, in addition to dislocation flow, are phase transformation (silicon and germanium), twinning (gallium arsenide and germanium at 400 °C), lattice rotations (spinel), shear (spinel), lattice rotations (copper) and lattice rotations and densification (TiN/NbN multilayers). The magnitude of the lattice rotation, about the normal to the foil, was measured at different positions under the indents. Indents in a partially recrystallized metallic glass Mg 66 Ni 20 Nd 14 were also examined. In this case a low-density porous region was formed at the indent tip and evidence of shear bands was also found. Further understanding of indentation deformation will be possible with three-dimensional characterization coupled with modelling which takes account of the variety of competing deformation mechanisms that can occur in addition to dislocation glide. Mapping the lattice rotations will be a particularly useful way to evaluate models of the deformation process.

The use of an analytical approach to determine the relation between hardness and yield strength for materials with a high ratio of yield strength to Young's modulus is re-examined. It is shown that predictions using the analogy of the spherical cavity fail to reproduce experimental and finite element results because the surface deflection that occurs during loading is not taken into account. A modification is proposed to allow this. This gives a greatly improved prediction of the relationship between the hardness and yield strength of a material. It also enables the effect of the indenter shape on the measured hardness to be incorporated and explains why in some very hard materials, indentation is observed to be completely elastic.

In a bilayer system, the decay rate of an excited quasiparticle is enhanced by momentum and energy transfer to low energy plasmonic modes. These correspond to antisymmetric charge density oscillations that propagate acoustically, with ω∼q. Within the random phase approximation, we study the relaxation rate dependence on the excitation energy above the Fermi level and suggest an experimental situation that can probe this estimate.

Large area thin film position sensitive detectors based on amorphous silicon technology have been prepared on polyimide substrates using the conventional plasma-enhanced chemical vapour deposition. The sensors have been characterised by spectral response, light intensity dependence and linearity measurements in a bent state in order to evaluate the properties in real working conditions. The obtained one-dimensional (1D) position sensors with 10 mm width and 20 mm length present a non-linearity of ±1% which are comparable to the ones produced on glass substrates.

We have investigated the spectrum of localized modes in both finite and phase inhomogeneous long one-dimensional Josephson junctions in the presence of an external magnetic field. For finite junctions these excitations correspond to evanescent waves localized near the edges. Both the frequency and the characteristic decay lengths depend on the magnetic field. In particular, a different behavior is expected for the Meissner state and the mixed state in which wholesale penetration of Josephson vortices occurs. The related problem of the spectrum of modes localized near phase inhomogeneities occurring well inside a long junction has been also tackled. This problem is relevant to the case in which Abrikosov vortices penetrate the electrodes and become pinned near the junction plane.

The subband levels of quantum wells grown in a periodic array form minibands whose bandwidth {delta} depends on the probability of interlayer tunneling. In the presence of a strong magnetic field, this system of minibands can exhibit various Coulomb-interaction-driven spin polarization instabilities at an integral value of the filling factor {nu}. We investigate in particular the Hartree-Fock phase diagram in the case in which the n=0 spin-up and n=1 spin-down Landau levels are separated by an energy smaller than {delta}. A spin-density-wave ground state is shown to occur at filling factor {nu}=2. (c) 2000 The American Physical Society.

We investigate theoretically how the proximity of an Abrikosov vortex influences the physical properties of a long Josephson junction. We find that dI c , the contribution to the critical current associated with the presence of the vortex, is generally positive ~the critical current is increased ! and is crucially dependent on the specific boundary conditions satisfied by the transport current. In the case in which the latter has a bulk component in the vicinity of the vortex, dI c is proportional to the coupling c between the vortex and the junction. The situation is however more complex when the transport current is purely a surface phenomenon. In this case dI c strongly depends on the distance between the vortex and the edges of the junction, and is in general much smaller than that of the bulk current case unless a special commensurability condition is met. In particular we show that a contribution to dI c proportional to c is obtained in this case only when an integer number of Josephson vortices can be accommodated between the location of the vortex and one of the edges of the junction. @S0163-1829~98!10137-6#

Consistently with the results of the one vortex analysis of Ref. 10 we show that in the presence of a finite concentration of trapped Abrikosov vortices the critical current of the junction can actually be larger than that of a vortex free junction. The present paper is organized as follows: In Sec. II the model and the theory of the coupling between the junction and the perturbing vortices are introduced. There three common geometrical configurations for the AV’s with respect to the junction plane are also discussed. In Sec. III we present the theory for the case in which the AV’s are well separated ~as compared to the range of their interaction with the junction!. In Sec. IV we tackle the opposite case of a high concentration of AV’s, a regime which requires a rather different approach. Finally Sec. V provides a discussion of our results and the conclusions.

The investigation on electronic density of states (DOS) and photoluminescence processes in a-C:H films has attracted, in the last years, interest, due to the foreseen technological application of carbon based materials. In this paper we present a new model for electronic DOS of a-C:H having sp2 fraction less than a percolation threshold. This model is able to explain the optical absorption coefficient for photon energies in the range 0.7 to 3.5 eV. Moreover, with this model we correlate, as it happens in a-Si:H, the photoluminescence quantum efficiency and the density of states close to the Fermi energy. Such states, however, can have either diamagnetic or paramagnetic nature so that some of them can be detected by electron spin resonance and others by optical transitions.

We have studied the magnetic field dependence of the c-axis critical current of a layered superconductor when a pinned, disordered lattice of anisotropic vortices parallel to the superconducting planes is present. The model employed is based on the Josephson coupling picture of layered superconductors. In this case, the Josephson phase between adjacent layers varies randomly along the superconducting planes and its spatial correlations determine the value of an average critical current scale. We show that under these conditions the usual Fraunhofer oscillations are absent and this critical current is proportional to exp (−H ext / H 0 ) , where H 0 is crucially determined by the anisotropy and depends weakly on the size of the superconductor. The relevance of our results to transport properties recently observed in the high-Tc cuprates is discussed.

We have developed a theory of the current-voltage characteristic of a Josephson junction in the presence of randomly distributed, pinned misaligned Abrikosov vortices oriented perpendicularly to the junction plane. Under these conditions the Josephson phase difference {var_phi} acquires an interesting stochastic dependence on the position in the plane of the junction. In this situation it is possible to define an average critical current which is determined by the spatial correlations of this function. Due to the inhomogeneity, we find that for finite voltage bias the electromagnetic waves propagating in the junction display a broad spectrum of wavelengths. This is at variance with the situation encountered in homogeneous junctions. The amplitude of these modes is found to decrease as the bias is increased. We predict that the presence of these excitations is directly related to a remarkable feature in the current-voltage characteristic. The dependence of the position and the magnitude of this feature on the vortex concentration has been determined. {copyright} {ital 1997} {ital The American Physical Society}

It is shown that inelastic scattering suffered by tunneling electrons in the barrier of an S-I-S Josephson junction can lead to a remarkable nonmonotonic temperature dependence of the critical current of the structure. The understanding of this effect rests on the fact that under suitable conditions the inevitable loss of coherence can be more than compensated by a temperature-dependent exponential enhancement of the pair tunneling probability.

In inhomogeneous Josephson junctions the Eck peak characterizing the current-voltage characteristics is predicted to be replaced by a rather different yet prominent feature whose location and shape strongly depend on the strength of the applied magnetic field and the spatial correlations of the associated distorted Abrikosov flux lattice.

The magnetization as a function of external applied magnetic field {ital M}({ital H}{sub ext}) of polycrystalline YBa{sub 2}Cu{sub 3}O{sub 7} (poly-YBCO) exhibits behavior that is more consistent with the geometrical barrier model of Zeldov {ital et} {ital al}. than that of either the Bean-Livingston surface-barrier model or the Bean critical state strong-pinning model. Correlation of the magnetization measurements with transport measurements suggests that the irreversible properties of poly-YBCO, including the critical current density {ital J}{sub {ital c}}, are dominated by surface-barrier effects. Observation of an increasing of {ital J}{sub {ital c}} with {ital H}{sub ext} at intermediate fields is consistent with a theoretical model that describes the transport behavior in the case of vortex lattice formation within the superconducting grains that form the Josephson junctions.

We present a study of finite-size effects in a small Josephson junction. Explicit expressions for the total magnetic field have been found for the case of the Meissner state and for that of an ordered array of Abrikosov vortices penetrating the electrodes. We have determined how the behavior of the critical current [ital I][sub [ital c]] as a function of the strength of an external magnetic field depends on the ratio [ital L]/[lambda][sub [ital x]] of the width of the junction to the appropriate London penetration length. For small [ital L]/[lambda][sub [ital x]] in particular, significant deviations from the familiar Fraunhofer pattern are found in a number of situations. We find that, in general, for the same field strength, because of an interesting cancellation property of the Josephson phase gradient, vortex penetration tends to increase the critical current. Moreover, for suitable vortex configurations [ital I][sub [ital c]] is found to be determined by the magnetization and to actually increase with the field. The relevance of our results for junctions made out of high-temperature superconductors is discussed.

Within linear response the long range oscillations caused by short or long ranged impurities embedded in an otherwise homogeneous electron gas reflect the singularities of the static response function. By making use of the theory of the many-body local fields and the results of recent quantum Monte Carlo studies we have calculated the exact dependence of the amplitude of these oscillations on the density in a two dimensional electron Fermi liquid.

We have developed a theory of the effect of a pinned ordered lattice of anisotropic vortices on the critical current Jc of a layered superconductor. The external field Hext is taken to be such that vortices lie in the plane of the layers. In this case Jc is determined by the interlayer Josephson coupling and depends on the distribution of the Josephson phase between adjacent superconducting layers. In view of the anisotropic field penetration we find that the usual Fraunhofer oscillations are absent, and that the critical current decreases as 1− H ext /H 0 , with the magnetic field scale H0 determined by the anisotropy of the material. Our results provide a possible explanation for some of the interesting transport properties recently observed in high-Tc cuprates.

We present a quantitative theory of the quasiparticle properties in a Fermi liquid. Our approach uses as an input our previous result for the quasiparticle energy which incorporates the vertex corrections associated with charge and spin-density fluctuations through suitably defined many-body local fields. The method is explicitly applied to the case of the quasi-two-dimensional electron liquid occurring in silicon inversion layers. In particular, we discuss results for the effective mass ${\mathit{m}}^{\mathrm{*}}$ and the modified Land\'e factor ${\mathit{g}}^{\mathrm{*}}$ (Wilson ratio) that are in reasonable agreement with reported findings. Our calculations are performed by making use of a self-consistent static model for the many-body local fields and are consequently free of arbitrary parameters.

We present exact expressions for the conduction electron phase shifts for the two-impurity Anderson model in terms of the impurity Green functions. We show that, for the symmetric model, to all orders in the perturbation theory in U, the only allowed value of the phase shifts is π/2. It is also shown that, quite generally, a vanishing of the phase shifts (signaling a RKKY phase) must be associated with the development of a gap in the impurity single particle excitation spectrum. In the symmetric case this is in turn associated with a divergence of the linear coefficient of the heat capacity. The implications of these results on the physics of the transition from Kondo to RKKY phases are briefly discussed.

The ground state of a semiconductor superlattice (SL) placed in a tilted magnetic field is shown to exhibit a spin-density wave structure when the energy spectrum favors crossings between opposite-spin Landau minibands. The SL is modeled as an array of infinitely attractive quantum wells, whose single energy level is broadened into a miniband of width $\ensuremath{\Delta}$ when weak interwell tunneling is considered. In the presence of the Coulomb interaction, by tailoring the relationship between $\ensuremath{\Delta}$ and the cyclotron and Zeeman energies, the system transitions between paramagnetic, ferromagnetic, spin-density wave (SDW), and ferromagnetic-paramagnetic stripe ordering. These results are obtained by solving numerically a spin-density-wave gap equation derived at $T=0$ K in a self-consistent formalism. We find that for a given value of the difference between the Landau energy and the Zeeman splitting, the initial paramagnetic or ferromagnetic order becomes unstable with respect to the formation of a SDW for $\ensuremath{\Delta}$ within a certain range. At larger $\ensuremath{\Delta}$, the system exhibits alternate ferromagnetic-paramagnetic stripes. In the SDW regime, the fractional polarization is up to the order of several tens of percent.

Evidence is presented for the finite wave vector crossing of the two lowest one-dimensional spin-split subbands in quantum point contacts fabricated from two-dimensional hole gases with strong spin-orbit interaction. This phenomenon offers an elegant explanation for the anomalous sign of the spin polarization filtered by a point contact, as observed in magnetic focusing experiments. Anticrossing is introduced by a magnetic field parallel to the channel or an asymmetric potential transverse to it. Controlling the magnitude of the spin-splitting affords a novel mechanism for inverting the sign of the spin polarization., Comment: 4 pages, 3 figures

We have identified two useful exact properties of the perturbative expansion for the case of a two-dimensional electron liquid with Rashba or Dresselhaus spin-orbit interaction and in the absence of magnetic field. The results allow us to draw interesting conclusions regarding the dependence of the exchange and correlation energy and of the quasiparticle properties on the strength of the spin-orbit coupling which are valid to all orders in the electron-electron interaction., 6 pages, 1 figure

We present a microscopic theory for the temperature dependence of the critical Josephson current density j c (T) flowing through an insulating barrier situated between two layered superconductors. Our theory is quite general and allows us to address the question of the dependence of j c (T) on the bandwidth for electronic motion along the direction perpendicular to the barrier. In the limit in which k B T c is much smaller than this quantity the standard relationship due to Ambegaokar and Baratoff is recovered. In the opposite limit, however, the critical current is substantially modified. We show in particular that in this case j c (T) is generally quenched

We discuss by analytic means the theory of the high-density limit of the unpolarized two-dimensional electron liquid in the presence of Rashba or Dresselhaus spin-orbit coupling. A generalization of the ring-diagram expansion is performed. We find that in this regime the spin-orbit coupling leads to small changes of the exchange and correlation energy contributions, while modifying also, via repopulation of the momentum states, the noninteracting energy. As a result, the leading corrections to the chirality and total energy of the system stem from the Hartree-Fock contributions. The final results are found to be vanishing to lowest order in the spin-orbit coupling, in agreement with a general property valid to every order in the electron-electron interaction. We also show that recent quantum Monte Carlo data in the presence of Rashba spin-orbit coupling are well understood by neglecting corrections to the exchange-correlation energy, even at low density values., 11 pages, 5 figures

We present a detailed study of the structural characteristics of molecular beam epitaxy grown nonpolar InN films with a- and m-plane surface orientations on r-plane sapphire and (100) gamma-LiAlO2, respectively, and semipolar (10 (1) over bar1) InN grown on r-plane sapphire. The on-axis rocking curve (RC) widths were found to exhibit anisotropic dependence on the azimuth angle with minima at InN [0001] for the a-plane films, and maxima at InN [0001] for the m-plane and semipolar films. The different contributions to the RC broadening are analyzed and discussed. The finite size of the crystallites and extended defects are suggested to be the dominant factors determining the RC anisotropy in a-plane InN, while surface roughness and curvature could not play a major role. Furthermore, strategy to reduce the anisotropy and magnitude of the tilt and minimize defect densities in a-plane InN films is suggested. In contrast to the nonpolar films, the semipolar InN was found to contain two domains nucleating on zinc-blende InN(111) A and InN(111) B faces. These two wurtzite domains develop with different growth rates, which was suggested to be a consequence of their different polarity. Both, a- and m-plane InN films have basal stacking fault densities similar or even lower compared to nonpolar InN grown on free-standing GaN substrates, indicating good prospects of heteroepitaxy on foreign substrates for the growth of InN-based devices. Original Publication: Vanya Darakchieva, Mengyao Xie, N Franco, F Giuliani, B Nunes, E Alves, C L Hsiao, L C Chen, T Yamaguchi, Y Takagi, K Kawashima and Y Nanishi, Structural anisotropy of nonpolar and semipolar InN epitaxial layers, 2010, JOURNAL OF APPLIED PHYSICS, (108), 7, . http://dx.doi.org/10.1063/1.3487923 Copyright: American Institute of Physics http://www.aip.org/

A powerful, continuous-wave millimeter radiation source is presented. An electrostatic Cockcroft-Walton accelerator (2.5 MV) drives an FEL (free-electron laser) of 1 MW power. The accelerator has a new design in order to obtain a very powerful (50 MW) electron beam and very small ripple. A recovery system is used to increase RF power and efficiency. The FEL oscillator is 1.5-m long, with a permanent magnet helical wiggler. The cavity is equipped with Bragg mirrors. The FEL is set at the high voltage terminal. >

The magnetic phase diagram of a periodic system of identical quantum wells subject to a strong magnetic field is investigated within the Hartree–Fock approximation. Weak tunneling between the wells accounts for the broadening of the individual energy levels of a single well into minibands of bandwidth Δ. For small tunneling probability, the quasi-two-dimensional system undergoes a ferromagnetic-to-paramagnetic transition as in the case of a single electron gas layer. For larger tunneling probability a critical value of Δc is reached for which spin flip excitations between minibands can become soft and lead to a spin density wave coupling between the bands with Q=π/a, with a the superlattice period.

The free electron behavior in InN is studied on the basis of decoupled bulk and surface accumulation electron densities in InN films measured by contactless optical Hall effect. It is shown that the variation in the bulk electron density with film thickness does not follow the models of free electrons generated by dislocation-associated nitrogen vacancies. This finding, further supported by transmission electron microscopy results, indicates the existence of a different thickness-dependent doping mechanism. Furthermore, we observe a noticeable dependence of the surface electron density on the bulk density, which can be exploited for tuning the surface charge in future InN based devices. Original Publication:Vanya Darakchieva, T Hofmann, M Schubert, Bo Sernelius, Bo Monemar, Per Persson, Finn Giuliani, E Alves, H Lu and W J Schaff , Free electron behavior in InN: On the role of dislocations and surface electron accumulation, 2009, Applied Physics Letters, (94), 2, 022109.http://dx.doi.org/10.1063/1.3065030Copyright: American Institute of Physicshttp://www.aip.org/

In the high-density limit the exchange energy easily overcomes the correlation energy in both two- and three-dimensional electron liquids. It is therefore reasonable to inquire if the class of exchange driven instabilities first discussed by Overhauser within the Hartree-Fock theory could be of relevance in this limit. Our analysis shows that this is not the case at least for distorted states represented by a single Slater determinant.

Precise measurement of the optical Hall effect in InN using magneto-optical generalized ellipsometry at IR and THz wavelengths, allows us to decouple the surface accumulation and bulk electron densities in InN films by non-contact optical means and further to precisely measure the effective mass and mobilities for polarizations parallel and perpendicular to the optical axis. Studies of InN films with different thicknesses, free electron densities and surface orientations enable an intricate picture of InN free electron properties to emerge. Striking findings on the scaling factors of the bulk electron densities with film thickness further supported by transmission electron microscopy point to an additional thickness dependent doping mechanism unrelated to dislocations. Surface electron accumulation is observed to occur not only at polar but also at non-polar and semi-polar wurtzite InN, and zinc blende InN surfaces. The persistent surface electron density shows a complex behavior with bulk density and surface orientation. This behavior might be exploited for tuning the surface charge in InN.

We have developed a new microscopic approach designed to study the effects of the electron-electron interaction on various normal state quasiparticle properties in two-dimensional electronic systems. In our treatment the effects of charge and spin fluctuation induced vertex corrections are explicitly accounted for through the introduction of appropriate Hubbard-type many-body local field corrections . Our analysis is based on a novel self-consistent determination of the many-body local fields in two-dimensional systems for which some useful and new exact results have been derived. Although quite general our theory finds its natural application in the calculation of the quasiparticle effective mass and the anomalous Lande g -factor in silicon inversion layers, which display a pronounced dependence on the carrier density, a clear signal of interaction effects. It will be shown that, within the Landau theory of the Fermi liquids, the concomitant inclusion of previously neglected many-body effects associated with charge and spin fluctuation induced vertex corrections is crucial in attaining a satisfactory description of the observed phenomena.

We have obtained an analytic expression for the ring diagrams contribution to the correlation energy of a two dimensional electron liquid as a function of the uniform fractional spin polarization. Our results can be used to improve on the interpolation formulas which represent the basic ingredient for the constructions of modern spin-density functionals in two dimensions., Comment: 3 pages, 1 figure

We discuss a general form of the exchange energy for a homogeneous system of interacting electrons in two spatial dimensions, which is particularly suited in the presence of a generic spin-orbit interaction. The theory is best formulated in terms of a generalized fractional electronic polarization. Remarkably, we find that a net generalized polarization does not necessarily translate into an increase in the magnitude of the exchange energy, a fact that, in turn, favors unpolarized states. Our results account qualitatively for the findings of recent experimental investigations.

The density of states in the energy region near Fermi level for hydrogenated amorphous carbon thin films is presented. The different types of states are identified in their origin and the problem of their detection is considered. It is shown that only some of these states are accessible to detection by electron spin resonance. A quantitative correlation between their density and the quantum efficiency of the room temperature photoluminescence process is achieved. Such correlation applies to films having a wide range of physical properties deposited by different techniques.

The problem of the Friedel oscillations in two- and three-dimensional electron Fermi liquids is examined by means of the many-body local fields theory as aided by the most recent results of accurate numerical studies based on the quantum Monte Carlo method. Within linear response, an exact answer is obtained for the amplitude of the electron density distortion due to both short- and long-ranged impurity potentials. It is discussed how a measurement of the local environment of an impurity embedded in an otherwise homogeneous electron liquid can be used to characterize the systems as a Fermi liquid as well as to extract the magnitude of the static many-body corrections beyond the random phase approximation for wave vector equal to $2{k}_{F}$.

Non-Fermi liquid behavior In this chapter we begin the study of electronic systems that are not Landau Fermi liquids. These systems are like totalitarian societies in which the behavior of the individual is subordinated to the needs of the organization: their low-energy excitations are collective, rather than single-particle-like. A strongly collective behavior is not at all unusual in condensed matter. For example, the low energy excitations of a crystal lattice are acoustic phonons, which are collective oscillations of the atoms about their equilibrium positions. However, such examples are usually associated with a broken symmetry (translational symmetry in this case): when it comes to homogeneous electron liquids, the familiar picture of Landau's quasiparticles is so ingrained that we tend to regard any departure from it as a surprising phenomenon. Nevertheless, departures from the normal Fermi liquid pattern can and do occur in two typical scenarios: In three- and two-dimensional systems in which the electron liquid is strongly correlated , i.e., when the order of magnitude of the coulomb interaction greatly exceeds the kinetic bandwidth, In quasi-one-dimensional systems, for any strength of the interaction. A trivial example of the first scenario is offered by the three-dimensional electron liquid at very low-density. In this case the electrons form a Wigner crystal and their collective behavior arises immediately from the loss of translational symmetry. Amuch more complex example is offered by the two-dimensional electron liquid at high magnetic field. Because the kinetic energy is effectively suppressed by the magnetic field, the structure of the groundstate and the low-lying excitations is entirely controlled by the coulomb interaction.