We are honored to dedicate this article to Emmanuel Rashba on the occasion of his 95 birthday. In the ideal disorder-free situation, a two-dimensional band gap insulator has an activation energy for conductivity equal to half the band gap, $Δ$. But transport experiments usually exhibit a much smaller activation energy at low temperature, and the relation between this activation energy and $Δ$ is unclear. Here we consider the temperature-dependent conductivity of a two-dimensional narrow gap semiconductor on a substrate containing Coulomb impurities, mostly focusing on the case when amplitude of the random potential $Γ\gg Δ$. We show that the conductivity generically exhibits three regimes and only the highest temperature regime exhibits an activation energy that reflects the band gap. At lower temperatures, the conduction proceeds through nearest-neighbor or variable-range hopping between electron and hole puddles created by the disorder. We show that the activation energy and characteristic temperature associated with these processes steeply collapse near a critical impurity concentration. Larger concentrations lead to an exponentially small activation energy and exponentially long localization length, which in mesoscopic samples can appear as a disorder-induced insulator-to-metal transition. We arrive at a similar disorder driven steep insulator-metal transition in thin films of three-dimensional topological insulators with very large dielectric constant, where due to confinement of electric field internal Coulomb impurities create larger disorder potential. Away from neutrality point this unconventional insulator-to-metal transition is augmented by conventional metal-insulator transition at small impurity concentrations, so that we arrive at disorder-driven re-entrant metal-insulator-metal transition.
A granular system slightly below the percolation threshold is a collection of finite metallic clusters, characterized by wide spectrum of sizes, resistances, and charging energies. Electrons hop from cluster to clusters via short insulating "links" of high resistance. At low temperatures all clusters are Coulomb blockaded and the dc-conductivity is exponentially suppressed. At lowest T the leading transport mechanism is variable range cotunneling via largest (critical) clusters, leading to the modified Efros-Shklovsky law. At intermediate temperatures the principal suppression of the conductiv…
In the ideal disorder-free situation, a two-dimensional band gap insulator has an activation energy for conductivity equal to half the band gap $Δ$. But transport experiments usually exhibit a much smaller activation energy at low temperature, and the relation between this activation energy and $Δ$ is unclear. Here we consider the temperature-dependent conductivity of a two-dimensional insulator on a substrate containing Coulomb impurities, with random potential amplitude $Γ\gg Δ$. We show that the conductivity generically exhibits three regimes of conductivity, and only the highest temperatur…
We demonstrate that forward electron-electron scattering due to Coulomb interation in a two-dimensional ballistic electron gas leads to the (T\ln {T})^{-1} temperature dependence of the thermal conductivity, which is logarithmically suppressed compared to the usual Fermi liquid behaviour.
We reconsider the theory of magnetoresistance in hopping semiconductors. First, we have shown that the random potential of the background impurities affects significantly preexponential factor of the tunneling amplitude which becomes to be a short-range one in contrast to the long-range one for purely Coulomb hopping centers. This factor to some extent suppresses the negative interference magnetoresistance and can lead to its decrease with temperature decrease which is in agreement with earlier experimental observations. We have also extended the theoretical models of positive spin magnetoresi…
Interplay between changes of energy levels and tunneling amplitudes caused by localized electrons on-site Coulomb interaction depending on non-equilibrium electron filling numbers is analyzed. Specific features of local tunneling conductivity spectra for different positions of localized states energy relative to the Fermi level have been investigated by means of self-consistent mean field approximation in the presence of non-equilibrium effects. The conditions when modifications of tunneling transfer amplitude due to changes of electron filling numbers in the presence of on-site Coulomb intera…
We present the results of local tunneling conductivity spatial distribution detailed theoretical investigations in vicinity of impurity atom for a wide range of applied bias voltage. We observed Fano resonance in tunneling conductivity resulting from interference between resonant tunneling channel through impurity energy level and direct tunneling channel between the tunneling contact leads. We have found that interference between tunneling channels strongly modifies form of tunneling conductivity measured by the scanning tunneling microscopy/spectroscopy (STM/STS) depending on the distance va…
I. Introduction (Preface, Basic properties of semiconductor nanostructures). II. Theory of Coulomb-blockade oscillations (Periodicity of the oscillations, Amplitude and lineshape). III. Experiments on Coulomb-blockade oscillations (Quantum dots, Disordered quantum wires, Relation to earlier work on disordered quantum wires). IV. Quantum Hall effect regime (The Aharonov-Bohm effect in a quantum dot, Coulomb blockade of the Aharonov-Bohm effect, Experiments on quantum dots, Experiments on disordered quantum wires).
Spatial distribution of local tunneling conductivity was investigated for deep and shallow impurities on semiconductor surfaces. Non-equilibrium Coulomb interaction and interference effects were taken into account and analyzed theoretically with the help of Keldysh formalism. Two models were investigated: mean field self-consistent approach for shallow impurity state and Hubbard-{I} model for deep impurity state. We have found that not only above the impurity but also at the distances comparable to the lattice period both effects interference between direct and resonant tunneling channels and …
We study electron transport through a semiconductor superlattice subject to an electric field parallel to and a magnetic field perpendicular to the growth axis. Using a single miniband, semiclassical balance equation model with both elastic and inelastic scattering, we find that (1) the current-voltage characteristic becomes multistable in a large magnetic field; and (2) ``hot'' electrons display novel features in their current-voltage characteristics, including absolute negative conductivity (ANC) and, for sufficiently strong magnetic fields, a spontaneous dc current at zero bias. We discuss …
We present a model which deepens into the role that normal scattering has on the thermal conductivity in semiconductor bulk, micro and nanoscale samples. Thermal conductivity as a function of the temperature undergoes a smooth transition from a kinetic to a collective regime that depends on the importance of normal scattering events. We demonstrate that in this transition, the key point to fit experimental data is changing the way to perform the average on the scattering rates. We apply the model to bulk Si with different isotopic compositions obtaining an accurate fit. Then we calculate the t…
We study theoretically the relative importance of short-range disorder in determining the low-temperature 2D mobility in GaAs-based structures with respect to Coulomb disorder which is known to be the dominant disorder in semiconductor systems. We give results for unscreened and screened short-range disorder effects on 2D mobility in quantum wells and heterostructures, comparing with the results for Coulomb disorder and finding that the asymptotic high-density mobility is always limited by short-range disorder which, in general, becomes effectively stronger with increasing `carrier density' in…
We present a consistent theoretical description of few-particle effects in the optical spectra of semiconductor quantum dots, based on a direct-diagonalization approach. We show that, because of the strong Coulomb interaction among electrons and holes, each configuration of the confined few-particle system leads to its characteristic signature in the optical spectra. We discuss quantitative predictions and comparison with experiments for both absorption and luminescence.
Using previously developed exciton scattering model accounting for the interband, i.e., exciton-biexciton, Coulomb interactions in semiconductor nanocrystals (NCs), we derive a closed set of equations for 2D double-quantum coherence signal. The signal depends on the Liouville space pathways which include both the interband scattering processes and the inter- and intraband optical transitions. These processes correspond to the formation of different cross-peaks in the 2D spectra. We further report on our numerical calculations of the 2D signal using reduced level scheme parameterized for PbSe N…
The thermal conductivity of several diamond-like materials is calculated from a kinetic-collective model. From this approach, a thermal conductivity expression is obtained that includes a transition from a kinetic (free) to a collective (hydrodynamic) behavior of the phonon field. The expression contains only three parameters. Once fitted to natural occurring silicon, the same parameters for the other materials are directly calculated from theoretical relations. The results are in good agreement with experimental data.
By explicitly considering surface roughness at the atomic level, we quantitatively show that the thermal conductivity of Si nanowires can be lower than Casimir's classical limit. However, this violation only occurs for deep surface degradation. For shallow surface roughness, the Casimir formula is shown to yield a good approximation to the phonon mean free paths and conductivity, even for nanowire diameters as thin as 2.22 nm. Our exact treatment of roughness scattering is in stark contrast with a previously proposed perturbative approach, which is found to overpredict scattering rates by an o…
We show that Coulomb drag in hydrodynamic bilayer systems leads to additional viscosity terms in the hydrodynamic equations, i.e., the drag and drag-Hall viscosities, besides the well-known kinematic and Hall viscosities. These new viscosity terms arise from a change of the stress tensor due to the interlayer Coulomb interactions. All four viscosity terms are tunable by varying the applied magnetic field and the electron densities in the two layers. At certain ratios between the electron densities in the two layers, the drag viscosity dramatically changes the longitudinal transport resulting i…
Coulomb correlations in the optical spectra of semiconductor quantum dots are investigated using a full-diagonalization approach. The resulting multi-exciton spectra are discussed in terms of the symmetry of the involved states. Characteristic features of the spectra like the nearly equidistantly spaced s-shell emission lines and the approximately constant p-shell transition energies are explained using simplified Hamiltonians that are derived taking into account the relative importance of various interaction contributions. Comparisons with previous results in the literature and their interpre…
Electronic transport in the regime where carrier-carrier collisions are the dominant scattering mechanism has taken on new relevance with the advent of ultraclean two-dimensional materials. Here we present a combined theoretical and experimental study of ambipolar hydrodynamic transport in bilayer graphene demonstrating that the conductivity is given by the sum of two Drude-like terms that describe relative motion between electrons and holes, and the collective motion of the electron-hole plasma. As predicted, the measured conductivity of gapless, charge-neutral bilayer graphene is sample- and…
When the excitation of carriers in real space is focused down to the nanometer scale, the carrier system can no longer be viewed as homogeneous and ultrafast transport of the excited carrier wave packets occurs. In state-of-the-art semiconductor structures like low-dimensional heterostructures or monolayers of transition metal dichalcogenides, the Coulomb interaction between excited carriers becomes stronger due to confinement or reduced screening. This demands a fundamental understanding of strongly interacting electrons and holes and the influence of Coulomb correlations. To study the corres…
We argue that the unscreened Coulomb interaction in graphene provides a positive, universal, and logarithmic correction to scaling of zero-temperature conductivity with frequency. The combined effect of the disorder due to wrinkling of the graphene sheet and the long range electron-electron interactions is a finite positive contribution to the dc conductivity. This contribution is disorder strength dependent and thus non-universal. The low-energy behavior of such a system is governed by the line of fixed points at which both the interaction and disorder are finite, and the density of states is…
We describe a measurement method that enables the correct estimation of the charging energy of an unintentional quantum dot (QD) in the channel of a metal-oxide-semiconductor field-effect transistor (MOSFET). If the channel has a dominant QD with a large charging energy and an array of stray QDs with much weaker charging, this method eliminates the additional voltage drops due to stray QDs by regarding the stray QDs as series resistors. We apply this method to a short-channel MOSFET and find that the charging energy of the dominant QD can indeed be smaller than the size of the Coulomb diamond.
In this review, we describe in detail two important spin-transport phenomena: the extrinsic spin-Hall effect (coming from spin-orbit interactions between electrons and impurities) and the spin-Coulomb drag. The interplay of these two phenomena is analyzed. In particular, we discuss the influence of scattering between electrons with opposite spins on the spin current and the spin accumulation produced by the spin-Hall effect. Future challenges and open questions are briefly discussed.
A novel approach for the control of exciton-exciton Coulomb coupling in semiconductor macroatoms/molecules is proposed. We show that by applying properly tailored external fields, we can induce ---or significantly reinforce--- excitonic dipoles, which in turn allows to control and magnify intra- as well as inter-dot few-exciton effects. Such dipole-dipole interaction mechanism will be accounted for within a simple analytical model, which is found to be in good agreement with fully three-dimensional calculations. The proposed approach may play an important role for the design and realization of…
We present measurements of one-dimensional superconductor-semiconductor Coulomb islands, fabricated by gate confinement of a two-dimensional InAs heterostructure with an epitaxial Al layer. When tuned via electrostatic side gates to regimes without sub-gap states, Coulomb blockade reveals Cooper-pair mediated transport. When sub-gap states are present, Coulomb peak positions and heights oscillate in a correlated way with magnetic field and gate voltage, as predicted theoretically, with (anti) crossings in (parallel) transverse magnetic field indicating Rashba-type spin-orbit coupling. Overall …
The effect of Coulomb scattering on graphene conductivity in field effect transistor structures is discussed. Inter-particle scattering (electron-electron, hole-hole, and electron-hole) and scattering on charged defects are taken into account in a wide range of gate voltages. It is shown that an intrinsic conductivity of graphene (purely ambipolar system where both electron and hole densities exactly coincide) is defined by strong electron-hole scattering. It has a universal value independent of temperature. We give an explicit derivation based on scaling theory. When there is even a small dis…
We present a numerical model study of the zero-temperature infrared optical properties of (III,Mn)V diluted magnetic semiconductors. Our calculations demonstrate the importance of treating disorder and interaction effects simultaneously in modelling these materials. We find that the conductivity has no clear Drude peak, that it has a broadened inter-band peak near 220 meV, and that oscillator weight is shifted to higher frequencies by stronger disorder. These results are in good qualitative agreement with recent thin film absorption measurements. We use our numerical findings to discuss the us…
While using first-principles-based Boltzmann transport equation approach to predict the thermal conductivity of crystalline semiconductor materials has been a routine, the validity of the approach is seldom tested for high-temperature conditions. Most previous studies only focused on the phononic contribution, and neglected the electronic part. Meanwhile, the treatment on phonon transport is not rigorous as a few ingredients, such as four-phonon scatterings, phonon renormalization and thermal expansion, are ignored. In this paper, we present a Boltzmann transport equation study on high-tempera…
In the absence of an external field, the Rashba spin-orbit interaction (SOI) in a two-dimensional electron gas in a semiconductor quantum well arises entirely from the screened electrostatic potential of ionized donors. We adjust the wave functions of a quantum well so that electrons occupying the first (lowest) subband conserve their spin projection along the growth axis (Sz), while the electrons occupying the second subband precess due to Rashba SOI. Such a specially designed quantum well may be used as a spin relaxation trigger: electrons conserve Sz when the applied voltage (or current) is…
We use terahertz pulses to induce resonant transitions between the eigenstates of optically generated exciton populations in a high-quality semiconductor quantum-well sample. Monitoring the excitonic photoluminescence, we observe transient quenching of the $1s$ exciton emission, which we attribute to the terahertz-induced $1s$-to-$2p$ excitation. Simultaneously, a pronounced enhancement of the $2s$-exciton emission is observed, despite the $1s$-to-$2s$ transition being dipole forbidden. A microscopic many-body theory explains the experimental observations as a Coulomb-scattering mixing of the …
We consider effects of Coulomb interaction in a granular normal metal at not very low temperatures suppressing weak localization effects. In this limit calculations with the initial electron Hamiltonian are reduced to integrations over a phase variable with an effective action, which can be considered as a bosonization for the granular metal. Conditions of the applicability of the effective action are considered in detail and importance of winding numbers for the phase variables is emphasized. Explicit calculations are carried out for the conductivity and the tunneling density of states in the…
The contribution of bulk and surface to the electrical resistance along crystallographic \textit{b}- and \textit{c}-axes as a function of crystal thickness gives evidence for a temperature independent surface states in an antiferromagnetic narrow-gap semiconductor CrSb$_{2}$. ARPES shows a clear electron-like pocket at $Γ$-$Z$ direction which is absent in the bulk band structure. First-principles calculations also confirm the existence of metallic surface states inside the bulk gap. Whereas combined experimental probes point to enhanced surface conduction similar to topological insulators, sur…
We present a theory of the Anomalous Hall Effect (AHE) in ferromagnetic (Ga,Mn)As in the regime when conduction is due to phonon-assisted hopping of holes between localized states in the impurity band. We show that the microscopic origin of the anomalous Hall conductivity in this system can be attributed to a phase that a hole gains when hopping around closed-loop paths in the presence of spin-orbit interactions and background magnetization of the localized Mn moments. Mapping the problem to a random resistor network, we derive an analytic expression for the macroscopic anomalous Hall conducti…
Relativistic band theoretical calculations reveal that intrinsic spin Hall conductivity in hole-doped archetypical semiconductors Ge, GaAs and AlAs is large $[\sim 100 (\hbar/e)(Ωcm)^{-1}]$, showing the possibility of spin Hall effect beyond the four band Luttinger Hamiltonian. The calculated orbital-angular-momentum (orbital) Hall conductivity is one order of magnitude smaller, indicating no cancellation between the spin and orbital Hall effects in bulk semiconductors. Furthermore, it is found that the spin Hall effect can be strongly manipulated by strains, and that the $ac$ spin Hall conduc…
Dispersionless (flat) electronic bands are investigated regarding their conductance properties. Due to "caging" of carriers these bands are usually insulating at partial filling, at least on the non-interacting level. Considering the specific example of a $\mathcal{T}_3$--lattice we study long-range Coulomb interactions. A non-trivial dependence of the conductivity on flat band filling is obtained, exhibiting an infinite number of zeros. Near these zeros, the conductivity rises linearly with carrier density. At densities half way in between adjacent conductivity-zeros, strongly enhanced conduc…
We derive the matrix elements of Coulomb interaction between states with different number of electrons and holes in a semiconductor nanocrystal within the 8-band $\mathbf{k}\cdot\mathbf{p}$ theory. These matrix elements are responsible for multiple exciton generation which may contribute to the enhancement of the efficiency of solar cells. Our calculations are performed within the multi band envelope function formalism based on the states resulting from diagonalization of the 8-band $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian. We study in detail and compare two contributions to the inter-band Coul…
Recently, the existence of Dirac/Weyl cones in three dimensional systems has been demonstrated experimentally. While in high energy physics the isotropy of the Dirac/Weyl cones is guaranteed by relativistic invariance, in condensed matter systems corrections to this can occur, one possible type being a tilt. In this paper we study the effect of of tilted Weyl cones in collective effects. We study both the opticql conductivity as well as the polarization function. We also investigate the perturbative effect of long-range Coulomb interactions using a renormalization group calculation. We find th…
Electrons in double-layer semiconductor heterostructures experience a special type of spin-orbit interaction which arises in each layer from the perpendicular component of the Coulomb electric field created by electron density fluctuations in the other layer. We show that this interaction, acting in combination with the usual spin-orbit interaction, can generate a spin current in one layer when a charge current is driven in the other. This effect is symmetry-wise distinct from the spin Hall drag. The spin current is not, in general, perpendicular to the drive current.
In semiconductor-superconductor hybrid structures a topological phase transition is expected as a function of chemical potential or magnetic field strength. We show that signatures of this transition can be observed in nonlinear Coulomb blockade transport through a ring shaped structure. In particular, for a fixed electron parity of the ring, the flux periodicity of the neutral excitation spectrum changes from the usual h/2e periodicity to a characteristic h/e periodicity when tuning the system from the topologically trivial to the nontrivial phase. We relate the h/e periodicity to the recentl…
We study electrical and optical conductivities of hole gas in $p$-doped bulk III-V semiconductors described by the Luttinger Hamiltonian. We provide exact analytical expressions of the Drude conductivity, inverse relaxation time for various impurity potentials, Drude weight and optical conductivity in terms of the Luttinger parameters $γ_1 $ and $γ_2$. The back scattering is completely suppressed as a result of the helicity conservation of the heavy and light hole states. We find that the inverse relaxation time of heavy holes is much less than that of the light holes for Coulomb-type and Gaus…
We compute the Coulomb correction $\mathcal{C}$ to the a. c. conductivity of interacting massless Dirac particles in graphene in the collisionless limit using the polarization tensor approach in a regularization independent framework. Arbitrary parameters stemming from differences between logarithmically divergent integrals are fixed on physical grounds exploiting only spatial $O(2)$ rotational invariance of the model which amounts to transversality of the polarization tensor. Consequently $\mathcal{C}$ is unequivocally determined to be $(19- 6π)/12$ within this effective model. We compare our…
Semiconductor nanowires provide promising low-dimensional systems for the study of quantum transport phenomena in combination with superconductivity. Here we investigate the competition between the Coulomb blockade effect, Andreev reflection, and quantum interference, in InAs and InP nanowires connected to aluminum-based superconducting electrodes. We compare three limiting cases depending on the tunnel coupling strength and the characteristic Coulomb interaction energy. For weak coupling and large charging energy, negative differential conductance is observed as a direct consequence of the BC…
A Coulomb impurity placed in an undoped Weyl semimetal spontaneously surrounds itself with a cloud of condensed Weyl fermions. We find that the ground-state of this system exhibits an experimentally accessible Landau zero-charge effect: the fermion condensate completely screens out the impurity charge. In a narrow band gap semiconducor this effect manifests itself in the near universality of observable charge of a highly-charged recombination center.
We work out a semiclassical theory of shot noise in ballistic n+-i-n+ semiconductor structures aiming at studying two fundamental physical correlations coming from Pauli exclusion principle and long range Coulomb interaction. The theory provides a unifying scheme which, in addition to the current-voltage characteristics, describes the suppression of shot noise due to Pauli and Coulomb correlations in the whole range of system parameters and applied bias. The whole scenario is summarized by a phase diagram in the plane of two dimensionless variables related to the sample length and contact chem…
The metal-semiconductor (M-S) junction based devices are commonly used in all sorts of electronic devices. Their electrical properties are defined by the metallic phase properties with a respect to the semiconductor used. Here we make an in-depth survey on the origin of the M-S junction at the atomic scale by studying the properties of the AuIn2 nanoelectrodes formed on the InP(001) surface by the in situ electrical measurements in combination with a detailed investigation of atomically resolved structure supported by the first-principle calculations of its local electrical properties. We have…
The paper discusses the fundamental behavior of the dynamical lattice thermal conductivity k(W) of bulk cubic semiconductor crystals. The calculation approach is based on solving Boltzmann-Peierls Phonon Transport Equation in the frequency domain after excitation by a dynamical temperature gradient, within the framework of the single relaxation time approximation and using modified Debye-Callaway model. Our model allows us to obtain a compact expression for k(W) that captures the leading behavior of the dynamical thermal conduction by phonons. This expression fulfills the causality requirement…
Although semiconductor Bloch equations have been widely used for decades to address ultrafast optical phenomena in semiconductors, they have a few important drawbacks: (i) Coulomb terms between free electron-hole pairs require Hartree-Fock treatment which, in its usual form, preserves excitonic poles but loses biexcitonic resonances. (ii) Solving the resulting coupled differential equations imposes heavy numerics which completely hide the physics. This can be completely avoided if, instead of free electron-hole pairs, we use correlated pairs, i.e., excitons. Their interactions are easy to hand…
We review experimental and theoretical results on thermal transport in semiconductor nanostructures (multilayer thin films, core/shell and segmented nanowires), single- and few-layer graphene, hexagonal boron nitride, molybdenum disulfide and black phosphorus. Different possibilities of phonon engineering for optimization of electrical and heat conductions are discussed. The role of the phonon energy spectra modification on the thermal conductivity in semiconductor nanostructures is revealed. The dependence of thermal conductivity in graphene and related two-dimensional (2D) materials on tempe…
The ability to control the size of the electronic bandgap is an integral part of solid-state technology. Atomically-thin two-dimensional crystals offer a new approach for tuning the energies of the electronic states based on the interplay between the environmental sensitivity and unusual strength of the Coulomb interaction in these materials. By engineering the surrounding dielectric environment, we are able to tune the electronic bandgap in monolayers of WS2 and WSe2 by hundreds of meV. We exploit this behavior to present an in-plane dielectric heterostructure with a spatially dependent bandg…
Motivated by the results of recent transport and optical conductivity studies, we propose a semi-infinite two-dimensional lattice model for interacting massive Dirac electrons in the pressurized organic conductor $α$-(BEDT-TTF)$_2$I$_3$, and address the problem of domain wall conductivity in a charge-ordered insulating phase under realistic experimental conditions. Using the extended Hubbard model at a mean field level, we present results of extensive numerical studies around the critical region of the model, reporting on the resistivity and optical conductivity calculated by means of the Naka…
We examine transport and microwave properties of two coupled quantum dots taken in parallel connection to the common left lead and connected to separate leads at their right side. In addition, the area between the left lead and the double-dot structure is threaded by Aharonov-Bohm magnetic flux. We determine the energies and populations of double-dot levels on the microscopic basis taking into account the interdot Coulomb interaction and show that at large lead-to-lead bias the population inversion can be achieved. For the case of strong Coulomb repulsion, this inversion leads to level crossin…
The static dielectric function in AA-stacked bilayer graphene (BLG), subjected to an electric field applied perpendicular to layers, is calculated analytically within the random phase approximation (RPA). This result is used to calculate the screened Coulomb interaction and the electrical conductivity. The screened Coulomb interaction, which here can be tuned by the perpendicular electric field, shows a power-law decay as $1/(γ^{2}+V^2)$ at long-distance limit where $V$ and $γ$ are the electrical potential and the inter-layer hopping energy respectively, indicating that the Coulomb interaction…
We develop the microscopic theory of the extrinsic spin Hall conductivity of a two-dimensional electron gas, including skew-scattering, side-jump, and Coulomb interaction effects. We find that while the spin-Hall conductivity connected with the side-jump is independent of the strength of electron-electron interactions, the skew-scattering term is reduced by the spin-Coulomb drag, so the total spin current and the total spin-Hall conductivity are reduced for typical experimental mobilities. Further, we predict that in paramagnetic systems the spin-Coulomb drag reduces the spin accumulations in …
We study the effects of Coulomb interaction and inter-grain quantum tunnelling in an array of metallic grains using the phase-functional approach for temperatures $T$ well below the charging energy $E_{c}$ of individual grains yet large compared to the level spacing in the grains. When the inter-grain tunnelling conductance $g\gg1$, the conductivity $σ$ in $d$ dimensions decreases logarithmically with temperature ($σ/σ_{0}\sim1-\frac{1}{2πgd}\ln(gE_{c}/T)$), while for $g\to0$, the conductivity shows simple activated behaviour ($σ\sim \exp(-E_c/T)$). We show, for bare tunnelling conductance $g …
