Read this paper on arXiv. Transfer-matrix methods are used for a tight-binding description of electron transport in the presence of spin-orbit SO couplings. Spin-dependent partial conductances are evaluated. We show that, as the magnitude of SO interactions increases, the separation of spin-switching channels form non-spin-switching ones is gradually erased. We examine procedures designed to produce spin-polarized incident beams, namely: i imposing spin-dependent amplitudes on the incident wavefunctions; and ii including a Zeeman-like term in the Hamiltonian, while keeping the incident beams fully spin-unpolarized.

For procedure ii we show that the exiting polarization displays a maximum as a function of the intensity of SO couplings. For moderate site disorder, and both weak and strong SO interactions, no evidence is found for a decay of exiting polarization against increasing system length.

With very low site disorder, as well as weak SO couplings, a spin-filter effect takes place, as polarization increases with increasing system length. In this paper we consider electronic transport in two-dimensional 2D systems with spin-orbit SO interactions. Our purpose here is to study the statistics of the direct-current DC conductance of such systems, in particular its spin-dependent properties and their dependence on various externally-imposed parameters.

In Sec. III we give numerical results for the statistics of spin-dependent conductances, first for spin-unpolarized systems and then, with the help of some additional working hypotheses, for the polarized case. For the latter we also investigate the behavior of the polarization itself, and of spin-correlation functions. IV we summarize and discuss our results. In Eq.

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Here we use the implementation of Refs. The form Eq. In two dimensions one should not expect significant discrepancies between results from either type of approach, as long as one is treating systems without lateral confinement. Since we shall not attempt detailed numerical comparisons to experimental data, the simplified formulation described in the preceding paragraphs seems adequate for our purposes. We apply the TM approach specific to tight-binding Hamiltonians like Eq. Consider a strip of the square lattice, cut along one of the coordinate directions.

The introduction of SO couplings along the bonds, see Eqs. The matrices P k and the subdiagonal I of Eq. In our calculations of the two-terminal DC conductance we follow the procedure described in Ref. In this scheme one considers a disordered system described by Eq. It is seen that Eq. The methods of Ref. For the spinless case treated in Ref. For example, with the notation given in Eq.

In practice one finds that final results for the conductance do not depend strongly on the precise value of k xas long as it is not too close to zero. In some cases, e. Here, k y can be set to zero since we only consider periodic boundary conditions in the transverse direction. The plane wave-like incident states used are straightforward adaptations of those given for the spinless case, with the spinors of Eq.

So in this case the incident beam is fully spin-unpolarized. Data for P g are compressed stretched along the horizontal vertical axis to account for the doubling in number of transmission channels for this case, compared to the fixed-spin ones. The curve for P g is in very good quantitative agreement with that given in Fig.Electrical resistivity also called specific electrical resistance or volume resistivity and its inverse, electrical conductivity, is a fundamental property of a material that quantifies how strongly it resists or conducts electric current.

A low resistivity indicates a material that readily allows electric current. Electrical conductivity or specific conductance is the reciprocal of electrical resistivity. It represents a material's ability to conduct electric current.

In an ideal case, cross-section and physical composition of the examined material are uniform across the sample, and the electric field and current density are both parallel and constant everywhere. Many resistors and conductors do in fact have a uniform cross section with a uniform flow of electric current, and are made of a single material, so that this is a good model.

See the adjacent diagram. Both resistance and resistivity describe how difficult it is to make electrical current flow through a material, but unlike resistance, resistivity is an intrinsic property.

This means that all pure copper wires which have not been subjected to distortion of their crystalline structure etc. Every material has its own characteristic resistivity. For example, rubber has a far larger resistivity than copper. If the pipes are the same size and shape, the pipe full of sand has higher resistance to flow.

Resistance, however, is not solely determined by the presence or absence of sand. It also depends on the length and width of the pipe: short or wide pipes have lower resistance than narrow or long pipes.

The above equation can be transposed to get Pouillet's law named after Claude Pouillet :. The resistance of a given material is proportional to the length, but inversely proportional to the cross-sectional area. For less ideal cases, such as more complicated geometry, or when the current and electric field vary in different parts of the material, it is necessary to use a more general expression in which the resistivity at a particular point is defined as the ratio of the electric field to the density of the current it creates at that point:.

As shown below, this expression simplifies to a single number when the electric field and current density are constant in the material. If the current density is constant, it is equal to the total current divided by the cross sectional area:.

When the resistivity of a material has a directional component, the most general definition of resistivity must be used.A semiconductor material has an electrical conductivity value falling between that of a conductorsuch as metallic copper, and an insulatorsuch as glass. Its resistivity falls as its temperature rises; metals are the opposite.

Its conducting properties may be altered in useful ways by introducing impurities " doping " into the crystal structure. When two differently-doped regions exist in the same crystal, a semiconductor junction is created. The behavior of charge carrierswhich include electronsions and electron holesat these junctions is the basis of diodestransistors and all modern electronics.

Some examples of semiconductors are silicongermaniumgallium arsenideand elements near the so-called " metalloid staircase " on the periodic table. After silicon, gallium arsenide is the second most common semiconductor and is used in laser diodes, solar cells, microwave-frequency integrated circuits and others.

Silicon is a critical element for fabricating most electronic circuits. Semiconductor devices can display a range of useful properties, such as passing current more easily in one direction than the other, showing variable resistance, and sensitivity to light or heat.

Because the electrical properties of a semiconductor material can be modified by doping, or by the application of electrical fields or light, devices made from semiconductors can be used for amplification, switching, and energy conversion.

The conductivity of silicon is increased by adding a small amount of the order of 1 in 10 8 of pentavalent antimonyphosphorusor arsenic or trivalent borongalliumindium atoms. This process is known as doping and resulting semiconductors are known as doped or extrinsic semiconductors. Apart from doping, the conductivity of a semiconductor can equally be improved by increasing its temperature.

This is contrary to the behaviour of a metal in which conductivity decreases with increase in temperature. The modern understanding of the properties of a semiconductor relies on quantum physics to explain the movement of charge carriers in a crystal lattice.

When a doped semiconductor contains mostly free holes it is called " p-type ", and when it contains mostly free electrons it is known as " n-type ".

The semiconductor materials used in electronic devices are doped under precise conditions to control the concentration and regions of p- and n-type dopants.

A single semiconductor crystal can have many p- and n-type regions; the p—n junctions between these regions are responsible for the useful electronic behavior.

### Electrical resistivity and conductivity

Some of the properties of semiconductor materials were observed throughout the mid 19th and first decades of the 20th century. The first practical application of semiconductors in electronics was the development of the cat's-whisker detectora primitive semiconductor diode used in early radio receivers.

Developments in quantum physics in turn led to the development of the transistor in[2] the integrated circuit inand the MOSFET metal—oxide—semiconductor field-effect transistor in A large number of elements and compounds have semiconducting properties, including: [7].

Most common semiconducting materials are crystalline solids, but amorphous and liquid semiconductors are also known. These include hydrogenated amorphous silicon and mixtures of arsenicselenium and tellurium in a variety of proportions.Martin L. E-mail: mkirk unm. E-mail: shultz ncsu. Although different bridge types monomer vs.

The results of these observations are described in valence bond terms, with resonance structure contributions to the ground state bridge wavefunction being different for SQ—Bridge—NN and Au n —S—Bridge—S—Au n systems. Their work supports an argument that the bridge Green's function, G Bis not the same for electron transfer and conductance.

Herein, we address these difficulties and the concept of bridge electronic structure transferability between conductance and exchange. Our results are described in valence bond terms, with resonance structure contributions to the ground state bridge wavefunction being different for SQ—Bridge—NN and Au n —S—Bridge—S—Au n systems. This formula is used to calculate the voltage dependent current, I Vacross a molecular junction, which is determined by integrating the transmission function, T EVaccording to eqn 7.

All electron transport properties were computed using the ATK software package that includes virtual nanolab associated analysis modules. The molecular projected self-consistent Hamiltonian MPSH technique has been used to understand the molecular orbital origin of the resonant peaks in the transmission spectra.

The sulfur orbital contributions to the MPSH states are important in modulating the conductance, since they directly connect the electrodes to the molecule and allow for delocalization of the bridge wavefunction in the scattering region.

The computed conductance as a function of the experimentally determined SQ—Bridge—NN magnetic exchange coupling constants using monomeric and dimeric bridge molecules is presented in Fig.

The second observation is that the data for different bridge types monomer vs. The best fits of eqn 12 to our g mb vs. Beratan and Waldeck also observed a nonlinear relationship between g mb and heterogeneous electron transfer rate constants, k ET. As introduced above, the resonance structures shown in Fig. This is partly due to the fact that only high energy zwitterionic and biradical resonance structures can be drawn for the S—Ph—Ph—S electrode linkage.

The nature of the charge transfer is indicated by the computed electron density difference map EDDM in Fig. Thus, the nature of the charge transfer in di-bridged SQ—Ph 2 —NN is analogous to what has been observed previously in the mono-bridged SQ—Ph—NN biradical, 20,39 highlighting quinoidal resonance structure contributions to the ground state wavefunction. Tunneling gaps and bridge—bridge electronic coupling, H BBcalculated from experimental data for the phenylene- and thiophene series provide a convincing explanation for the more pronounced g mb vs.

Namely, contributions from ECN resonance structures Fig. With respect to the importance of quinoidal resonance contributions, aromaticity has been shown to reduce conductance values in single molecule junctions.

**Electrical conductivity - Metals**

Received 7th AugustAccepted 14th September Bottom: Molecular bridge B connects spin centers to facilitate magnetic exchange coupling. Only the HOMO is dominant in the bias window and therefore it maximally contributes to g mb. The LUMO is at higher energy and lies outside of the bias window. As such, it does not contribute to g mb. B Left: Computed zero-bias energy vs. A 2 V bias window is depicted in yellow and the Fermi energy is shown as a dashed line. Bridge carbon atoms of contact are indicated by blue arrows.

The data indicate that current is not directly proportional to magnetic exchange coupling. The data are fit to separate empirical power law functions with identical exponents, with best fits shown as black lines.

Best fits to the Eq.Distribution of the conductance P g at the critical point of the metal-insulator transition is presented for three and four dimensional orthogonal systems.

## Semiconductor

The form of the distribution is discussed. Dimension dependence of P g is proven. Rn As the conductance g in disordered systems is not the self-averaged quantity, the knowledge of its probability distribution is extremely important for our understanding of transport.

This problem is of special importance at the critical point of the metal-insulator transition [1]. While the distribution of the conductance in the metallic phase is known to be Gaussian in agreement with the random-matrix theory [2] and the localized regime is characterized by the log-normal distribution of g [2], the form of the critical distribution remains still unknown.

Among the problems which are not solved yet we mention e. Several attempts has been made to characterize conductance distribution at the critical point. Using the Migdal- Kadanoff renormalization treatment, huge conductance fluctuations has been predicted in [3].

The form of P g for 2D symplectic models was found in [6, 7]. Recently, P g has been studied also for system in magnetic field, both in 3D [8] and in 2D. Documents: Advanced Search Include Citations. Abstract Distribution of the conductance P g at the critical point of the metal-insulator transition is presented for three and four dimensional orthogonal systems.

Powered by:.A study of the distribution of conductances, P gfor quasi-one-dimensional multichain pseudorandom systems is here presented. The results are compared with those obtained for the truly random disordered systems with the same geometry. A rich variety of shapes of P g is thus evidenced in the crossover-transport regime and, in the case of identical interacting chains composing the device, we have shown that the conductance distribution of the system can be obtained from the results for the single pseudorandom chain.

This is a preview of subscription content, log in to check access. Rent this article via DeepDyve. Umbach, S. Washburn, R. Laibowitz, R. Webb, Phys. B 30 Stone, Phys. Lee, Stone, Phys. JETP Lett. Google Scholar. Belitz, S. Kirkpatrick, Rev.

Lee, T.

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On Sunday, Washington raced out to a 17-point lead and held on for a 26-24 home victory versus San Francisco. Kirk Cousins threw for 330 yards and two touchdowns for the Redskins on the afternoon. Through six games, Washington ranks 6th in total offense and is scoring 23. Philadelphia comes into this game with a defense that ranks 19th in yards allowed and surrenders 20. The Philadelphia Eagles have won five of their first six games overall and are emerging as one of the best teams in the National Football League.

Second year QB Carson Wentz has thrown for 1,584 yards and 13 touchdowns and has helped the Eagles open up a two-game division lead in the NFC East. On Thursday, Wentz threw for 222 yards and three touchdowns to lead Philadelphia to a 28-23 road triumph over Carolina. Philadelphia comes into this contest ranked third in total offense and scoring 27.

Washington is very improved on defense, ranking 5th in yards allowed and giving up 22. Washington is 10-3 ATS in its last 13 games on the road. Washington is 4-1 ATS in its last 5 games when playing on the road against Philadelphia.

### Spin-dependent conductance statistics in systems with spin-orbit coupling

The total has gone OVER in 6 of Washington's last 7 games on the road. The total has gone OVER in 4 of Philadelphia's last 5 games when playing at home against Washington. Free Betting Pick: OVER 48Washington CB Josh Norman (ribs, lung) was unable to suit up last week, but could return to action for this game.

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