Spin-dependent Hall effect in degenerate semiconductors: a theoretical study

Spin transport and spin current detection in semiconductors

The conductivity and Hall effect of p-type doped Zn(1−x)MnxTe layers are described and analyzed in terms of a two-fluid model where part of the carriers are weakly localized as bound magnetic polarons. At low temperature, the Hall effect is dominated by the spin-dependent component (extraordinary Hall effect), in good agreement with a crude estimate taking into account the properties of the valence band. The long range ferromagnetic interaction appears to be induced by the weakly localized holes.

We study magnetotransport in conical helimagnet crystals using the nonequilibriun Boltzmann equation approach. Spin dependent magnetoresistance exhibits dramatic properties for high and low electron concentrations at different temperatures. For spin up electrons we find negative magnetoresistance despite only considering a single carrier type. For spin down electrons we observe giant magnetoresistance due to depletion of spin down electrons with an applied magnetic field. For spin up carriers, the magnetoresistance is negative, due to the increase in charge carriers with a magnetic field. In addition, we investigate the spin dependent Hall effect. If a magnetic field reaches some critical value for spin down electrons, giant Hall resistance occurs, i.e. Hall current vanishes. This effect is explained by the absence of spin down carriers. For spin up carriers, the Hall constant dramatically decreases with field, due to the increase in spin up electron density. Because of the giant spin dependent magnetoresistance and Hall resistivity, conical helimagnets could be useful in spin switching devices.

The linewidth of spontaneous emission from degenerate semiconductors under strongly induced excitation at relatively high temperature a is shown to be directly related to the diffusivity-mobility ratio of the electrons in such semiconductors. This is confirmed by means of an example based on experimental observation

A Superconducting QUantum Interference Device (SQUID) modulated by a fast oscillating magnetic flux can be used as a parametric amplifier, providing gain with very little added noise. Here, we develop linearized models to describe the parametrically flux-pumped SQUID in terms of an impedance. An unpumped SQUID acts as an inductance, the Josephson inductance, whereas a flux-pumped SQUID develops an additional, parallel element which we have coined the ``pumpistor.'' Parametric gain can be understood as a result of a negative resistance of the pumpistor. In the degenerate case, the gain is sensitive to the relative phase between the pump and signal. In the nondegenerate case, gain is independent of this phase. We develop our models first for degenerate parametric pumping in the three-wave and four-wave cases, where the pump frequency is either twice or equal to the signal frequency, respectively. We then derive expressions for the nondegenerate case where the pump frequency is not a multiple of the signal frequency, where it becomes necessary to consider idler tones which develop. For the nondegenerate three-wave case, we present an intuitive picture for a parametric amplifier containing a flux-pumped SQUID where current at the signal frequency depends upon the load impedance at an idler frequency. This understanding provides insight and readily testable predictions of circuits containing flux-pumped SQUIDs.

We obtain an analytical expression for the probability density of the Gaussian vector with a degenerate covariance matrix. The expression generalizes a similar expression for the nondegenerate case. A definition of the Gaussian vector on the basis of a probability density, which is common for the degenerate and nondegenerate cases, is given. Examples of using the obtained probability density for the synthesis of optimal signal-processing algorithms are presented.

In this paper we consider a geometric viewpoint to analyze the behaviour of the Conjugate Gradient (CG) method, for the solution of a symmetric linear system, when at current step a pivot breakdown possibly occurs (degenerate case). As well known this can occur when the system matrix is indefinite or singular. In the latter case the CG gets stuck, since the steplength along the current search direction cannot be computed. We show here that a simple geometric interpretation can be provided for the degenerate case, as long as some basics on projective geometry in the Euclidean space are considered.

Electrical properties of layered copper oxyselenides (BiO)Cu 1 − xSe and (Bi 1 − xSr x)OCuSe

We have developed a versatile, fully automated Hall measurement setup for operations between room temperature and 750K and in magnetic fields up to ±10 kOe. Our compact sample holder design with localized heating and minimal heat losses enables precise temperature stability (better than ±10 mK at 750K) and low power consumption (20-25W). The setup is housed within a 26mm air gap between the pole pieces of an electromagnet. The sample holder, enclosed in a quartz tube for a controlled atmosphere, can accommodate various sample shapes and sizes, which can be contacted using adjustable pressure-point contacts. Despite its compact size, bulk thermoelectric samples measuring up to 10mm laterally can be analyzed successfully. A phase-sensitive lock-in technique and electromagnetic shielding ensure excellent sensitivity, allowing nanovolt Hall signal measurements in high-carrier-concentration samples. We have successfully applied this setup to diverse materials, including a lightly doped germanium (1014 cm-3), degenerate semiconductors from the half-Heusler family (1021 cm-3), and superionic thermoelectrics (1018 cm-3), demonstrating its versatility and reliability. Our results align well with those from commercial systems where available.

We consider a neutral spinor condensate moving in a periodic magnetic field. The spatially dependent magnetic field induces an effective spin dependent Lorentz force which in turn gives rise to a spin dependent Hall effect. Simulations of the Gross-Pitaevskii equation quantify the Hall effect. We discuss possible experimental realizations.

We prove the existence of multidimensional traveling-wave solutions to the scalar equation for the transport of solutes (contaminants) with nonlinear adsorption and spatially periodic convection-diffusion-adsorption coefficients under the assumption that the nonlinear adsorption function satisfies the Lax and Oleinik entropy conditions. In the nondegenerate case, we also prove the uniqueness of the traveling waves. These traveling waves are analogues of viscous shock profiles. They propagate with effective speeds that depend on the periodic porous media only up to their mean states, and are given by an averaged Rankine-Hugoniot relation. This is a direct consequence of the fact that the transport equation is in conservation form. We use the sliding domain method, the continuation method, spectral theory, maximum principles, and a priori estimates. In the degenerate case, the traveling waves are weak solutions of a degenerate parabolic equation and are only Holder continuous. We obtain them by taking suitable limits on the non-degenerate traveling waves. The uniqueness of the degenerate traveling waves is open.

This paper deals with multichannel time series, and extends the autocorrelation method for fitting the time series from the nondegenerate case to the general case. We shall show that the AR model obtained by solving the normal equations is always stable even in the degenerate case. The multichannel Levinson algorithm for solving the normal equations is extended from the nondegenerate case to the general case. In the nondegenerate case, the first n+1 values of the auto-correlation sequence of the obtained AR model of order n are identical with those of the original data. The next considered is the extrapolation problem of an autocorrelation sequence, that is, given data <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{R_{0}, R_{1},..., R_{n}}</tex> , it is to construct a model whose first n+1 values of the autocorrelation sequence are identical with these data. We shall show that, even in the degenerate case, when the given data <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">{R_{0}, R_{1},..., R_{n}}</tex> are taken from the autocorrelation sequence of a purely nondeterministic time series, they are identical with the first n+1 values of the autocorrelation sequence of the AR model of order n.

Asymptotic spreading of a time periodic diffusion equation with degenerate monostable nonlinearity

We propose a finite volume scheme for convection–diffusion equations with nonlinear diffusion. Such equations arise in numerous physical contexts. We will particularly focus on the drift-diffusion system for semiconductors and the porous media equation. In these two cases, it is shown that the transient solution converges to a steady-state solution as t tends to infinity. The introduced scheme is an extension of the Scharfetter–Gummel scheme for nonlinear diffusion. It remains valid in the degenerate case and preserves steady-states. We prove the convergence of the scheme in the nondegenerate case. Finally, we present some numerical simulations applied to the two physical models introduced and we underline the efficiency of the scheme to preserve long-time behavior of the solutions.

Nernst coefficient, magnetoresistance, and magnetothermoelectric power together with electrical conductivity, Hall coefficient, and thermoelectric power of α-Ag 2 Te are measured as functions of the e.m.f., E of the galvanic cell Ag|AgI|Ag 2 Te|Pt, where E may be considered to represent the relative position of the Fermi level in the Ag 2 Te specimen. The experimental results exhibit consistent agreement with the Lorentz-Sommerfeld theory for degenerate two-band semiconductors with energy independent mean free paths of carriers. Relative thermal conductivity is also measured, showing minimum at a E value expected from the theory.