Hall resistance in the hopping regime, a "Hall Insulator"?

The Hall conductivity and resistivity of strongly localized electrons at low temperatures and at small magnetic fields are obtained. It is found that the results depend on whether the conductivity or the resistivity tensors are averaged to obtain the macroscopic Hall resistivity. In the second case the Hall resistivity always {\it diverges} exponentially as the temperature tends to zero. But when the Hall resistivity is derived from the averaged conductivity, the resulting temperature dependence is sensitive to the disorder configuration. Then the Hall resistivity may approach a constant value as $T\to 0$. This is the Hall insulating behavior. It is argued that for strictly dc conditions, the transport quantity that should be averaged is the resistivity.Comment: Late

Introduction to tensorial resistivity probability tomography

The probability tomography approach developed for the scalar resistivity method is here extended to the 2D tensorial apparent resistivity acquisition mode. The rotational invariant derived from the trace of the apparent resistivity tensor is considered, since it gives on the datum plane anomalies confined above the buried objects. Firstly, a departure function is introduced as the difference between the tensorial invariant measured over the real structure and that computed for a reference uniform structure. Secondly, a resistivity anomaly occurrence probability (RAOP) function is defined as a normalised crosscorrelation involving the experimental departure function and a scanning function derived analytically using the Frechet derivative of the electric potential for the reference uniform structure. The RAOP function can be calculated in each cell of a 3D grid filling the investigated volume, and the resulting values can then be contoured in order to obtain the 3D tomographic image. Each non-vanishing value of the RAOP function is interpreted as the probability which a resistivity departure from the reference resistivity obtain in a cell as responsible of the observed tensorial apparent resistivity dataset on the datum plane. A synthetic case shows that the highest RAOP values correctly indicate the position of the buried objects and a very high spacial resolution can be obtained even for adjacent objects with opposite resistivity contrasts with respect to the resistivity of the hosting matrix. Finally, an experimental field case dedicated to an archaeological application of the resistivity tensor method is presented as a proof of the high resolution power of the probability tomography imaging, even when the data are collected in noisy open field conditions.Comment: 8 pages, 7 figure

Radiation induced oscillations of the Hall resistivity in two-dimensional electron systems

We consider the effect of microwave radiation on the Hall resistivity in two-dimension electron systems. It is shown that the photon-assisted impurity scattering of electrons can result in oscillatory dependences of both dissipative and Hall components of the conductivity and resistivity tensors on the ratio of radiation frequency to cyclotron frequency. The Hall resistivity can include a component induced by microwave radiation which is an even function of the magnetic field. The phase of the dissipative resistivity oscillations and the polarization dependence of their amplitude are compared with those of the Hall resistivity oscillations. The developed model can clarify the results of recent experimental observations of the radiation induced Hall effect.Comment: 4 pages, 1 figur

Model for the magnetoresistance and Hall coefficient of inhomogeneous graphene

We show that when bulk graphene breaks into n-type and p-type puddles, the in-plane resistivity becomes strongly field dependent in the presence of a perpendicular magnetic field, even if homoge- neous graphene has a field-independent resistivity. We calculate the longitudinal resistivity \rho_{xx} and Hall resistivity \rho_{xy} as a function of field for this system, using the effective-medium approximation. The conductivity tensors of the individual puddles are calculated using a Boltzmann approach suit- able for the band structure of graphene near the Dirac points. The resulting resistivity agrees well with experiment, provided that the relaxation time is weakly field-dependent. The calculated Hall resistivity has the sign of the majority carrier and vanishes when there are equal number of n and p type puddles.Comment: 5 pages, 4 figure

Deviations from Matthiessen rule and resistivity saturation effects in Gd and Fe

According to earlier first-principles calculations, the spin-disorder contribution to the resistivity of rare-earth metals in the paramagnetic state is strongly underestimated if Matthiessen's rule is assumed to hold. To understand this discrepancy, the resistivity of paramagnetic Fe and Gd is evaluated by taking into account both spin and phonon disorder. Calculations are performed using the supercell approach within the linear muffin-tin orbital method. Phonon disorder is modeled by introducing random displacements of the atomic nuclei, and the results are compared with the case of fictitious Anderson disorder. In both cases the resistivity shows a nonlinear dependence on the square of the disorder potential, which is interpreted as a resistivity saturation effect. This effect is much stronger in Gd than in Fe. The non-linearity makes the phonon and spin-disorder contributions to the resistivity non-additive, and the standard procedure of extracting the spin-disorder resistivity by extrapolation from high temperatures becomes ambiguous. An "apparent" spin-disorder resistivity obtained through such extrapolation is in much better agreement with experiment compared to the results obtained by considering only spin disorder. By analyzing the spectral function of the paramagnetic Gd in the presence of Anderson disorder, the resistivity saturation is explained by the collapse of a large area of the Fermi surface due to the disorder-induced mixing between the electronic and hole sheets.Comment: 9 pages, 7 figure

Resistivity scaling model for metals with conduction band anisotropy

It is generally understood that the resistivity of metal thin films scales with film thickness mainly due to grain boundary and boundary surface scattering. Recently, several experiments and ab initio simulations have demonstrated the impact of crystal orientation on resistivity scaling. The crystal orientation cannot be captured by the commonly used resistivity scaling models and a qualitative understanding of its impact is currently lacking. In this work, we derive a resistivity scaling model that captures grain boundary and boundary surface scattering as well as the anisotropy of the band structure. The model is applied to Cu and Ru thin films, whose conduction bands are (quasi-)isotropic and anisotropic respectively. After calibrating the anisotropy with ab initio simulations, the resistivity scaling models are compared to experimental resistivity data and a renormalization of the fitted grain boundary reflection coefficient can be identified for textured Ru.Comment: 12 pages, 7 figure

Low-resistivity homogeneous elastomers

Mixture of polyurethane polyelectrolyte and soluble, conducting organic compound produces homogeneous elastomer which has resistivity several orders of magnitude less than polyelectrolyte alone. Elastomeric material has novel resistivity dependence on temperature, that is, resistivity changes dramatically over narrow temperature range in vicinity of glass transition temperature