Electrical resistivities of two icosahedral (I) Al-Pd-Re alloys have been measured between room temperature and mK temperatures. One quasicrystalline (QC) polygrain Al-Pd-Re sample exhibited insulating behavior in its resistivities, increasing by a factor of r=R(4 K)/R(300 K)=7.76; its room temperature resistivity was 9,890 μΩ cm. A “phenomenological” expression fitted the conductivity data well between 300 K to 0.5 K. Below 0.4 K a crossover to an activated variable-range hopping law was observed. Low temperature magnetoresistance ratio data and fits using the wave function shrinkage theory are presented. A second QC Al-Pd-Re sample had a small resistance temperature ratio r=2.12. The room temperature resistivity was extremely large, ρ(300 K)≈40,980 μΩ cm. Its conductivity could be described well using a simple temperature power law between 300 K to 20 K. Below 20 K there was a crossover to a new behavior. Below 1 K, the conductivity could be fitted using a very weakly insulating power law where σ(T)≈11.37T 0.032 in (Ω cm)−1, suggesting that this sample is located just below the metal-insulator transition. The magnetoconductivity data could not be fitted successfully using the 3D weak localization (WL) theory and inserting into it physical and realistic fitting magnitudes for the inelastic magnetic field B in.

Electrical resistivities of several quasicrystalline (QC) icosahedral Al–Cu–Ru alloys have been measured between room temperature and mK temperatures. None of the Al–Cu–Ru samples exhibited “insulating” behaviors in their resistivities. One sample had a large resistivity of ≈49,000 μΩ cm at room temperature. Its resistivity increased with decreasing temperatures by a factor of 3.2 and exhibited a maximum around 2 K. Fitting discrepancies between the experimental magnetoconductivity data and the weak localization and electron–electron interaction theories suggest that the weak localization theory poorly describes the electronic conduction behavior of this highly resistive quasicrystalline sample.

A simple electronic circuit is described using four common and very inexpensive analog multiplexer/demultiplexer chips. These analog switches are used to select eight different wiring configurations to a van der Pauw sample. Several interfacing schemes to a PC are suggested. The van der Pauw resistivity and Hall voltage expressions are also summarized.

Speer carbon composition resistors, in particular the 470 Ω and 220 Ω 1/2 W grade 1002 resistors, have been used as secondary thermometers at temperatures below 4 K for many years. Their zero field resistances have been measured between 300 K and 4 K using a “dip” probe. Above 10 K, the resistance behavior can be explained using a simple temperature power law, R ( T ) ≈ R 0 / T 0.16 . The resistance measurements have been extended to 0.02 K using dilution refrigerators. Between 4 K and 0.3 K, the resistances exhibited activated laws having hopping exponents y ≈ 0.5. Below 0.3 K, the 470 Ω resistors exhibit a crossover to a weaker activated law. Crossover resistance expressions suggest that the resistances follow a Mott variable-range hopping (VRH) law below 0.05 K. The low temperature magnetoresistance (MR) data showed changes of less than ±12 % of the zero field resistance values in fields up to 10 T. Fits using the wave function shrinkage and the forward interference models gave only fair agreement with the MR data.

The magnetoresistance (MR) properties of several thin polycrystalline bismuth films have been measured over a wide temperature interval (0.42K ≤ T ≤ 292 K) and a magnetic field range (0 T ≤ B ≤ 45 T). In most cases, the magnetic field was oriented in the transverse direction, with the field parallel to the substrate of the film and also perpendicular to the current direction. These MR results are different from those in either the perpendicular or parallel field orientations. The anomalous behavior of the transverse magnetoresistance can be explained considering partially diffused scattering of the carriers at the top and bottom surfaces of the films. The data are fitted using a phenomenological model, based upon the theory of Way and Kao and also using the two carrier expressions of Pippard and Fawcett (P-F).

Hall coefficient measurements have been performed on polycrystalline bismuth films of 9180 Angstrom and 11850 Angstrom thickness at different temperatures in perpendicular magnetic fields. At T = 270 K, the Hall coefficient data increased in magnitude by a factor of three and saturated at high fields. Fits of the Pippard-Fawcett Hall coefficient expression were made to the data using four fitting parameters, three of which were extracted from the perpendicular magnetoresistance data at 270 K. Data at lower temperatures are presented. (C) 2003 Elsevier B.V. All rights reserved.

Magnetoresistance (MR) ratios r = R(B)/R(0) have been measured in parallel fields on a polycrystalline heat-treated bismuth film at different temperatures. MR ratios vs. B's exhibit "maximums" followed by decreases, described by a B-1 law. Electron Fermi energies have been extracted. The MR data are explained using a Landau tube "sweeping" model and a MR expression of Pippard and of Fawcett. There is a second maximum in the MR ratios at 38 T followed by a second decrease. This second decrease could arise from the "sweeping" of the next lowest Landau tubes outside the Fermi surface of the single hole pocket. (C) 2004 Elsevier B.V. All rights reserved.

The electronic transport properties of a polycrystalline (3420 A thick) bismuth film have been measured over a wide temperature interval (0.23 K < T < 292 K) and a magnetic field range (0 T < B < 25 T). The results for the polycrystalline film are very different and anomalous from those of an epitaxial thin bismuth film. The zero field resistance increases by a factor of five. The magnetoresistance (MR) values in perpendicular magnetic fields have the same magnitude at low temperatures as compared to the MR values at room temperature. The Hall coefficient data in perpendicular fields show oscillations at liquid helium temperatures; there should be no Shubnikovde Haas oscillations in a polycrystalline bismuth film. The sign of the Hall coefficient at room temperature is positive in small fields and becomes negative in large fields. In contrast, the Hall coefficient is always negative in thick bismuth films. The magnetoresistances in parallel magnetic fields show maxima at intermediate fields followed by decreases at high field values; in theory there should be a small or no MR in the parallel field orientation. The most anomalous behaviours are large Hall voltages and Hall coefficients in parallel magnetic fields; the parallel Hall data also have oscillations at low temperatures. The magnetoresistance in transverse fields is anomalous and can be explained by strong diffused boundary scattering at the top and bottom surfaces of the film. Acceptable fits to most of the transport data are obtained using the two carrier expressions of Pippard and of Fawcett and using the Drude expression.

Hall coefficient measurements have been performed on a polycrystalline 11875Å Bismuth film in fields oriented parallel to the current flow. Classical theory predicts no Hall voltages and no magnetoresistances (MRs) in parallel fields. Probably owing to diffused and specular scattering off the rough surfaces of the crystallites, Hall voltages and parallel MR's are easily measured. Hall coefficient data in parallel Bs are summarized at 295, 78, and 1.49K. The data are interpreted using the Pippard–Fawcett expression and the Landau tube model that contributes additional carriers at high fields.

Resistivity and magnetoresistance measurements have been performed on insulating icosahedral AlPdRe quasicrystal (QC) bar samples. At temperatures in the range , the resistivities follow a simple inverse temperature law: ρ(T) = ρ0/T(1.0 ± 0.1). Below 1 K, the resistivity of a weakly insulating sample exhibited a simple inverse temperature law where ρ(T) = ρ0/T0.33 and not an activated variable-range hopping (VRH) law. Strongly insulating samples exhibit saturation of their resistivities to finite values as . These saturation resistivity values are believed to arise from the presence of a second metallic phase located within the quasicrystal's structure. By extrapolating the measured resistivities at 22 mK to absolute zero, the saturation conductivity values were estimated at T = 0 K and subtracted from the conductivity data points. These 'corrected' data, corresponding only to the QC phase, were found to follow activated VRH laws, having hopping exponents y that vary in the range . The activated VRH behaviours are observed only below 1 K. The magnetoresistances (MRs) of these samples are also anomalous. The MRs can be explained by including contributions from both the saturation conductivity values and from the QC MR ratios, estimated using the wavefunction shrinkage model.

We have observed that the conductivity σ(T) for the Al70Pd22.5Re7.5 quasicrystal, with a resistivity ratio r = R(4.2 K)/R(300 K) = 13.2, obeys the variable-range hopping law, σ(T) = σ0/exp [(T0/T)]μ, in the temperature range between 64 mK and 1.6 K. The hopping exponent μ is extracted to be 0.23, close to the Mott exponent of 1/4, and T0 is 3.5 K. This insulating behaviour is consistent with the prediction of a previously determined scaling law that bulk Al70Pd22.5Re7.5 samples having r ≥ 12.8 will be insulating. Large positive magnetoresistances (MRs) were observed in this sample. The percentage change in the MR = ΔR(B, T)/R(0, T), as high as 185% at T = 0.11 K and B = 17 T, is the largest value ever reported in Al–Pd–Re QCs, to our knowledge. The difficulties using existing MR theories to explain the MR data for this insulating sample near the metal–insulator transition are discussed.

Electronic transport measurements have been made on bulk icosahedral Al 70 Pd 22.5 Re 7.5 quasicrystal (QC's) samples, having increasingly larger resistance temperature ratios, r T = R (4.2 K)/ R (292 K). Data were taken between 0.023 K to 292 K and in magnetic fields up to 17.9 T. Both the zero field resistivity and the magnetoresistance (MR) changed from metallic behavior to weakly insulating behavior to highly insulating behavior, as the resistance temperature ratios γt's of the samples were made larger. For the insulating samples, the resistivities ρ 's followed simple inverse temperature power laws above 50 K going as ρ ( T ) = a 0 / T z , where z = 1 ± 0.1. The insulating QC samples exhibited saturation behaviors of their resistivities below 2 K. Below 0.3 K, the strongly insulating QC's displayed activated variable-range hopping (VRH) laws in their conductivity; the hopping exponents y's in the VRH laws varied between 0.19 ≤ y ≤ 0.43. A simple model including conductivity contributions both from the primary insulating QC phase and from a secondary metallic phase yielded good fits to the resistivity and MR data.

Using theories of the magnetoresistance in the variable-range hopping regime, we are able to interpret the low magnetic field magnetoresistance data taken at liquid helium temperatures of an insulating Al70Pd22.5Re7.5 quasicrystal having a resistivity ratio R=ρ(4.2 K)/ρ(300 K) equal to 77.

The temperature dependence of the magnetoresistance (MR) of insulating Al70Pd22.5Re7.5 quasicrystals taken at liquid-helium temperatures can be explained by the theories of MR-the forward interference and the wave-function shrinkage-in the variable-range hopping (VRH) regime. By analyzing the MR data with the theories mentioned above, a crossover from Mott VRH conduction to Efros-Shklovskii VRH conduction at liquid helium temperatures was identified in a highly resistive Al70Pd22.5Re7.5 sample. The rapid decrease in the negative MR of highly resistive samples at low temperatures might be attributed to the conduction via the states in the Coulomb gap.

Magnetoconductance (MC) measurements have been performed on a 2140 Å thick tungsten carbide film at temperatures very close to the superconducting transition temperature Tc of the film. The data are dominated by superconducting fluctuations. A novel three-dimensional phenomenological model is proposed to explain the MC data, yielding good fits. The Larkin beta factor, βLarkin, appeared as a fitting parameter. An expression proposed by Larkin for βLarkin failed badly for temperatures extremely close to Tc. But at intermediate and high temperatures compared to Tc, Larkin's expression gave very good agreement in fits to the MC data. At temperatures very close to Tc, a crossover from three dimensions to two dimensions was observed in the behaviour of the MC of the film.

Numerical calculations are presented for predicting the large positive magnetoresistance ratios R(B)/R(0) which are often observed in insulating materials. The magnetic field causes shrinkage of the localized electronic wave function, resulting in less overlapping between the hopping sites and hence a relatively large increase of the resistance in the insulating material. Two specific cases are considered: (a) an insulating 3D sample that exhibits a "Mott" variable-range hopping law in its zero-field resistance and (b) an insulating 3D sample that exhibits an "Efros–Shklovskii" variable-range hopping law in its zero field resistance. The numerical calculations are tabulated. The general 3D "soft gap" case is also discussed.

Magnetoresistance (MR) ratios R(B,T)/R(0,T) have been measured in an insulating three-dimensional amorphous nickel-silicon film that exhibits the Mott variable-range hopping (VRH) law in its zero-field resistance behavior. Surprisingly, the resistance displayed a decrease in small fields; only in moderately strong magnetic fields did the resistance exhibit a large increase over its zero-field value. These results are described by a phenomenological empirical model of two hopping processes acting simultaneously-the orbital magnetoconductance (forward-interference) model yielding negative magnetoresistances and the wave-function shrinkage model contributing positive magnetoresistances. The fits use numerical values for estimating the R(B,T)/R(0,T) ratios, based upon the wave-function shrinkage model. The model includes three fitting parameters, whose magnitudes are extracted from the MR ratio data at T = 10.5 K. Agreement between the predicted and measured data is acceptable at high temperatures. A crossover of the conductivity to an Efros-Shklovskii (ES) variable-range hopping law is observed around T = 6 K. At lower temperatures for this ES case, predicted values for the R(B,T)/R(0,T) ratios are fitted to the data. For a second weakly insulating film, which also exhibits a Mott VRH law in its resistance, the negative magnetoresistance contribution is greatly depressed.

High magnetic field measurements for the magnetoresistance ratios R(B,T)/R(0,T) have been made on an insulating amorphous nickel–silicon thin film. In zero field, the resistance of this insulating film exhibits a “soft gap” variable-range hopping law in the liquid helium temperature region. In small fields, negative magnetoresistance values are observed, which can be explained using the forward interference (orbital momentum) theory. In intermediate and large fields, the magnetoresistance is positive and large and can be explained using the wave function shrinkage theory. A phenomenological model incorporating both processes gives very acceptable fits to the experimental data.

Zirconium oxynitride insulating films make excellent thermometry at 4K and above. The resistance is almost independent of magnetic fields up to 30T and exhibits good temperature sensitivity and good reproducibility upon temperature cycling. However below 4K, this material exhibits an anomalous negative magnetoresistance (MR); for example at 86mK, the resistance decreases by a factor of 24 in a 17T field as compared to its zero-field value. The negative magnetoresistnce behavior is explained using a model proposed by Movaghar, Schweitzer and Osaka. Fits to the negative MR data are good above 0.3K but become poorer at lower temperatures.