Mott Law Research Articles

Variable range hopping in finite one-dimensional and anisotropic two-dimensional systems

The variable range hopping conduction is simulated in a strongly anisotropic two-dimensional (2D) percolation model, which consists of parallel conducting chains coupled to each other weakly via rare “impurities”. The exponential temperature dependence of resistance has been calculated for samples of different size, interchain distance, and impurity concentration in two directions, longitudinal and perpendicular to the chain direction. In the limiting case of single finite chains the results are in good agreement with existing analytical expressions for both the length and temperature dependences, but with a low temperature limit, depending on the chain length and localization length. In the 2D case it was shown that there exists a crossover in relative behaviour between the longitudinal and transverse resistance of a finite system, which however disappears from the limit of infinite systems, where the hopping conduction should be always isotropic and obeys the 2D Mott law.

Electrical Conductivity of CuIr2S4

The temperature dependence of electrical conductivity of CuIr2S4 has been measured. In the range 4.2–50 K the conductivity can be described in terms of the Mott law, while in the range 50–200 K the experimental data are best described in terms of a small polaron model, taking into account the influence of the temperature dependence of the vibrations of the atoms in their effect on the resonance integral.

Nonradiative relaxation of photoexcited O01 centers in glassy SiO2

The processes involved in the excited-state relaxation of hole O 1 0 centers at nonbridging oxygen atoms in glassy SiO2 were studied using luminescence, optical absorption, and photoelectron emission spectroscopy. An additional nonradiative relaxation channel, in addition to the intracenter quenching of the 1.9-eV luminescence band, was established to become operative at temperatures above 370 K. This effect manifests itself in experiments as a negative deviation of the temperature-dependent luminescence intensity from the well-known Mott law and is identified as thermally activated external quenching with an energy barrier of 0.46 eV. Nonradiative transitions initiate, within the external quenching temperature interval, the migration of excitation energy, followed by the creation of free electrons. In the final stages, this relaxation process becomes manifest in the form of spectral sensitization of electron photoemission, which is excited in the hole O 1 0 -center absorption band.

Electron localization and conductivity in quasicrystals at low temperatures

In the quasicrystalline case the electronic states at the Fermi level might be localized by the quasiperiodic potential itself, and there is only the formal analogy with Anderson type localization. A perfect quasicrystal at low temperatures exists at the “critical” state of metal–insulator transition. The power-law temperature dependence of electronic conductivity experimentally observed at T<5 K in i-Al-Pd-Re quasicrystal is obtained on “critical” wave functions. A “scenario” is proposed to explain the existence of the Mott law for the variable range hopping conductivity in quasicrystals.

Electrical properties of amorphous SiCxNyHz-ceramics derived from polyvinylsilazane

Abstract Electrical properties of monolithic, amorphous SiCxNyHz-ceramics derived from 1,3,5-trimethyl-1,3,5-trivinylcyclotrisilazane via polymer pyrolysis were investigated from room temperature to 400 °C using impedance spectroscopy. Depending on the pyrolysis temperature Tp, the d.c. conductivity varies up to 8 orders of magnitude. The temperature dependence of samples pyrolysed at low temperatures (Tp=700–1200 °C) follows a Mott law, whereas samples pyrolysed at high temperature (Tp=1400 °C) show an Arrhenius dependence. Structural changes during pyrolysis were characterized by solid state magic angle spinning nuclear magnetic resonance spectroscopy, Raman spectroscopy and X-ray diffractometry. NMR and especially Raman measurements indicate the formation of sp2-carbon atoms, which rearrange towards graphitic-like domains with increasing pyrolysis temperature. This observation can explain the related increase of the d.c.-conductivity.

Transport Properties of Ca 1 – x MnO 3 – δ + x CeO 2 (0 < x ≤ 0.15) Mixtures

Data are presented on the temperature-dependent electrical conductivity and thermoelectric power of Ca1 – x MnO3 – δ + xCeO2 (0 < x ≤ 0.15) mixtures obtained as intermediate products in the synthesis of Ca1 – x Ce x MnO3 – δ solid solutions. The electrical properties of the mixtures are shown to be dominated by those of the perovskite-like phase Ca1 – x MnO3 – δ and to depend on Ca concentration. All of the samples with 0 ≤ x ≤ 0.15 exhibit n-type conductivity. The charge transport in CaMnO3 – δ below 930 K is attributable to small-polaron hopping. At higher temperatures, conduction through delocalized states seems to prevail. In the Ca1 – x MnO3 – δ + xCeO2 mixtures with 0.05 ≤ x ≤ 0.15, small-polaron hopping is observed between 160 and 920 K. Below 160 K, the temperature variation of conductivity in the samples with x = 0.1 and 0.15 follows Mott's law.

Electronic transport in quasicrystals

Mobility of electrons in quasicrystals is considered in the framework of the fractional Fermi surface (FS) model, i.e., a multiconnected FS with many electron-hole pockets. The Mott law for the variable range hopping conductivity is obtained when intervalley scattering processes with small momentum transfer are taken into account. The transition to the power-law temperature dependence is discussed.

Transport Properties and Magnetoresistance in Pr0.7Pb0.3MnO3 Single Crystals

Large Pr0.7Pb0.3MnO3 single crystals with high quality have been prepared by flux growth by using the acceleration crucible rotation technique. The temperature dependence of the resistivity and magnetoresistance have been measured. It is found that the transition temperature in resistivity is 50 K higher than the Curie temperature. Below the transition temperature, the resistivity exhibits a metallic behavior, the low temperature resistivity can be fitted well by AT2.5. Above the transition temperature, the resistivity can be fitted well by Mott's law, and a larger effective paramagnetic moment than the theoretical value has been observed. A large low-field magnetoresistance has been obtained.

Growth and Electric Transport of Ca-doped PrBa2Cu3O7-δSingle Crystals

Crystal growth of Ca-doped PrBa 2 Cu 3 O 7-δ (Pr-123) single crystals by slow cooling of Pr 3 O 11 -CaCO 3 -BaCO 3 -CuO melts (self-flux technique) in ambient air atmosphere was studied. As the first approach the growth of Ca-free crystals in Al 2 O 3 and ZrO 2 crucibles was investigated. The best quality crystals with the average size of 5 x 5 x 0.2mm 3 were obtained from Al 2 O 3 crucibles for Ba/Cu = 0.41 and 15 wt.% (2.41 mol.%) of stoichiometric Pr-123 solute in the melt. Next, using CaCO 3 as calcium source (0.09 -12.68 wt.%), the good quality Pr 1-x Ca x Ba 2 Cu 3 O 7-δ crystals with 0 ≤ x ≤ 0.26 were grown in the Al 2 O 3 crucibles from the solution with fixed value of Ba/Cu = 0.41. The oxygenated single crystals with size up to 5 x 8 x 0.2 mm 3 were used for electric transport investigations from four-probe resistivity measurements. The temperature dependence of resistivity of Ca-doped Pr-123 crystals is typical for systems with locallized states and, in principle, follows the Mott law for variable-range hopping (VRH).

Growth and Electric Transport of Ca-doped PrBa2Cu3O7-δSingle Crystals

Crystal growth of Ca-doped PrBa2Cu3O (Pr-123) single crystals by slow cooling of Pr3O11-CaCO3-BaCO3-CuO melts (self-flux technique) in ambient air atmosphere was studied. As the first approach the growth of Ca-free crystals in Al2O3 and ZrO2 crucibles was investigated. The best quality crystals with the average size of 5 x 5 x 0.2mm3 were obtained from Al2O3 crucibles for Ba/Cu = 0.41 and 15 wt.% (2.41 mol.%) of stoichiometric Pr-123 solute in the melt. Next, using CaCO3 as calcium source (0.09 -12.68 wt.%), the good quality Pr1-x CaxBa2Cu3O crystals with 0 ≤ x ≤ 0.26 were grown in the Al2O3 crucibles from the solution with fixed value of Ba/Cu = 0.41. The oxygenated single crystals with size up to 5 x 8 x 0.2 mm3 were used for electric transport investigations from four-probe resistivity measurements. The temperature dependence of resistivity of Ca-doped Pr-123 crystals is typical for systems with locallized states and, in principle, follows the Mott law for variable-range hopping (VRH).

Superlocalization of waves and electrons and hopping conductivity on classical and superconductive fractals

We have found an unexpected paradoxical situation in the percolation transition: the superconductive behavior below and above the threshold. We have found also the two different density of states d s=4/3 and d v=1.05 and the inverse localization lengths for fractons with the scalar and vector interactions, respectively. In this concept the wave functions of electrons or waves on an incipient percolation cluster and fractal dilute structure exhibit superlocalization behavior of the form ψ( r)∝exp[− r d φ ] with values of d φ1 =1.73 and d φ2 =2.4 for the former and the latter. Applications of these results for thermally activated hopping conductivity σ( t)∝exp[−( T 0/ T) β ] between impurities on a random fractal structure give the values of β=2/5 for the scalar and β=1/2 (Mott's law) for the vector interactions, respectively. Band states are localized in classical and superlocalized in superconductive percolations.

Variable range hopping conductivity in quasicrystals

The Fermi surface of a perfect icosahedral quasicrystal at zero temperature consists of infinite number of electron-hole pockets, and therefore electronic states are localized. It is shown that in this state the Mott law for the variable range hopping conductivity is fulfilled at very low temperatures.

Low-temperature electron transport in Si with an MBE-grown Sb δ layer

Studies of the electrical properties of Si single crystals with \ensuremath{\delta}(Sb) layers of various sheet densities ${N}_{D},$ of Sb atoms $(5\ifmmode\times\else\texttimes\fi{}{10}^{12}--3\ifmmode\times\else\texttimes\fi{}{10}^{14}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}2})$ have furnished detailed information about the low-temperature features of the electron transport in this system. The metal-type conductivity of \ensuremath{\delta} layers at ${N}_{D}&gt;~3\ifmmode\times\else\texttimes\fi{}{10}^{13}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ exhibits manifestations of the weak localization of electrons and electron-electron interaction in a two-dimensional system. The temperature dependence of electron phase relaxation time, the spin-orbit interaction time, and parameter ${\ensuremath{\lambda}}^{D}$ of the electron-electron interaction are determined. It is found that a decrease in the electron density in the \ensuremath{\delta} layer is accompanied by decrease in the parameter ${\ensuremath{\lambda}}^{D}.$ The effect of electron heating by an electric field is used to find the temperature dependence of the electron-phonon relaxation time. At low temperature the hopping-type conductivity of \ensuremath{\delta} layers at ${N}_{D}&lt;~1\ifmmode\times\else\texttimes\fi{}{10}^{13}{\mathrm{cm}}^{\mathrm{\ensuremath{-}}2}$ is realized; at sufficiently low temperatures (10 K) the two-dimensional Mott law of variable-range hopping is seen. The nonlinearity of the current-voltage characteristics observed is well described by the theory of non-Ohmic hopping conductivity in moderately strong electric fields.

High-pressure resistance of PuTe up to 25 GPa

The electrical resistance of a single crystal of PuTe has been measured up to $\ensuremath{\sim}25 \mathrm{GPa}$ and as a function of temperature down to 1.3 K. At low pressure, the resistance R displays the expected activated behavior, i.e., an upturn at low temperature and a change of curvature at $\ensuremath{\sim}200 \mathrm{K}$ as at ambient pressure. Surprisingly, the resistance at 1.5 K is enhanced by increasing pressure. For the NaCl phase, we propose a model where the conductivity \ensuremath{\sigma} is composed of three contributions; a constant 0 K term $\ensuremath{\sigma}(0)$ as expected in a semimetal, the Mott's law $\ensuremath{\sigma}\ensuremath{\propto}\mathrm{exp}\ensuremath{-}{(T}_{0}{/T)}^{1/4}$ indicating variable-range hopping conductivity below 100 K, and an exponential term $\mathrm{exp}(\ensuremath{-}{E}_{g}{/2k}_{B}T)$ due to a band gap. At 0.2 GPa, the activation energies ${T}_{0}$ and ${E}_{g}$ equal 23 meV and 0.185 eV, and increase up to 110 meV and $\ensuremath{\sim}0.4 \mathrm{eV}$ at 4.2 GPa, respectively. As a possible origin of the Mott's law behavior, we suggest a mechanism of hopping conduction involving the $5f$ states of the Pu ions. Between 10.7 GPa and 12.7 GPa, R strongly decreases over the whole temperature range. We attribute this collapse to the NaCl-CsCl structural transition. This effect indicates a strong increase of the state density and is in agreement with theoretical predictions. Above 12.7 GPa, the upturn tends to disappear and the temperature variation of R progressively approaches that of a metal. Our data suggest a magnetic transition below 15 K in the CsCl phase.

Conduction Electron Resonance and Transport Properties of a Nonaligned Carbon Nanotube Thick Film for Field Emission Display

We present electron spin resonance spectra and the electronic transport characteristics of multiwalled carbon nanotubes (CNTs) which were screen printed in a thick‐film form for field emission displays. Electron spin resonance spectra showed a Dysonian line due to conduction electrons, and the reduced temperature dependence of the g‐value indicates the metallic properties of CNTs. Zero‐field resistivity and magnetoresistance were measured as a function of temperature T in the range 1.7–390 K and magnetic field, respectively. The resistivity of nanotubes for temperatures of 10–390 K indicates that the system is intrinsically metallic and the characteristics are well described by Mott's law in temperatures above 10 K. We found that the main contribution to the conductivity comes from carriers that hop directly between localized states via variable range hopping. The temperature dependence above 10 K is in good agreement with that of an individual multiwalled CNT. However, below 10 K, the resistivity is well fit to Efros' law, confirming the presence of a coulomb gap for the system. With a decrease of the temperature below 10 K the charge carriers in the system are localized by strong disorder, bringing a nearly insulating state. Using a diode configuration, we measured the field electron emission characteristics and found that the CNT thick film appears to emit electrons with a density of accompanying highly bright light emission. The emission current‐voltage characteristics can be fitted to a straight line in agreement with the Fowler‐Nordheim equation, which confirms that the emission current resulted from field emission of the CNT thick film. © 2000 The Electrochemical Society. All rights reserved.

Electrical properties of self-assembled carbon networks

In the past years, the interest in the physics of mesoscopic device structures has increased as the patterning of such systems became more and more applicable. Mesoscopic structures uncover new physics since size effects play an important role. For patterning, self-organizing processes are promising, but they can also bear difficulties. Self-organization phenomena are, however, interesting from a physical point of view and offer cheap possibilities for production purposes. But they are not totally regular, and one process is restrained to a limited number of structures and materials. For the understanding of the electrical behavior of these mesoscopic structures, the form and the slight variation of one from the other have to be taken into account as well as the material properties. In this paper, we present an electrical characterization of carbon networks produced by a self-organizing process. The net structure consists of hexagonal basis cells with a diameter of about 1 \ensuremath{\mu}m and the dimensions of the interconnections of about 100 nm. We find that in the temperature range from 4.2 to 150 K, the specific resistivity \ensuremath{\rho} depends on temperature T as $\ensuremath{\rho}(T)\ensuremath{\propto}{T}^{\ensuremath{-}0.3}\mathrm{exp}([{T}_{0}/T{]}^{1/p})$ and the transport mechanism, therefore, is variable range hopping. For $4.2\mathrm{K}&lt;T&lt;26\mathrm{K},$ it is $p=4$ and the local activation energy scales as ${\ensuremath{\varepsilon}}_{a}(T)\ensuremath{\propto}{T}^{3/4}.$ In the temperature range from 4.2 to 30 K, the current-voltage characteristics exhibit a temperature-dominated part in the low-voltage regime and a voltage-dominated part in the high-voltage regime. The first can be described according to Mott's law, whereas the second scales as $\ensuremath{\sigma}(E)={\ensuremath{\sigma}}_{1}\mathrm{exp}(A*{E}^{n}),$ where A and ${\ensuremath{\sigma}}_{1}$ depend on temperature. A change of the factor n from 1 to 0 takes place with increasing electric field.

Effects of Strong Correlation and Randomness in the Vicinity of the Mott Transition in the Quasi-One-Dimensional Hubbard Model

We study the strong correlation effects in the vicinity of the Mott metal-insulator transition using coupled clean or disordered Hubbard chains with a infinitely large coordinate number $D_{\perp}\to\infty$ in the direction perpendicular to the chains and with a long-range transverse hopping. Strong electron correlation effects are treated partially non-perturbatively with the use of the exact results for the 1D Hubbard model. In the case of clean systems, the thermodynamic and transport quantities which characterize the Mott transition from the Fermi liquid state, such as the specific heat coefficient, the Drude weight, and the compressibility, are obtained as functions of hole-doping $\delta=1-n$ ($n$, electron density) by the systematic expansion in terms of the inverse of the transverse hopping range $l_{\perp}$. We find that the $\delta$-dependence of these quantities shows non-universal behaviors with exponents depending on the strength of electron-electron interaction. In the presence of disorder, it is shown that the frequency-dependence of the dynamical conductivity obeys the Mott's law, implying the possibility of {\it Mott glass state} for $\delta \to 0$, provided that there exists a finite range interaction.

Electronic excitations and luminescence in MgO:Ge single crystals

MgO single crystals, doped with Ge2+ ‘mercury-like’ ions, were grown. The emission of Ge2+ centres (∼3.2 eV) can be efficiently excited at 4s2→4s4p electron transitions in Ge2+ ions (4.8–6.4 eV) as well as at the formation of electron–hole (e–h) pairs by 8–36 eV photons. The absorption of one photon of 25 or 30 eV leads to the creation of two or three e–h pairs, respectively. The thermal quenching of the emission begins at ∼500 K and follows the Mott law with an activation energy E=0.52 eV. Taking advantage of the relatively high thermal stability of Ge2+ luminescence, high temperature thermostimulated luminescence (up to 775 K) of MgO:Ge crystals has been investigated.

Semimetallic and semiconductor properties of some superhard and ultrahard fullerites in the range 300–2 K

Electrical resistivity and magnetoresistance were measured on samples with disordered structures synthesized from pure C60 and C70 at pressures in the range 8–12.5GPa and temperatures of 900–1500K. Different types of behaviour were observed: semimetallic, VRH and semiconducting, depending on the degree of disorder and the particular short-range order of the samples. A negative magnetoresistance was observed at T<10K on samples with a semimetallic type of conductivity synthesized at 8GPa pressure. The temperature dependence of resistivity in the sample with a disordered crystalline structure based on 3D-polymerized C60 molecules fits Mott's law for hopping conductivity. T3/2, T2 and T4 dependencies of conductivity are observed for samples with densities of 2.8 and 3.05g/cm3 synthesized at a pressure of 12.5GPa. The effect of hydrostatic pressure on the resistivity of cross-linked layered carbon structures obtained from C60 at P=8GPa,T=1600K was investigated up to 0.6GPa at room temperature. An approximately linear decrease of resistivity was observed with a very small value of the derivative dlnρ/dp=0.06/GPa, which correlates with a very low compressibility of the material.

Analytic structure of one-dimensional localization theory: Re-examining Mott's Law

It is argued that the behavior of two-particle correlation functions for a one-dimensional system of disordered electrons is not only governed by the localization length, l, but also involves a dynamical characteristic length, lln(1/omega). This is shown to be consistent with spectral properties of the underlying Heun-type operator. One consequence of this fact is that the Mott law for the low-frequency electrical conductivity should be amended to Resigma(omega) approximately omega(2)ln (3)(1/omega).