Variable Range Hopping Behavior Research Articles

Granular metallicity as a minimal normal state for superconductivity

We report the evolution of electrical transport properties in insulating FeSe films with electron doping induced by the ionic liquid gating technique. Superconductivity never emerges in the strong insulators with variable-range hopping behavior but is shown to arise once the resistance of the normal state varies as $ln(1/T)$, indicating that this behavior corresponds to the minimal conducting character for developing superconductivity. Our work points toward granular metallicity for the $ln(1/T)$ behavior, suggesting that the emergence of superconductivity requires at least an insulating state containing metallic granules. Moreover, it unravels an electronic segregation in proximity to superconductor-insulator transition, which calls for a comprehensive understanding of this segregated phase.

Enhancing superconductivity of Lu5Rh6Sn18 by atomic disorder

For a number of skutterudite-related cage compounds, such as cubic ${R}_{3}{M}_{4}{\mathrm{Sn}}_{13}$ ($R=\mathrm{Ca}$ or La, $M=\text{transition}$ $d$-electron metal) or tetragonal ${\mathrm{Y}}_{5}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$, we have previously reported the impact of various atomic defects in the crystal lattices on the normal-state and superconducting properties of these clathrates. In these quasiskutterudites the nanoscale disorder and/or local inhomogeneity in composition lead to an abnormal increase in the superconducting transition temperature ${T}_{c}$. Here we investigate the impact of atomic defects in the superconductors ${\mathrm{Lu}}_{5\ensuremath{-}\ensuremath{\delta}}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$ (tetragonal symmetry $I{4}_{1}/acd$). We have documented that ${\mathrm{Lu}}_{5}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$ does not crystallize in the assumed stoichiometry but forms a 5-6-18 phase with a Lu deficiency ($\ensuremath{\delta}\ensuremath{\approx}0.5$). Our comprehensive investigations of electronic structure and thermodynamic and electrical transport properties documented a ${T}_{c}$ increase in the more disordered sample (sample 1). The quality of two investigated samples (sample 1 and sample 2) with similar stoichiometry but different local inhomogeneity was obtained by microanalysis and electron transmission microscopy observations. The band structure calculations show a hybridization pseudogap in the electronic bands of stoichiometric ${\mathrm{Lu}}_{5}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$ at about 0.3 eV in respect to the Fermi level ${\ensuremath{\epsilon}}_{F}$. The ab initio calculations predict the scenario that vacancies could shift this pseudogap towards ${\ensuremath{\epsilon}}_{F}$, which is manifested by the Mott variable-range hopping behavior in the resistivity $\ensuremath{\rho}\ensuremath{\sim}{T}^{\ensuremath{-}1/4}$ of more homogeneous sample 2.

Observation of 2D transport in Sn- and In-doped Bi2−xSbxTe3−ySey topological insulator

Here we report magnetotransport properties of Bi2−xSbxTe3−ySey (BSTS), In- and Sn-doped BSTS single crystals, grown through modified Bridgeman technique. In- and Sn-doped BSTS single crystals show bulk insulation in temperature dependency resistivity measurements and are confirmed from the observed impurity band mediated three dimensional variable-range hopping behavior at low temperatures over virgin BSTS with metallic bulk. Magnetotransport measurements for BSTS and Sn-doped BSTS reveal a zero field sharp positive cusp and is identified as two dimensional (2D) weak antilocalization (WAL) effect, which is the consequence of π Berry phase of the carriers. For In-doped BSTS single crystals, crossover is identified from WAL to weak localization with field variation at low temperatures and also with an increase in temperature from 2 K. For all the single crystals, phase coherence lengths (lϕ) are determined by fitting low field magnetotransport data with Hikami–Larkin–Nagaoka equation. Temperature dependency of phase coherence lengths is described with 2D electron–electron (e–e) and 2D electron–phonon (e–p) interactions for virgin and In-doped BSTS single crystals while for Sn-doped BSTS specimen lϕ(T) follows T−0.53 power law.

Enhancing superconductivity of Y5Rh6Sn18 by atomic disorder

For a number of skutterudite-related cage compounds, such as cubic ${R}_{3}{M}_{4}{\mathrm{Sn}}_{13}$ ($R=\mathrm{Ca}$ or La, $M=\text{transition}$ $d$-electron metal) or tetragonal ${\mathrm{Y}}_{5}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$, we have previously reported the impact of various atomic defects in the crystal lattices on the normal-state and superconducting properties of these clathrates. In these quasiskutterudites the nanoscale disorder and/or local inhomogeneity in composition lead to an abnormal increase in the superconducting transition temperature ${T}_{c}$. Here we investigate the impact of atomic defects in the superconductors ${\mathrm{Lu}}_{5\ensuremath{-}\ensuremath{\delta}}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$ (tetragonal symmetry $I{4}_{1}/acd$). We have documented that ${\mathrm{Lu}}_{5}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$ does not crystallize in the assumed stoichiometry but forms a 5-6-18 phase with a Lu deficiency ($\ensuremath{\delta}\ensuremath{\approx}0.5$). Our comprehensive investigations of electronic structure and thermodynamic and electrical transport properties documented a ${T}_{c}$ increase in the more disordered sample (sample 1). The quality of two investigated samples (sample 1 and sample 2) with similar stoichiometry but different local inhomogeneity was obtained by microanalysis and electron transmission microscopy observations. The band structure calculations show a hybridization pseudogap in the electronic bands of stoichiometric ${\mathrm{Lu}}_{5}{\mathrm{Rh}}_{6}{\mathrm{Sn}}_{18}$ at about 0.3 eV in respect to the Fermi level ${\ensuremath{\epsilon}}_{F}$. The ab initio calculations predict the scenario that vacancies could shift this pseudogap towards ${\ensuremath{\epsilon}}_{F}$, which is manifested by the Mott variable-range hopping behavior in the resistivity $\ensuremath{\rho}\ensuremath{\sim}{T}^{\ensuremath{-}1/4}$ of more homogeneous sample 2.

Thermoelectric properties of paracostibite fabricated using chemically synthesized Co–Sb–S nanoparticles as building blocks

Paracostibite (CoSbS) is a promising candidate for n-type thermoelectric materials. In this study, a nanostructured CoSbS pellet was fabricated using chemically synthesized Co–Sb–S nanoparticles as building blocks. The CoSbS pellet showed the highest electrical conductivity (σ = 141 S/cm at 661 K) and lowest thermal conductivity [κ ≅ 2 W/(m K)] among the reported CoSbS. Detailed analysis of the electrical transport process in a wide temperature range (3 K–661 K) revealed the existence of a donor level. At a temperature less than 170 K, the resistivity showed Mott variable-range hopping behavior, while the band conduction became dominant as the temperature increased. Nanograins in the pellet significantly enhanced phonon scattering, resulting in suppression of κ. The maximum dimensionless figure of merit value was 0.05 at 661 K, which is comparable with previously reported values for CoSbS TE materials.

Semiconducting nature and thermal transport studies of ZrTe3

We report electrical and thermal transport properties of polycrystalline ZrTe3. The polycrystalline sample shows semiconducting behavior in contrast to the established semi-metallic character of the compound. However the charge density wave (CDW) transition remains intact and its clear signatures are observed in thermal conductivity and Seebeck coefficient, in the wide temperature range 50–100 K. The thermal conductivity points to additional scattering from the low frequency phonons (phonon softening) in the vicinity of CDW transition. The transport in the polycrystalline compounds is governed by smaller size polarons in the variable range hopping (VRH) region. However, the increasing disorder in polycrystalline compounds suppresses the CDW transition. The VRH behavior is also observed in the Seebeck coefficient data in the similar temperature range. The Seebeck coefficient suggests a competition between the charge carriers (electrons and holes).

Semiconducting Y–Ba–Cu–O thin films sputtered on MgO and SiOx/Si substrates: Morphological, electrical and optical properties for infrared sensing applications

Semiconducting YBa2Cu3O6+x (x<0.5, YBCO) films were deposited by direct current (DC) sputtering at temperatures ranging from Tsub=150 to 610°C; the substrates were either MgO (001) or SiOx/Si (001). All films exhibited a granular microstructure. Films deposited at Tsub≤500°C were purely amorphous, but films deposited at Tsub≥550°C also exhibited the presence of crystallized tetragonal phase. DC conductivity of purely amorphous films followed a variable range hopping (VRH) behavior from 180 to 330K, in line with hopping between localized hole states around the Fermi level. DC conductivity of the partially crystallized films followed first a thermally activated behavior at high temperature, in line with energy transitions to extended states, then a VRH behavior at lower temperature. For purely amorphous films deposited at Tsub=150°C on SiOx/Si, ellipsometry measurements showed refractive index value n≈2.25, suggesting a low oxygen content (x≈0.1), as confirmed by the optical conductivity vs. wavelength behavior. An infrared sensing demonstrator (metal/YBCO, Tsub=150°C, on SiOx/Si) exhibited a high-pass pyroelectric response at 850nm wavelength. The response maximum at 40kHz modulation frequency was followed by a slow decrease up to 3MHz. The −3dB bandwidth in the 12 to 85kHz range indicated a device, two to three orders of magnitude faster than the usual pyroelectric detectors.

Hall and field-effect mobilities in few layered p-WSe₂ field-effect transistors.

Here, we present a temperature (T) dependent comparison between field-effect and Hall mobilities in field-effect transistors based on few-layered WSe2 exfoliated onto SiO2. Without dielectric engineering and beyond a T-dependent threshold gate-voltage, we observe maximum hole mobilities approaching 350 cm2/Vs at T = 300 K. The hole Hall mobility reaches a maximum value of 650 cm2/Vs as T is lowered below ~150 K, indicating that insofar WSe2-based field-effect transistors (FETs) display the largest Hall mobilities among the transition metal dichalcogenides. The gate capacitance, as extracted from the Hall-effect, reveals the presence of spurious charges in the channel, while the two-terminal sheet resistivity displays two-dimensional variable-range hopping behavior, indicating carrier localization induced by disorder at the interface between WSe2 and SiO2. We argue that improvements in the fabrication protocols as, for example, the use of a substrate free of dangling bonds are likely to produce WSe2-based FETs displaying higher room temperature mobilities, i.e. approaching those of p-doped Si, which would make it a suitable candidate for high performance opto-electronics.

Sensitive photo-thermal response of graphene oxide for mid-infrared detection.

This study characterizes the effects of incident infrared (IR) radiation on the electrical conductivity of graphene oxide (GO) and examines its potential for mid-IR detection. Analysis of the mildly reduced GO (m-GO) transport mechanism near room temperature reveals variable range hopping (VRH) for the conduction of electrons. This VRH behavior causes the m-GO resistance to exhibit a strong temperature dependence, with a large negative temperature coefficient of resistance of approximately -2 to -4% K(-1). In addition to this hopping transport, the presence of various oxygen-related functional groups within GO enhances the absorption of IR radiation significantly. These two GO material properties are synergically coupled and provoke a remarkable photothermal effect within this material; specifically, a large resistance drop is exhibited by m-GO in response to the increase in temperature caused by the IR absorption. The m-GO bolometer effect identified in this study is different from that exhibited in vanadium oxides, which require added gold-black films that function as IR absorbers owing to their limited IR absorption capability.

Magneto-transport properties of a random distribution of few-layer graphene patches

In this study, we address the electronic properties of conducting films constituted of an array of randomly distributed few layer graphene patches and investigate on their most salient galvanometric features in the moderate and extreme disordered limit. We demonstrate that, in annealed devices, the ambipolar behaviour and the onset of Landau level quantization in high magnetic field constitute robust hallmarks of few-layer graphene films. In the strong disorder limit, however, the magneto-transport properties are best described by a variable-range hopping behaviour. A large negative magneto-conductance is observed at the charge neutrality point, in consistency with localized transport regime.

Tunable electronic properties and low thermal conductivity in synthetic colusites Cu26−xZnxV2M6S32 (x ≤ 4, M = Ge, Sn)

We have first synthesized Cu26−xZnxV2M6S32 (x ≤ 4, M = Ge, Sn) with the cubic colusite structure and measured the thermoelectric properties. For both M = Ge and Sn, the samples with x = 0 show moderately large thermopower of +27 μV/K at 300 K. The metallic conduction of p-type carriers and Pauli-paramagnetic behavior are consistent with the electron-deficient character expected from the formal charge Cu261+V25+M64+S322−. The substitution of Zn for Cu results in significant increases in both the electrical resistivity and thermopower. The resistivity of the samples with x = 4 displays a three-dimensional variable-range hopping behavior at low temperatures. These facts indicate that the doped electrons fill the unoccupied states in the valence band and thereby the Fermi level moves to the localized electronic states at the top of the band. The lattice thermal conductivity is as low as ∼1 W/Km at 300 K for all samples. The structural and thermoelectric properties of the colusites are discussed in comparison with those of doped tetrahedrite Cu12−xZnxSb4S13.

Growth, structure and physical properties of gadolinium doped Sr 2 IrO 4 single crystal

Abstract A series of Gd-doped Sr2IrO4 single crystals were grown using a flux method. Analysis of the temperature-dependent resistance of these crystals reveals that these samples show two-dimensional weak localization at 150 to 300 K, while three-dimensional variable range hopping (VRH) behavior is observed at temperatures lower than 150 K. Two localization lengths are observed in the VRH behavior, with a transition temperature of around 88 K. Correspondingly, temperature-dependent magnetization observations along the ab-plane reveal magnetic anomalies at both 150 and 85 K. This work demonstrates the correlation between the electrical and magnetic properties of 5d transition-metal compounds.

Spin relaxation times of single-wall carbon nanotubes

We have measured temperature ($T$)- and power-dependent electron spin resonance in bulk single-wall carbon nanotubes to determine both the spin-lattice and the spin-spin relaxation times, ${T}_{1}$ and ${T}_{2}$. We observe that ${T}_{1}^{\ensuremath{-}1}$ increases linearly with $T$ from 4 K to 100 K, whereas ${T}_{2}^{\ensuremath{-}1}$ decreases by over a factor of two when $T$ is increased from 3 K to 300 K. We interpret the ${T}_{1}^{\ensuremath{-}1}\ensuremath{\propto}T$ trend as spin-lattice relaxation via interaction with conduction electrons (Korringa law) and the decreasing $T$ dependence of ${T}_{2}^{\ensuremath{-}1}$ as motional narrowing. By analyzing the latter, we find the spin hopping frequency to be 285 GHz. Last, we show that the Dysonian line shape asymmetry follows a three-dimensional variable-range hopping behavior from 3 K to 20 K; from this scaling relation, we extract a localization length of the hopping spins to be $\ensuremath{\sim}$100 nm.

Quasi‐One Dimensional in‐Plane Conductivity in Filamentary Films of PEDOT:PSS

AbstractThe mechanism and magnitude of the in‐plane conductivity of poly(3,4‐ethy‐lenedioxythiophene):poly(styrenesulfonate) (PEDOT:PSS) thin films is determined using temperature dependent conductivity measurements for various PEDOT:PSS weight ratios with and without a high boiling solvent (HBS). Without the HBS the in‐plane conductivity of PEDOT:PSS is lower and for all studied weight ratios well described by the relation $ \sigma = \sigma _0 {\rm exp}[- \left({{{{T_0}}\over{T}}} \right)^{0.5}] $ with T0 a characteristic temperature. The exponent 0.5 indicates quasi‐one dimensional (quasi‐1D) variable range hopping (VRH). The conductivity prefactor σ0 varies over three orders of magnitudes and follows a power law σ0∝c3.5PEDOT with cPEDOT the weight fraction of PEDOT in PEDOT:PSS. The field dependent conductivity is consistent with quasi‐1D VRH. Combined, these observations suggest that conductance takes place via a percolating network of quasi‐1D filaments. Using transmission electron microscopy (TEM) filamentary structures are observed in vitrified dispersions and dried films. For PEDOT:PSS films with HBS, the conductivity also exhibits quasi‐1D VRH behavior when the temperature is less than 200 K. The low characteristic temperature T0 indicates that HBS‐treated films are close to the critical regime between a metal and an insulator. In this case, the conductivity prefactor scales linearly with cPEDOT, indicating the conduction is no longer limited by a percolation of filaments. The lack of observable changes in TEM upon processing with the HBS suggests that the changes in conductivity are due to a smaller spread in the conductivities of individual filaments, or a higher probability for neighboring filaments to be connected rather than being caused by major morphological modification of the material.

The effect of tube filling on the electronic properties of Fe filled carbon nanotubes

Carbon nanotubes filled with Fe nanostructures (Fe-CNTs) were synthesized using an injection method in a 1-stage horizontal CVD furnace and a bubbling method in a 2-stage horizontal CVD reactor. Fe-CNTs were obtained through the pyrolysis of a mixture of dichlorobenzene and ferrocene in 5%H2/Ar. Metal impurities from the Fe-CNTs were removed using 1M HCl solution. CNTs filled with crystalline Fe nanoparticles, nanorods and nanowires were obtained using these procedures. An intimate interaction between the Fe and the CNT was established by HRTEM studies. The α-Fe phase was observed to be the most dominant fraction found in the synthesized Fe-CNTs. The Fe2O3 residue obtained from the TGA analysis revealed the amount of Fe filled inside the CNTs and this ranged between 3 and 31% by mass after purification. The temperature dependence of the conductivity in the temperature range between 2.5 and 100K for an entangled network of Fe-CNTs was measured. An increase in conductivity due to the increased Fe filling inside the CNTs with increased temperature was observed. The observed temperature dependence was explained in terms of variable range hopping (VRH) conduction mechanisms. A transition from Efros–Shklovskii behavior at low % Fe filling of the CNTs to Mott 3D VRH behavior at high % Fe filling of the CNTs was observed due to screening of the coulomb potential by electrons as the Fe % increases.

Influence of irradiation-induced disorder on the Peierls transition in TTF–TCNQ microdomains

The combined influence of electron irradiation-induced defects, substrate-induced strain and finite size effects on the electronic transport properties of individual micron-sized thin film growth domains of the organic charge transfer compound tetrathiafulvalene– tetracyanoquinodimethane (TTF–TCNQ) have been studied. The TTF–TCNQ domains have been isolated and electrically contacted by focused ion beam etching and focused ion and electron-beam-induced deposition, respectively. This allowed us to measure the temperature-dependent resistivity and the current–voltage characteristics of individual domains. The dependence of the resistivity on temperature follows a variable-range hopping behaviour which shows a crossover of the exponents as the Peierls transition is approached. The low temperature behaviour is analysed within the segmented rod model of Fogler, Teber and Shklovskii which was developed for charge-ordered quasi one-dimensional electron crystals (Fogler et al 2004 Phys. Rev. B 69 035413). The effect of substrate-induced biaxial strain on the Peierls transition temperature is discussed with regard to its interplay with the defect-induced changes.

Low-temperature polaronic relaxations with variable range hopping conductivity in FeTiMO6(M=Ta,Nb,Sb)

Low-temperature dielectric measurements on FeTiMO(6) (M = Ta,Nb,Sb) rutile-type oxides at frequencies from 0.1 Hz to 10 MHz revealed anomalous dielectric relaxations with frequency dispersion. Unlike the high-temperature relaxor response of these materials, the low-temperature relaxations are polaronic in nature. The relationship between frequency and temperature of dielectric loss peak follows T(-1/4) behavior. The frequency dependence of ac conductivity shows the well-known universal dielectric response, while the dc conductivity follows Mott variable range hopping (VRH) behavior, confirming the polaronic origin of the observed dielectric relaxations. The frequency domain analysis of the dielectric spectra shows evidence for two relaxations, with the high-frequency relaxations following Mott VRH behavior more closely. Significantly, the Cr- and Ga-based analogs, CrTiNbO(6) and GaTiMO(6) (M = Ta,Nb), that were also studied, did not show these anomalies.

Large bulk resistivity and surface quantum oscillations in the topological insulatorBi2Te2Se

Topological insulators are predicted to present interesting surface transport phenomena but their experimental studies have been hindered by a metallic bulk conduction that overwhelms the surface transport. We show that the topological insulator ${\text{Bi}}_{2}{\text{Te}}_{2}\text{Se}$ presents a high resistivity exceeding $1\text{ }\ensuremath{\Omega}\text{ }\text{cm}$ and a variable-range hopping behavior, and yet presents Shubnikov-de Haas oscillations coming from the topological surface state. Furthermore, we have been able to clarify both the bulk and surface transport channels, establishing a comprehensive understanding of the transport in this material. Our results demonstrate that ${\text{Bi}}_{2}{\text{Te}}_{2}\text{Se}$ is, to our knowledge, the best material to date for studying the surface quantum transport in a topological insulator.

Synthesis, characterization, electrical transport and magnetic properties of PEDOT–DBSA–Fe 3O 4 conducting nanocomposite

Electrical transport and magnetic properties of newly synthesized conducting polymer nanocomposites involving poly(3,4-ethylenedioxythiophene) (PEDOT) and Fe 3O 4 nanoparticles are studied. Nanocomposite samples of varying proportions of inorganic to organic components were synthesized by adding EDOT monomer stabilized in miceller solution of DBSA (dodecylbenzene sulphonic acid) to aqueous colloidal dispersion of Fe 3O 4 nanoparticles, followed by oxidative polymerization using ammonium peroxodisulphate (APS). Transmission electron microscopic (TEM) photographs show presence of distinct spherical Fe 3O 4 naonparticles having diameter range of 20–40 nm and they are incorporated within the polymer chain in the nanocomposite samples. Temperature-dependent DC conductivity analysis indicates a smooth cross-over of the charge conduction from the high temperature 3D Mott's variable range hopping (VRH) mechanism to the 2D ES (Efros and Shklovoskii)-VRH behaviour at low temperature. Temperature-dependent DC magnetization studies reveal enhancement of blocking temperature ( T B ) in the nanocomposite samples compared to that of bare Fe 3O 4 nanoparticles. Core shell morphology of the nanoparticles seems to be the cause for lowering the value of saturation magnetization of the Fe 3O 4 nanoparticles. Estimated magnetic domain sizes are comparable to those of grain sizes for the nanocomposite samples having lower content of nanoparticles (P 50 and P 100). Temperature-dependent AC-susceptibility data also supports the superparamagnetic behaviour.

Hopping versus bulk conductivity in transparent oxides: 12CaO∙7Al2O3

First-principles calculations of the mayenite-based oxide, [Ca12Al14O32]2+(2e−), reveal the mechanism responsible for its high conductivity. A detailed comparison of the electronic and optical properties of this material with those of the recently discovered transparent conducting oxide, H-doped UV-activated Ca12Al14O33, allowed us to conclude that the enhanced conductivity in [Ca12Al14O32]2+(2e−) is achieved by elimination of the Coulomb blockade of the charge carriers. This results in a transition from variable range-hopping behavior with a Coulomb gap in H-doped UV-irradiated Ca12Al14O33, to bulk conductivity in [Ca12Al14O32]2+(2e−). Further, the high degree of delocalization of the conduction electrons obtained in [Ca12Al14O32]2+(2e−) indicates that it cannot be classified as an electride, as originally suggested.