Variable-range Hopping Transport Research Articles

Spin-related negative magnetoresistance in germanium films

Herein, we report the transport properties of Ge films. The variable-range hopping transport at low temperatures (T≲50K) and thermal activation transport at high temperatures (T≳50K) are observed in our Ge films. In the different temperature regimes, the anomalous magnetotransport properties are observed. In the low-temperature regime (T≲15K), the negative magnetoresistance (MR) at low field and positive MR at high field can be seen. In the moderate-temperature regime (15K≲T≲100K), the positive MR curve gradually evolves from a linear curve to a parabolic curve with increasing temperature, and the MR magnitude appears to be insensitive to temperature. In the high-temperature regime (T≳100K), the positive MR value increases with increasing temperature. By considering the angular-dependent MR, we can determine that the negative MR comes from the spin-related mechanism, and the positive MR is caused by the orbital-related mechanism. However, further study is required to determine the exact mechanisms behind the anomalous magnetotransport properties.

Electronic transport mechanisms in a thin crystal of the Kitaev candidate α -RuCl3 probed through guarded high impedance measurements

α-RuCl3 is considered to be the top candidate material for the experimental realization of the celebrated Kitaev model, where ground states are quantum spin liquids with interesting fractionalized excitations. It is, however, known that additional interactions beyond the Kitaev model trigger in α-RuCl3 a long-range zigzag antiferromagnetic ground state. In this work, we investigate a nanoflake of α-RuCl3 through guarded high impedance measurements aimed at reaching the regime where the system turns into a zigzag antiferromagnet. We investigated a variety of temperatures (1.45–175 K) and out-of-plane magnetic fields (up to 11 T), finding a clear signature of a structural phase transition at ≈160 K as reported for thin crystals of α-RuCl3, as well as a thermally activated behavior at temperatures above ≈30 K, with a characteristic activation energy significantly smaller than the energy gap that we observe for α-RuCl3 bulk crystals through our angle resolved photoemission spectroscopy (ARPES) experiments. Additionally, we found that below ≈30 K, transport is ruled by Efros–Shklovskii variable range hopping (VRH). Most importantly, our data show that below the magnetic ordering transition known for bulk α-RuCl3 in the frame of the Kitaev–Heisenberg model (≈7 K), there is a clear deviation from VRH or thermal activation transport mechanisms. Our work demonstrates the possibility of reaching, through specialized high impedance measurements, the thrilling ground states predicted for α-RuCl3 at low temperatures in the frame of the Kitaev–Heisenberg model and informs about the transport mechanisms in this material in a wide temperature range.

Statistical Properties of Electric Potentials in a Variable-Range Hopping Regime

Variable-range hopping transport is studied from a new perspective. Unlike the well-known percolation model for variable-range hopping, which treats the connectivity of bonds between a pair of sites, the emphasis here is on the statistical properties of the voltage potential at these sites. The deviations in the voltage potentials are calculated from the rate equations. The variance and power spectra of the deviations show that there are two temperature regimes: nearest-neighbor hopping at high temperatures and variable-range hopping at low temperatures. The development of long-range order between the voltage deviations in the variable-range hopping regime is confirmed by showing the temperature dependence of the correlation length.

Transition between positive and negative magnetoresistance of zirconium oxynitride films in the variable-range hopping regime

In this research, the electrical transport properties of zirconium oxynitride films are studied. The transition from positive to negative magnetoresistance in the variable-range hopping transport regime is observed with the decrease in the temperature. The positive magnetoresistance is caused by the shrinkage effect of electronic wavefunctions. While, the negative magnetoresistance, which is independent of the magnetic field orientations, can be ascribed to the Zeeman splitting and/or the spin-flip hopping effect of the localized states. Further experimental studies are needed to reveal the exact transition mechanism.

Variable range hopping conductivity in molecular beam epitaxial InSb

A variable range hopping (VRH) transport mechanism can be induced in molecular beam epitaxial, n-type doped InSb wafers with focussed Ga+ ion beam damage. This technique allows areas of wafer to be selectively damaged and then subsequently processed into gated metal–insulator–semiconductor (MIS) devices where a disordered, two-dimensional (2D) device can be established. At high levels of damage (dose >1016 Ga+ ions cm−2) amorphous crystalline behavior results with activated conductivity characteristic of a three-dimensional system with VRH below 150 K. At lower doses (1014–1016 Ga+ ions cm−2) a thermally activated conductivity is induced at ∼0.9 K, characteristic of Mott phonon-assisted VRH. At 1 K the devices either conduct with conductivity >∼(e 2/h) where e is the fundamental charge and h is Planck’s constant, or are thermally activated depending on the dose level. The lightly damaged devices show weak antilocalization signals with conductivity characteristic of a 2D electronic system. As the Ga+ dose increases, the measured phase coherence length reduces from ∼500 nm to ∼100 nm. This provides a region of VRH transport where phase-coherent transport processes can be studied in the hopping regime with the dimensionality controlled by a gate voltage in an MIS-device.

Activated Hopping Transport in Nematic Conducting Aerogels

The transport properties of nematic aerogels, which consist of highly oriented Al$_2$O$_3\cdot$SiO$_2$ nanofibers coated with a graphene shell with a large number of defects, are studied. The temperature dependences of the electrical resistivity in the range of 9-40K strictly follow the formula derived to describe the variable range hopping (VRH) conductivity, in which exponent $\alpha$ changes from 0.4 to 0.9 when the number of layers in the graphene shell decreases from 4-6 to 1-2. The dependence of $\alpha$ on the shell thickness can be explained by a simultaneous change in the dimensionality of hopping transport and the character of the energy dependence of the density of localized states near the Fermi level. The fact that $\alpha$ approaches unity at the minimum graphene shell thickness indicates a gradual transition from VRH transport to nearest neighbor hopping (NNH) transport. The magnetoresistance measured at T = 4.2 K is negative, increases significantly with decreasing graphene shell thickness, and is approximated by a formula for the case of weak localization with a good accuracy. The phase coherence lengths are in a reasonable relation with the graphene grain sizes. The conducting aerogels under study complement the well-known set of materials that exhibit hopping electron transport at low temperatures, which is characteristic of media with strong carrier localization, and also a negative magnetoresistance, which usually manifests itself under weak localization conditions.

Charge localization crossover from Mott to Efros-Shklovskii type variable range hopping mechanism in In1−xPbxTe compounds

We have investigated the electrical transport properties of the In1−xPbxTe compounds. Small Pb-doping is not incorporated in the In-site but randomly distributed in the matrix, found from the X-ray diffraction and elemental mapping by energy-dispersive X-ray spectroscopy measurements. The random distribution of Pb elements induces robust charge localization at low temperatures causing the variable range hopping (VRH) transport. The electrical resistivity ρ(T) of pristine InTe exhibits semiconducting to metal transition near 175 K. From the analysis of temperature exponent, we found that the VRH transport is changed from Mott to Efros-Shklovskii (ES) type with decreasing temperature, where the crossover temperatures are found as 14.4 K (x=0.01) and 13.36 (x=0.02), respectively. The magnetoresistance (MR) of the InTe shows that the weak antilocalization at low temperature (T≤3 K) and low magnetic field (H≤1 T) competes with weak localization with increasing temperature (T≥5 K). It is noteworthy that small Pb-doping exhibits unconventional negative MR (NMR) behavior because it is not a magnetic or topological material. The unconventional NMR behavior of Pb-doped compounds is attributed to the quantum mechanical interference under the magnetic field in ES type VRH transport. The charge localization crossover from Mott to ES type VRH transport mechanism suggests the strong electron-electron Coulomb interaction in the compounds, leading to the significant change of density of states and inducing the Coulomb gap at low temperatures.

Electron-hole asymmetry in electrical conductivity of low-fluorinated graphene: numerical study

By using the real-space Green-Kubo formalism we study numerically the electron transport properties of low-fluorinated graphene. At low temperatures the diffuse transport regime is expected to be prevalent, and we found a pronounced electron-hole asymmetry in electrical conductivity as a result of quasi-resonant scattering on the localized states. For the finite temperatures in the variable-range hopping transport regime the interpretation of numerical results leads to the appearance of local minima and maxima of the resistance near the energies of the localized states. A comparison with the experimental measurements of the resistance in graphene samples with various fluorination degrees is discussed.

Crossover between Mott and Efros-Shklovskii variable-range hopping in Sr2IrO4 epitaxial thin films by misfit strain and isovalent doping

We report three-dimensional Mott variable-range hopping (3D Mott-VRH) transport of Sr2IrO4 epitaxial thin films, with a transition to Efros-Shklovskii variable-range hopping (ES-VRH) with increased misfit strain or isovalent doping. We have observed that the characteristic temperature of 3D Mott-VRH transport decreases under increased misfit strain, implying that the density of states near the Fermi energy is reconstructed. With further increased misfit strain (or doping with Ca or Ba ions), a crossover from the 3D Mott-VRH to ES-VRH transport takes place due to increased carrier localization by disorder, opening a Coulomb gap by increasing the effective electron-correlation. The results of magnetoresistance measurements also confirm that the disorder caused by misfit strain or isovalent doping plays an important role in the electronic transport of these Sr2IrO4 thin films. Our experimental observations propose that subtle external stimuli such as structural modifications can modulate the electronic properties of the relativistic Mott insulator, suggesting an unprecedented pathway for electronic device applications.

Magnetic polaron and unconventional magnetotransport properties of the single-crystalline compound EuBiTe3

We investigate the magnetic, thermal, and electrical transport properties on the single-crystalline compound ${\mathrm{EuBiTe}}_{3}$. The magnetization measurements reveal the antiferromagnetic transition at 7 K along the $ab$ plane with a stable ${\mathrm{Eu}}^{2+}$ ion. A short-range ferromagnetic interaction along the $c$ axis is inferred from magnetic susceptibility and heat capacity measurements, which we associate with the presence of magnetic polarons. The magnetic polaron gives rise to unconventional negative magnetoresistance such as the weak antilocalization (WAL) and weak localization crossover. The WAL of the angle-resolved magnetoconductivity is well described by the Al'tshuler and Aronov model along the longitudinal magnetoconductivity. The magnetic polaron is widely observed above N\'eel temperature up to 50 K, which is supported by the Majumdar-Littlewood model in a scaled magnetoresistance. Even though ${\mathrm{EuBiTe}}_{3}$ should have one hole per formula unit, the electrical conductivity $\ensuremath{\sigma}(T)$ exhibits strong localized insulating behavior. The transport mechanism of $\ensuremath{\sigma}(T)$ is distinguished by two different mechanism: Efros-Shklovskii-type variable range hopping (VRH) transport in the high-temperature range ($T\phantom{\rule{0.16em}{0ex}}\ensuremath{\ge}\phantom{\rule{0.16em}{0ex}}52$ K) and three-dimensional VRH transport in the low-temperature regime ($T\ensuremath{\le}$ 50 K). The VRH transport suggests that the insulating behavior of $\ensuremath{\sigma}(T)$ on the compound can originate from a Mott-type insulator with strong Coulomb interaction.

Electron Doping BaZrO3 via Topochemical Reduction.

We report the topochemical reduction of epitaxial thin films of the cubic perovskite BaZrO3. Reduction with calcium hydride yields n-type conductivity in the films, despite the wide band gap and low electron affinity of the parent material. X-ray diffraction studies show concurrent loss of out-of-plane texture with stronger reducing conditions. Temperature-dependent transport studies on reduced films show insulating behavior (decreasing resistivity with increasing temperature) with a combination of thermally activated and variable-range hopping transport mechanisms. Time-dependent conductivity studies show that the films are stable over short periods, with chemical changes over the course of weeks leading to an increase in electrical resistance. Neutron reflectivity and secondary ion mass spectrometry indicate that the source of the carriers is most likely hydrogen incorporated from the reducing agent occupying oxygen vacancies and/or interstitial sites. Our studies introduce topochemical reduction as a viable pathway to electron-dope and meta-stabilize low electron affinity and work function materials.

Graphene-WS2 heterostructures by a lithography free method: their electrical properties

We have developed a lithography free technique for the fabrication of two-dimensional (2D) material based heterostructures. We fabricated graphene-WS2 heterostructured devices using a transmission electron microscope grid as a shadow mask and their electrical transport characteristics were studied by electrical and magneto transport measurements. Graphene was directly deposited on a Si/SiO2 substrate by radio frequency plasma enhanced chemical vapor deposition. WS2 was synthesized by first depositing WO3 followed by sulfurization. The temperature dependence of the resistance and magnetoresistance are measured for graphene, WS2, and graphene-WS2 heterostructure. At low temperatures, the transport is found to follow the variable-range hopping (VRH) process, where logarithmic R exhibits a T−1/3 temperature dependence, an evidence for the 2D Mott VRH transport. The measured low-field magnetoresistance also exhibits a quadratic magnetic field dependence ∼B2, consistent with the 2D Mott VRH transport.

Enhanced mobility and controlled transparency in multilayered reduced graphene oxide quantum dots: a charge transport study

Reduced graphene oxide (rGO) layers are known to be significantly conductive along the basal plane throughout delocalized sp2 domains. Defects present in rGO implies in disordered systems with numerous localized sites, resulting in a charge transport governed mainly by a 2D variable range hopping (VRH) mechanism. These characteristics are observed even in multilayered rGO since the through-plane conduction is expected to be insubstantial. Here, we report on the multilayer assembly of functionalized rGO quantum dots (GQDs) presenting 3D VRH transport that endows elevated charge carrier mobility, ca ∼ 236 cm2 V−1 s−1. Polyelectrolyte-wrapped GQDs were assembled by layer-by-layer technique (LbL), ensuring molecular level thickness control for the formed nanostructures, along with the adjustment of the film transparency (up to 92% in the visible region). The small size and the random distribution of GQDs in the LbL structure are believed to overcome the translational disorder in multilayered films, contributing to a 3D interlayer conduction that enhances the electronic properties. Such high-mobility, transparency-tunable films assembled by a cost-effective method possess interesting features and wide applicability in optoelectronics.

Large Magnetoresistance and Electrical Transport Properties in Reduced Graphene Oxide Thin Film

We report a systematic study of room temperature large positive and negative magnetoresistance (MR) in the reduced graphene oxide (RGO) thin-film devices grown by pulsed-laser deposition (PLD) at high and low applied magnetic fields, respectively. Raman spectroscopy, X-ray photoelectron spectroscopy, and electrical measurements on the RGO films help to explain the observed MR properties in the device. The temperature-dependent (5–400 K) electrical characterization of the thin films shows two distinct transport regimes: at low temperature, it follows 2-D Efros-Shoklovoski variable range hopping (VRH) transport mechanism and above 200 K, the device shows Arrhenius-like transport behavior. The crossover from VRH transport to Arrhenius transport is due to shortening in the characteristic lengths in the disordered 2-D system. We interpret the source of negative MR by vacancy and disorder-induced magnetic moments and the diffuse scattering at crystallite boundaries. At the high applied magnetic field, the lifting in degeneracy due to the Lorentz force explains the large positive MR effect. The highest value of the measured MR (160%) is surprisingly high for a non-magnetic material at room temperature, which can be attributed to the greater inhomogeneity in the PLD grown wafer-scale RGO thin films.

Magnetothermopower and giant magnetoresistance in the spin-glass CuCrTiS4 thiospinel

The transport properties of the thiospinel CuCrTiS4 have been investigated in detail, focusing on the possible interplay between charges and spins, and its consequence on transport, and more specifically on the thermoelectric properties. The chemical homogeneity of a CuCrTiS4 polycrystalline sample synthesized by a direct reaction of the constitutive elements has been carefully probed by X-ray diffraction and transmission electron microscopy techniques. This thiospinel exhibits below 75 K, in its paramagnetic regime, a variable range hopping (VRH) conduction, associated with a giant magnetoresistance (MR), which persists below the spin-glass transition temperature at 8 K, reaching -95% in 9 T at 5 K. All the MR data can be rescaled as a function of H/T and described using a Brillouin function with S = 3/2. This demonstrates that the paramagnetic fluctuations strongly impact the transport properties, and this is confirmed by the Seebeck coefficient which depends on the magnetic field at low temperature, with a large negative magnetothermopower (MTEP) effect of -26% at 20 K, i.e., the thermopower is reduced as the spin alignment reduces the spin entropy. This first report of MTEP in CuCrTiS4 shows that this thiospinel behaves rather similarly to strongly correlated oxides, with MR and MTEP enhanced in the case of VRH transport with paramagnetic spins, such as in cobalt misfits or colossal MR manganites.

Large negative giant magnetoresistance at room temperature and electrical transport in cobalt ferrite-polyaniline nanocomposites

At room temperature, a large negative out-of-plane magnetoresistance (MR), [R(H)-R(0)]/R(0), with a value of −35.76% at magnetic field of 9 T has been obtained in the cobalt ferrite (CoFe2O4)/polyaniline (PANI) nanocomposites with CoFe2O4 loading of 40.0 wt% prepared by surface initiated polymerization (SIP) method, which is strongly related to the weak localization (WL) model in the weak disordered system. The negative MR at room temperature in the CoFe2O4/PANI nanocomposites exhibits the obvious nanoparticle loading and magnetic field dependent properties. Both thermal activated transport model and Mott variable range hopping (VRH) model are applied to express the electrical transport mechanism for the temperature regimes of 180–290 K and 50–180 K, accordingly. The electrical transport in the CoFe2O4/PANI nanocomposites obeys the 3D VRH transport mechanism at low temperature range of 50–180 K. The estimated activation energy Eg for the CoFe2O4/PANI nanocomposites with different CoFe2O4 nanoparticle loadings of 10.0, 20.0, 40.0, and 60.0 wt% is 61, 63, 65, and 87 meV, respectively. The coating of PANI on the surface of CoFe2O4 nanoparticle reveals the significant effect on both the remanence and coercivity of CoFe2O4 nanoparticle.

Electronic phase separation in insulating (Ga, Mn) As with low compensation: super-paramagnetism and hopping conduction

In the present work, low compensated insulating (Ga,Mn)As with 0.7% Mn is obtained by ion implantation combined with pulsed laser melting. The sample shows variable-range hopping transport behavior with a Coulomb gap in the vicinity of the Fermi energy, and the activation energy is reduced by an external magnetic field. A blocking super-paramagnetism is observed rather than ferromagnetism. Below the blocking temperature, the sample exhibits a colossal negative magnetoresistance. Our studies confirm that the disorder-induced electronic phase separation occurs in (Ga,Mn)As samples with a Mn concentration in the insulator–metal transition regime, and it can account for the observed superparamagnetism and the colossal magnetoresistance.

A tunable palladium nanoparticle film-based strain sensor in a Mott variable-range hopping regime

Metal nanoparticle (NP) film, an important artificial material that exhibits electronic transport properties different from bulk metals, has often been employed to fabricate micro/nano electronic devices. In this paper, Pd NP film was formed on the surface of flexible polyethylene terephthalate (PET) sheet in order to fabricate a strain sensor by means of gas-phase cluster beam deposition. Three Pd NP film-based strain sensors with different NP coverages were fabricated, and their electronic transport properties and strain sensing behaviors were investigated. Despite the differences in inter-particle coupling strength induced by different NP coverages, the Mott variable-range hopping (VRH) transport was found to be dominant in all three sensors. Sensors made of Pd NP films with lower NP coverage were found to give strain gauges with greater sensitivity, and their strain sensing calibration curves deviated from the exponential law due to variations in the gauge factor during strain loading, which was originated from the topology change of the percolation network. Sensitivity could be optimized by regulating the NP coverage, which is readily tuned during device fabrication. The tunable sensitivity, up to 1000, as well as the variety in flexible substrate materials available make them extremely promising for developing micro- and nano-sized electromechanical devices. Besides, the investigations about the reliability and hysteresis performance of the sensors were carried out. Our strain sensors show an excellent performance to the long-term bending–unbending cyclic test.

Carrier thermoelectric transport model for black phosphorus field-effect transistors

As a new elemental two-dimensional material, layered black phosphorus (BP) has revealed its intriguing properties and is considered to be a potential thermoelectric material. However, the ambiguous carrier thermoelectric transport in layered BP limits its development. In this work, based on variable-range hopping transport and percolation theory, we have developed a unified thermoelectric-transport model to investigate the Seebeck effect of BP field-effect transistors (FETs). The proposed model can characterize the effect of temperature, disorder, and the carrier concentration on carrier thermoelectric transport. The simulation results show abnormal temperature-dependence with decreasing disorder degree in BP FETs. The proposed model will be helpful to understand the thermoelectric transport properties of layered BP and design desired thermoelectric devices.

Wafer scale integration of reduced graphene oxide by novel laser processing at room temperature in air

Physical properties of reduced graphene oxide (rGO) strongly depend on the ratio of sp2 to sp3 hybridized carbon atoms, the presence of different functional groups, and the characteristics of the substrates. This research for the very first time illustrates successful wafer scale integration of 2D rGO with Cu/TiN/Si, employing pulsed laser deposition followed by laser annealing of carbon-doped copper layers using nanosecond excimer lasers. The XRD, SEM, and Raman spectroscopy measurements indicate the presence of large area rGO onto Si having Raman active vibrational modes: D, G, and 2D. A high resolution SEM depicts the morphology and formation of rGO from zone-refined carbon formed after nanosecond laser annealing. Temperature-dependent resistance data of rGO thin films follow the Efros-Shklovskii variable range hopping (VRH) model in the low-temperature region and Arrhenius conduction in the high-temperature regime. The photoluminescence spectra also reveal a less intense and broader blue fluorescence spectra, indicating the presence of miniature sized sp2 domains in the near vicinity of π* electronic states which favor the VRH transport phenomena. This wafer scale integration of rGO with Si employing a laser annealing technique will be useful for multifunctional integrated electronic devices and will open a new frontier for further extensive research in these functionalized 2D materials.