Variable-range Hopping Regime Research Articles

Thermoelectric response across the semiconductor-semimetal transition in black phosphorus

By precisely tuning the ground state of black phosphorus with pressure from the semiconducting to semimetallic state, we track a systematic evolution of the Seebeck coefficient. Thanks to a manifest correlation between the Seebeck coefficient and resistivity, the Seebeck response in each conduction regime, i.e., intrinsic, saturation, extrinsic, and variable range hopping (VRH) regimes, is identified. In the former two regimes, the Seebeck coefficient behaves in accordance with the present theories, whereas in the latter two regimes available theories do not give a satisfactory account for its response. However, by eliminating the extrinsic sample dependence in the resistivity ρ and Seebeck coefficient S, the Peltier conductivity α=S/ρ allows us to unveil the intrinsic thermoelectric response, revealing vanishing fate for α in the VRH regime. The emerged ionized impurity scattering on entry to the semimetallic state is easily surpassed by electron-electron scattering due to squeezing of screening length accompanied by an increase of carrier density with pressure. Each carrier scattering participates an enhancement of the phonon drag contribution to the Seebeck effect, but creates the phonon drag peak with opposite sign at distinct temperature. In the low-temperature limit, a small number of carriers enhances a prefactor of T-linear Seebeck coefficient as large as what is observed in prototypical semimetals. A crucial but largely ignored role of carrier scattering in determining the magnitude and sign of the Seebeck coefficient is indicated by the observation that a sign reversal of the T-linear prefactor is concomitant with a change in dominant scattering mechanism for carriers. Published by the American Physical Society 2024

Spin dynamics of exchange-coupled nitrogen donors in heavily dopedn-type15RSiC monocrystals: Multifrequency EPR and EDMR study

Semiconductor devices based on $15R$ silicon carbide (SiC) show improved properties compared to other polytypes. Here, we report the investigation of nitrogen-doped $15R$ SiC monocrystals with $({N}_{\mathrm{D}}--{N}_{\mathrm{A}})\ensuremath{\sim}5\ifmmode\times\else\texttimes\fi{}{10}^{18}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}3}$ using multifrequency electron paramagnetic resonance (EPR) and electrically detected magnetic resonance (EDMR) spectroscopic methods in the microwave (MW) frequency range from 9.4 to 328.84 GHz and in the temperature range from 4.2 to 300 K. A single intensive $S$ line with $S=1/2$, at ${g}_{\ensuremath{\perp}}=2.0026(2)$, and ${g}_{\ensuremath{\parallel}}=2.0043(2)$ dominates the EPR spectrum in $15R$ SiC at $T<160$ K and was attributed to the exchange-coupled nitrogen (N) donors substituting quasicubic ``$k1$'' site having the deeper energy level in $15R$ SiC lattice. From the analysis of the temperature behavior of the integral intensity, magnetic field position, intensity, shape, and width of the $S$ line, it was concluded that at $T<90$ K, the exchange coupling occurs between localized donor electrons, while at $T=90\ensuremath{-}150$ K the interaction between exchange-coupled N donors and conduction electrons takes place. In the temperature interval from 20 to 160 K, the $S$-line EPR width was characterized by a two-phonon Orbach relaxation process with the activation energy of $\ensuremath{\sim}6.5$ meV corresponding to the valley-orbit splitting values for N donors in $15R$ SiC. The variable-range hopping regime obeying the ${T}^{1/4}$ law was found to take place at $T<20$ K leading to the appearance of the $S$ line in the EDMR spectrum at low temperatures. The appearance of the EDMR signal from exchange-coupled N donors is caused by the EPR-induced temperature-increase mechanism and the spin-flip hops process. The results obtained from MW conductivity measurements agree with EPR and EDMR data. The temperature variation of MW conductivity was described by several processes, including the electron-hopping process between N donor impurity atoms at $T<50$ K with activation energy ${\ensuremath{\varepsilon}}_{3}=1.5$ meV, electron transitions between Hubbard bands at $T=50--100$ K; the transition of the electrons from the donor energy levels to conduction band with ionization energy ${\ensuremath{\varepsilon}}_{1}=32$ meV at $T=100--200$ K and scattering of the conduction electrons by ionized donors occurred at the temperature higher than 200 K.

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.

Metal-insulator Transition in \({}^{70}\)Ge: Ga Semiconductor by Applying the Scaling Laws

In this article, we focus on the scaling theory of Abraham et al. without and with a magnetic field on the metallic side of the Metal-Insulator Transition (MIT) for the three-dimensional system \({}^{70}\)Ge: Ga, at very low temperatures. In particular, we have determined the zero temperature conductivity critical exponent when the MIT transition occurs with the variation of the impurity concentration \((\upsilon=0.503)\) and with the application of a magnetic field \((\upsilon=1.06)\). We have also estimated the critical magnetic field \(B_C\) that separates the metallic behavior \((B<B_C)\) from the variable-range hopping regime \((B>B_C)\). The data are for a \({}^{70}\)Ge: Ga sample prepared and reported by Itoh et al., Physical Review Letters 77 (1996), 4058 and Watanabe et al., Physical Review B 60 (1999), 15817.

A crossover from Efros–Shklovskii hopping to activated transport in a GaAs two-dimensional hole system at low temperatures

In this paper, we discuss low-temperature hopping-conductivity behavior in the insulating phase, in the absence of a magnetic field. We conduct a theoretical study of the crossover from hopping to activated transport in a GaAs two-dimensional hole system at low temperatures, finding that a crossover takes place from the Efros-Shklovskii variable-range hopping (VRH) regime to an activated regime in this system. This conductivity behavior in p-GaAs quantum wells is qualitatively consistent with the laws laid down in theories of localized electron interactions. Given sufficiently strong interactions, the holes in the localized states are able to hop collectively.

Study of Transport Phenomenon in Amorphous RexSi1 – x Thin Films on the Both Sides of the Metal–Insulator Transition at Very Low Temperatures

In this work, we study the electrical conductivity behaviors on the both sides of the metal-insulator transition (MIT) in RexSi1 – x amorphous thin films at very low temperature. In fact, our investigation re-analyzed the experimental measurements of RexSi1 – x obtained by K.G. Lisunov et al. On the insulating side of the MIT, the electrical conductivity can be interpreted by the existence of the variable range-hopping regime. However, on the metallic side of the MIT, the electrical conductivity is mainly due to electron–electron interactions and low localization effects.

Non-conventional ferromagnetism and high bias magnetoresistance in [formula omitted]: A simple phenomenological approach

A simple phenomenological approach is used to describe magnetization and magnetoresistance in thin films of oxygen-deficient rutile titanium dioxide (TiO2). Magnetization curves were successfully simulated by considering the ferromagnetic (FM) contribution of magnetically interacting oxygen vacancies (VO’s) forming a single-domain using the Stoner-Wohlfarth (SW) model combined with paramagnetic (PM) contribution of isolated VO’s described by a Langevin function. Whereas approximately half of the VO’s behave as ferromagnetically coupled, rotating coherently with the applied magnetic field, the remaining half of the VO’s tend to align individually with the local magnetic field overcoming the thermal fluctuation deviations. The conduction mechanism is described by variable range hopping (VRH) regime with electron hopping between VO’s centers in the TiO2-x matrix. The magnetoresistance (MR) curves are consistently simulated through the scaling with square of PM contribution of magnetization, indicating that resistance depends on the relative orientation of the magnetic moments associated with non-interacting VO’s dispersed in TiO2 matrix at low temperatures. Density functional theory (DFT) calculations were performed to validate the parametrization of the phenomenological approach used to described the ferromagnetic groundstate of the VO network and spin polarization in the VRH regime in the TiO2-x matrix. Spin-resolved density of states (DOS) calculations consistently reveal that magnetoresistance can be ascribed to electron hopping from defect-states located immediately below Fermi level to the bottom of conduction band states with an opposed spin-polarization.

Towards the insulator-to-metal transition at the surface of ion-gated nanocrystalline diamond films

Hole doping can control the conductivity of diamond either through boron substitution, or carrier accumulation in a field-effect transistor. In this work, we combine the two methods to investigate the insulator-to-metal transition at the surface of nanocrystalline diamond films. The finite boron doping strongly increases the maximum hole density which can be induced electrostatically with respect to intrinsic diamond. The ionic gate pushes the conductivity of the film surface away from the variable-range hopping regime and into the quantum critical regime. However, the combination of the strong intrinsic surface disorder due to a non-negligible surface roughness, and the introduction of extra scattering centers by the ionic gate, prevents the surface accumulation layer to reach the metallic regime.

HgTe quantum wells with inverted band structure: Quantum Hall effect and the large-scale impurity potential

We report on the longitudinal and Hall resistivities of a HgTe quantum well with inverted energy spectrum (dQW = 20.3 nm) measured in the quantum Hall (QH) regime at magnetic fields up to 9 T and temperatures 2.9–50 K. The temperature dependence of the QH plateau-plateau transition (PPT) widths and of variable range hopping (VRH) conduction on the Hall plateaus are analyzed. The data are presented in a genuine scale form both for PPT regions and for VRH regime. Decisive role of the long-range random potential (the potential of remote ionized impurities) in the localization-delocalization processes in the QH regime for the system under study is revealed.

Hall effect in two-dimensional systems with hopping transport and strong disorder

We reconsider the theory of Hall effect in the systems with hopping conduction. The purpose of the present study is to compare the percolation approach based on the optimal triad model with numerical simulations and recent experimental results. We show that, in the nearest neighbor hopping regime, the results of the percolation theory agree to the simulation. However, in the variable range hopping (VRH) regime, the optimal triad model fails to describe the numerical results. It is related to the extremely small probability to find the optimal triad of sites in the percolation cluster in the VRH regime. The contribution of these triads to the Hall effect appears to be small. We describe the Hall mobility in the VRH regime with the empirical law obtained from the numerical results. The law is in agreement with our recent experimental data in 2D quantum dot arrays with the hopping transport.

Quantum interference magnetoconductance of polycrystalline germanium films in the variable-range hopping regime

Direct evidence of quantum interference magnetotransport in polycrystalline germanium films in the variable-range hopping (VRH) regime is reported. The temperature dependence of the conductivity of germanium films fulfilled the Mott VRH mechanism with the form of in the low-temperature regime (). For the magnetotransport behaviour of our germanium films in the VRH regime, a crossover, from negative magnetoconductance at the low-field to positive magnetoconductance at the high-field, is observed while the zero-field conductivity is higher than the critical value (). In the regime of , the magnetoconductance is positive and quadratic in the field for some germanium films. These features are in agreement with the VRH magnetotransport theory based on the quantum interference effect among random paths in the hopping process.

Frequency Dependence of the Conductivity of Disordered Semiconductors in the Region of the Transition to the Fixed-Range Hopping Regime

The effect of hybridization of electron states on the high-frequency conductivity of disordered semiconductors is studied. It is shown that the dependence of the pre-exponential factor of the resonance integral on the intercenter separation in a pair determines the abruptness of the change in conductivity mechanisms near the transition of the frequency dependence of the real part of the conductivity σ1(ω) from sublinear to quadratic. The abruptness of the change of the conductivity regimes is associated with a rapid decrease in hopping distance with increasing frequency near the transition, which leads to a substantial relative decrease in the contribution from the phononless conductivity component in the variable-range hopping regime with increasing frequency and transition to the fixed-range hopping conductivity regime.

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.

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

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

Особенности частотной зависимости проводимости неупорядоченных полупроводников в области перехода к режиму с постоянной длиной прыжка

AbstractThe effect of hybridization of electron states on the high-frequency conductivity of disordered semiconductors is studied. It is shown that the dependence of the pre-exponential factor of the resonance integral on the intercenter separation in a pair determines the abruptness of the change in conductivity mechanisms near the transition of the frequency dependence of the real part of the conductivity σ_1(ω) from sublinear to quadratic. The abruptness of the change of the conductivity regimes is associated with a rapid decrease in hopping distance with increasing frequency near the transition, which leads to a substantial relative decrease in the contribution from the phononless conductivity component in the variable-range hopping regime with increasing frequency and transition to the fixed-range hopping conductivity regime.

Irreconcilable room temperature magnetotransport properties of polypyrrole nanoparticles and nanorods

The morphology of nanostructures plays a vital role in determining the conductivity of specimens and, consequently, affects the efficiency of magnetoelectronic devices such as magnetic field sensors. Herein, nanoparticles (NPs) and nanorods (NRs) of conducting polymer polypyrrole have been synthesized at room temperature via the chemical oxidative polymerization method. The positive and negative magnetoresistance signatures are respectively obtained in NPs and NRs morphology, respectively. Both morphologies have conduction in the variable range-hopping regime with the average charge carrier hopping length being highly influenced by the sign of magnetoresistance. This morphology dependence is not only interesting for fundamental research but it also allows for tuning magnetic field sensor materials to be usable at room temperature for the desired characteristics.

Current-Driven Instability of the Quantum Anomalous Hall Effect in Ferromagnetic Topological Insulators.

The instability of the quantum anomalous Hall (QAH) effect has been studied as a function of the electric current and temperature in ferromagnetic topological insulator thin films. We find that a characteristic current for the breakdown of the QAH effect is roughly proportional to the Hall-bar width, indicating that the Hall electric field is relevant to the breakdown. We also find that electron transport is dominated by variable range hopping (VRH) at low temperatures. Combining the current and temperature dependences of the conductivity in the VRH regime, the localization length of the QAH state is evaluated to be about 5 μm. The long localization length suggests a marginally insulating nature of the QAH state due to a large number of in-gap states.

Crossover from Efros–Shklovskii to Mott variable range hopping in monolayer epitaxial graphene grown on SiC

We report variable range hopping (VRH) transport in monolayer epitaxial graphene grown on SiC. A crossover from Efros–Shklovskii (E-S) VRH to Mott VRH can be observed by increasing the magnetic field applied perpendicular to the plane of graphene or by a low-temperature vacuum annealing process. Our new experimental results suggest that monolayer graphene on SiC is an interesting platform for probing VRH and crossover between different VRH regimes in a strongly disordered system.

Dependence of conductivity on thickness within the variable-range hopping regime for Coulomb glasses

In this paper, we provide some computational evidence concerning the dependence of conductivity on the system thickness for Coulomb glasses. We also verify the Efros–Shklovskii law and deal with the calculation of its characteristic parameter as a function of the thickness. Our results strengthen the link between theoretical and experimental fields.