Hopping Regime Research Articles

Electrical Conduction Mechanism of Mg-Doped ZrO2 Thin Films.

Amorphous ZrO2 thin films with increasing Mg content were deposited on quartz substrates, by dip coating method. The films are transparent in the visible domain and absorbent in UV, with an optical band gap that decreases with the increase of Mg content, from 5.42 eV to 4.12 eV. The temperature dependent conductivity measurements showed typical semiconductor comportment. The decrease of the electrical conductivity by Mg doping was related to the increase of the OH groups (37% to 63%) as seen from X-ray Photoelectron Spectroscopy. It was found out that the electrical conductivity obeys the Meyer-Neldel rule. This rule, previously reported for different disordered material systems is obtained for ZrO2 for the first time in the literature. Exploring novel aspects of Mg-doped ZrO2, the present study underscores the origin of the Meyer-Neldel rule explained by the small-polaron hopping model in the non-adiabatic hopping regime. Determination of the presence of such a conduction mechanism in the samples hold promise for comprehending the important aspects, which might be a concern in developing various devices based on Mg-doped ZrO2.

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

Extrinsic anomalous Hall effect in Mn doped GeSnTe semiconductors in the bad-metal hopping regime

We present high field magnetotransport studies of Ge1-x-y(SnxMny)Te bulk multiferroics with diamagnetic Sn and paramagnetic Mn concentration, 0.38 ≤ x ≤ 0.79 and 0.02 ≤ y ≤ 0.086, respectively. The zero-field resistivity, ρxx(T) takes significant contribution from defects below T ≤ 20 K however; a mixed scattering contribution from phonons and unusual sources is estimated from T ≈ 20–300 K. The carrier mobility shows anomalous temperature dependence from ∼T–0.2 to ∼T–0.5 which hints towards possible presence of polaronic effects resulting from coupling of holes with phonons. This anomalous behavior cannot be understood in terms of pure phononic scattering mechanism at high temperatures. From point of view of high magnetic field results, the transverse component of magneto-resistivity manifests anomalous Hall effect originating from extrinsic scattering sources, particularly the side jump mechanism reveals a dominating contribution. We also find that the correlation between the transverse and longitudinal conductivities follow the universal scaling law σxy ∼ σxxn where n = 1.6 in the low conductivity limit. The values n = 1.5 – 1.8 obtained for the present Ge1-x-y(SnxMny)Te alloys justify the bad-metal hopping regime of our crystals since the results fall in the low conductivity ferromagnetic family with σxx ≤ 104 (Ω cm)–1. The interpretation of the n = 1.6 scaling in the low conductivity regime is thus far not fully understood. However; the anomalous Hall resistivity scaling with modified relation by Tian et al., is indicative of the dominant side jump scattering along with noticeable role of skew scattering.

Effect of Wort Boiling System and Hopping Regime on Wort and Beer Stale-Flavor Aldehydes.

The main factor responsible for the sensory aging of beer is the increase in off-flavor aldehydes during beer storage. In pilot brews (200 L) of pale lager beer with different hopping regimes and wort boiling systems, 15 carbonyls were monitored using the GC-MS method. Factor analysis revealed several groups of aldehydes with similar behavior during wort boiling. The concentration of most of them decreased with atmospheric wort boiling and increased with the time and energy-saving pressurized boiling system. Wort clarification was a critical step because of the increase in carbonyl concentration, with the level of most carbonyls being higher in the final wort compared to sweet wort. The hopping regimes only affected the level of 3-methylbutan-2-one in the wort. The concentration of carbonyls decreased significantly (30-90%) during fermentation, except for trans-2-butenal, which increased by 59% on average, likely due to the release from imine complex. The concentration of free aldehydes in the fresh beers was similar for all variants used, but the pressurized wort boiling system could result in lower sensory stability of the beer due to the release of aldehydes from inactive complexes formed during fermentation. This aspect requires further investigation.

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.

Thermopower in Transition from Tunneling to Hopping.

The Seebeck effect of a molecular junction in a hopping regime or tunneling-to-hopping transition remains uncertain. This paper describes the Seebeck effect in molecular epitaxy films (OPIn where n = 1-9) based on imine condensation between an aryl amine and aldehyde and investigates how the Seebeck coefficient (S, μV/K) varies at the crossover region. The S value of OPIn linearly increased with increasing the molecular length (d, nm), ranging from 7.2 to 38.0 μV/K. The increasing rate changed from 0.99 to 0.38 μV·K-1 Å-1 at d = 3.4 nm (OPI4). Combined experimental and theoretical studies indicated that such a change stems from a tunneling-to-hopping transition, and the small but detectable length-dependence of thermopower in the long molecules originates from the gradual reduction of the tunneling contribution to the broadening of molecular orbital energy level, rather than its relative position to the Fermi level. Our work helps to bridge the gap between bulk and nanoscale thermoelectric systems.

Electronic properties of Cu2(Zn, Cd)SnS4 determined by the high-field magnetotransport

Resistivity, ρ(T), and magnetoresistance (MR) are investigated in the Cu2Zn1−x Cd x SnS4 single crystals for compositions x ≡ Cd/(Zn + Cd) = 0.15–0.24, in the temperature range of T ∼ 50–300 K in pulsed magnetic fields of B up to 20 T. The Mott variable-range hopping (VRH) conductivity is established within wide temperature intervals lying inside ΔT M ∼ 60–190 K for different x. The deviations from the VRH conduction, observable above and below ΔT M, are connected to the nearest-neighbor hopping regime and to the activation on the mobility threshold of the acceptor band (AB) with width W ≈ 16–46 meV. The joint analysis of ρ(T) and positive MR permitted determination of other important electronic parameters. These include the localization radius, α ≈ 19–30 Å, the density of the localized states, g(μ) ≈ (1.6–21) × 1017 meV−1 cm−3 at the Fermi level μ, and the acceptor concentration, N A ∼ (6–8) × 1019 cm−3, for various x and in conditions of different vicinity of the investigated samples to the metal–insulator transition. In addition, details of the AB structure, including positions of μ and of the mobility threshold, E c, are found depending on the alloy composition.

Topological Lifshitz transitions, orbital currents, and interactions in low-dimensional Fermi gases in synthetic gauge fields

Low-dimensional systems of interacting fermions in a synthetic gauge field have been experimentally realized using two-component ultra-cold Fermi gases in optical lattices. Using a two-leg ladder model that is relevant to these experiments, we have studied the signatures of topological Lifshitz transitions and the effects of the inter-species interaction U on the gauge-invariant orbital current in the regime of large intra-leg hopping Ω. Focusing on non-insulating regimes, we have carried out numerically exact density-matrix renormalization-group (DMRG) calculations to compute the orbital current at fixed particle number as a function of the interaction strength and the synthetic gauge flux per plaquette. Signatures of topological Lifshitz transitions where the number Fermi points changes are found to persist even in the presence of very strong repulsive interactions. This numerical observation suggests that the orbital current can be computed from an appropriately renormalized mean-field band structure, which is also described here. Quantitative agreement between the mean-field and the DMRG results in the intermediate interaction regime where U ≲ Ω is demonstrated. We also have observed that interactions can change the sign of the current susceptibility at zero field and induce Lifshitz transitions between two metallic phases, which is also captured by the mean-field theory. Correlation effects beyond mean-field theory in the oscillations of the local inter-leg current are also reported. We argue that the observed robustness against interactions makes the orbital current a good indicator of the topological Lifshitz transitions.

Nonadiabatic Dynamics of Polaron Hopping and Coupling with Water on Reduced TiO2.

By interplay between first-principles molecular dynamics and nonadiabatic molecular dynamics simulations based on the decoherence-induced surface-hopping approach, we investigate and quantify the mechanisms through which different electron polaron hopping regimes in the reduced anatase TiO2(101) surface influence recombination of photogenerated charge carriers, also in the presence of adsorbed water (H2O) molecules. The simulations reveal that fast hopping regimes promote ultrafast recombination of photogenerated charge-carriers. Conversely, charge recombination is delayed in the presence of slower polaron hopping and even more so if the polaron is pinned at one Ti-site, as typical following adsorption of H2O on the anatase(101) surface. These trends are related to the observed enhancement of the space and energy overlap between conduction band minimum and polaron band gap states, and the ensuing nonadiabatic couplings (NAC) strengths, during a polaronic hop. We expect these insights on the beneficial role of polaron diffusion pinning for the extended lifetime of photoexcitations in TiO2 to sustain ongoing developments of photocatalytic strategies based on this substrate.

Optimized Active Cooling and Refrigeration using Antidoted Graphene for Heat Management of Microelectronics

With the technology of artificial defects creating, we can tune the band structure and transport properties of many two-dimensional (2D) layered materials. One prototype materials system is the antidoted graphene sheet, where periodical pores are made using focuses ion or electron beams in the nanoscale. We here study the electrical conductivity, thermopower, and active rates of cooling and refrigeration of antidoted graphene samples with different pore-radii and interporous distances. We use a calculation method that takes into consider the sensitivity of transport to charge carrier energy, which can be used to describe the elastic and inelastic scatterings in diffusive, ballistic and quantum hopping regimes. It is found that our results from the new calculational approach are more consistent with the experimental data, compared to some traditional methodologies. It is also interesting to see that the optimized active rates of cooling and refrigeration are very robust against the distribution variations of interporous distance and the pore-radius, which implies easy industrialization and inexpensive manufacturing. The same analysis and investigation can also be extended to many other layered materials, including the transitional metal dichalcogenides (TMD), blue phosphorene, and tellurium.

Above-ordering-temperature large anomalous Hall effect in a triangular-lattice magnetic semiconductor.

While anomalous Hall effect (AHE) has been extensively studied in the past, efforts for realizing large Hall response have been mainly limited within intrinsic mechanism. Lately, however, a theory of extrinsic mechanism has predicted that magnetic scattering by spin cluster can induce large AHE even above magnetic ordering temperature, particularly in magnetic semiconductors with low carrier density, strong exchange coupling, and finite spin chirality. Here, we find out a new magnetic semiconductor EuAs, where Eu2+ ions with large magnetic moments form distorted triangular lattice. In addition to colossal magnetoresistance, EuAs exhibits large AHE with an anomalous Hall angle of 0.13 at temperatures far above antiferromagnetic ordering. As also demonstrated by model calculations, observed AHE can be explained by the spin cluster scattering in a hopping regime. Our findings shed light on magnetic semiconductors hosting topological spin textures, developing a field targeting diluted carriers strongly coupled to noncoplanar spin structures.

Nonequilibrium Carrier Transport in Quantum Dot Heterostructures.

Understanding carrier dynamics and transport in quantum dot based heterostructures is crucial for unlocking their full potential for optoelectronic applications. Here we report the direct visualization of carrier propagation in PbS CQD solids and quantum-dot-in-perovskite heterostructures using femtosecond transient absorption microscopy. We reveal three distinct transport regimes: an initial superdiffusive transport persisting over hundreds of femtoseconds, an Auger-assisted subdiffusive transport before thermal equilibrium is achieved, and a final hopping regime. We demonstrate that the superdiffusive transport lengths correlate strongly with the degree of energetic disorder and carrier delocalization. By tailoring the perovskite content in heterostructures, we obtained a superdiffusive transport length exceeding 90 nm at room temperature and an equivalent diffusivity of up to 106 cm2 s-1, which is 4 orders of magnitude higher than the steady-state values. These findings introduce promising strategies to harness nonequilibrium transport phenomena for more efficient optoelectronic devices.

Facile ab initio approach for self-localized polarons from canonical transformations

Electronic states in a crystal can localize due to strong electron-phonon (e-ph) interactions, forming so-called small polarons. Methods to predict the formation and energetics of small polarons are either computationally costly or not geared toward quantitative predictions. Here we show a formalism based on canonical transformations to compute the polaron formation energy and wavefunction using ab initio e-ph interactions. Comparison of the calculated polaron and band edge energies allows us to determine whether charge carriers in a material favor a localized small polaron over a delocalized Bloch state. Due to its low computational cost, our approach enables efficient studies of the formation and energetics of small polarons, as we demonstrate by investigating electron and hole polaron formation in alkali halides and metal oxides and peroxides. We outline refinements of our scheme and extensions to compute transport in the polaron hopping regime.

Bias-Polarity-Dependent Direct and Inverted Marcus Charge Transport Affecting Rectification in a Redox-Active Molecular Junction.

This paper describes the transition from the normal to inverted Marcus region in solid‐state tunnel junctions consisting of self‐assembled monolayers of benzotetrathiafulvalene (BTTF), and how this transition determines the performance of a molecular diode. Temperature‐dependent normalized differential conductance analyses indicate the participation of the HOMO (highest occupied molecular orbital) at large negative bias, which follows typical thermally activated hopping behavior associated with the normal Marcus regime. In contrast, hopping involving the HOMO dominates the mechanism of charge transport at positive bias, yet it is nearly activationless indicating the junction operates in the inverted Marcus region. Thus, within the same junction it is possible to switch between Marcus and inverted Marcus regimes by changing the bias polarity. Consequently, the current only decreases with decreasing temperature at negative bias when hopping is “frozen out,” but not at positive bias resulting in a 30‐fold increase in the molecular rectification efficiency. These results indicate that the charge transport in the inverted Marcus region is readily accessible in junctions with redox molecules in the weak coupling regime and control over different hopping regimes can be used to improve junction performance.

Emergent nonlinear phenomena in a driven dissipative photonic dimer

Collective effects leading to spatial, temporal or spatiotemporal pattern formation in complex nonlinear systems driven out of equilibrium cannot be described at the single-particle level and are therefore often called emergent phenomena. They are characterized by length scales exceeding the characteristic interaction length and by spontaneous symmetry breaking. Recent advances in integrated photonics have indicated that the study of emergent phenomena is possible in complex coupled nonlinear optical systems. Here we demonstrate that the out-of-equilibrium driving of a strongly coupled pair of photonic integrated Kerr microresonators (‘dimer’)—which, at the ‘single particle’ (that is, individual resonator) level, generate well-understood dissipative Kerr solitons—exhibits emergent nonlinear phenomena. By exploring the dimer phase diagram, we find regimes of soliton hopping, spontaneous symmetry breaking and periodically emerging (in)commensurate dispersive waves. These phenomena are not included in the single-particle description and are related to the parametric frequency conversion between the hybridized supermodes. Moreover, by electrically controlling the supermode hybridization, we achieve wide tunability of spectral interference patterns between the dimer solitons and dispersive waves. Our findings represent a step towards the study of emergent nonlinear phenomena in soliton networks and multimodal lattices. A pair of strongly coupled photonic microresonators shows nonlinear emergent behaviour, which can be understood by incorporating interactions in the theoretical description of nonlinear optical systems.

Mean-field simulation of hopping resistivity in a model with Coulomb interactions and current correlations

Simulations of hopping resistivity by mean-field methods rely on randomly generated site energies. Thus such effects as the presence of the Coulomb gap and electron current correlations have been simulated using predominantly Monte Carlo methods. This paper presents a method of mean-field calculation of hopping resistivity in a wide range of temperatures and electric fields. This method considers the long-range Coulomb interactions and at least partially accounts for the electron current correlations. Resulting curves reproduce the Mott law in the form predicted by Efros and Shklovskii and the experimentally observed electric field dependencies. Based on the results, a decrease of hopping energy is predicted with increasing temperature in the nearest-neighbor hopping regime. The report analyses the differences between the mean-field and the Monte Carlo approaches.

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.