Apparent power-law behavior of conductance in disordered quasi-one-dimensional systems

Role of Coulomb blockade in nonlinear transport of conducting polymers

NonlinearI-Vcharacteristics associated with Coulomb blockade (CB) in conducting polymers were systematically investigated. At low temperatures, a crossover from Ohmic to nonlinear behavior was observed, along with drastically enhanced noise in differential conductance right from the crossover. The fluctuation can be well explained by the Coulombic oscillation in the collective percolation system, where the charge transport is related to the Coulombic charging energy between crystalline domains. Furthermore, a distinct quantum conductance, the fingerprint of CB caused by the individual tunneling between crystalline grains, was observed in sub-100 nm devices, confirming a strong association between nonlinearI-Vcharacteristics and CB effect.

A robust and tunable Luttinger liquid in correlated edge of transition-metal second-order topological insulator Ta2Pd3Te5

The interplay between topology and interaction always plays an important role in condensed matter physics and induces many exotic quantum phases, while rare transition metal layered material (TMLM) has been proved to possess both. Here we report a TMLM Ta2Pd3Te5 has the two-dimensional second-order topology (also a quadrupole topological insulator) with correlated edge states - Luttinger liquid. It is ascribed to the unconventional nature of the mismatch between charge- and atomic- centers induced by a remarkable double-band inversion. This one-dimensional protected edge state preserves the Luttinger liquid behavior with robustness and universality in scale from micro- to macro- size, leading to a significant anisotropic electrical transport through two-dimensional sides of bulk materials. Moreover, the bulk gap can be modulated by the thickness, resulting in an extensive-range phase diagram for Luttinger liquid. These provide an attractive model to study the interaction and quantum phases in correlated topological systems.

Mesoscopic 3D Charge Transport in Solution-Processed Graphene-Based Thin Films: A Multiscale Analysis

Graphene and related 2D material (GRM) thin films consist of 3D assembly of billions of 2D nanosheets randomly distributed and interacting via van der Waals forces. Their complexity and the multiscale nature yield a wide variety of electrical characteristics ranging from doped semiconductor to glassy metals depending on the crystalline quality of the nanosheets, their specific structural organization ant the operating temperature. Here, the charge transport (CT) mechanisms are studied that are occurring in GRM thin films near the metal-insulator transition (MIT) highlighting the role of defect density and local arrangement of the nanosheets. Two prototypical nanosheet types are compared, i.e., 2D reduced graphene oxide and few-layer-thick electrochemically exfoliated graphene flakes, forming thin films with comparable composition, morphology and room temperature conductivity, but different defect density and crystallinity. By investigating their structure, morphology, and the dependence of their electrical conductivity on temperature, noise and magnetic-field, a general model is developed describing the multiscale nature of CT in GRM thin films in terms of hopping among mesoscopic bricks, i.e., grains. The results suggest a general approach to describe disordered van der Waals thin films.

One-dimensional Luttinger liquids in a two-dimensional moiré lattice

The Luttinger liquid (LL) model of one-dimensional (1D) electronic systems provides a powerful tool for understanding strongly correlated physics, including phenomena such as spin-charge separation¹. Substantial theoretical efforts have attempted to extend the LL phenomenology to two dimensions, especially in models of closely packed arrays of 1D quantum wires^2-13, each being described as a LL. Such coupled-wire models have been successfully used to construct two-dimensional (2D) anisotropic non-Fermi liquids^2-6, quantum Hall states^7-9, topological phases^10,11 and quantum spin liquids^12,13. However, an experimental demonstration of high-quality arrays of 1D LLs suitable for realizing these models remains absent. Here we report the experimental realization of 2D arrays of 1D LLs with crystalline quality in a moiré superlattice made of twisted bilayer tungsten ditelluride (tWTe₂). Originating from the anisotropic lattice of the monolayer, the moiré pattern of tWTe₂ hosts identical, parallel 1D electronic channels, separated by a fixed nanoscale distance, which is tuneable by the interlayer twist angle. At a twist angle of approximately 5 degrees, we find that hole-doped tWTe₂ exhibits exceptionally large transport anisotropy with a resistance ratio of around 1,000 between two orthogonal in-plane directions. The across-wire conductance exhibits power-law scaling behaviours, consistent with the formation of a 2D anisotropic phase that resembles an array of LLs. Our results open the door for realizing a variety of correlated and topological quantum phases based on coupled-wire models and LL physics.

Multiscale Charge Transport in van der Waals Thin Films: Reduced Graphene Oxide as a Case Study

Large area van der Waals (vdW) thin films are assembled materials consisting of a network of randomly stacked nanosheets. The multiscale structure and the two-dimensional (2D) nature of the building block mean that interfaces naturally play a crucial role in the charge transport of such thin films. While single or few stacked nanosheets (i.e., vdW heterostructures) have been the subject of intensive works, little is known about how charges travel through multilayered, more disordered networks. Here, we report a comprehensive study of a prototypical system given by networks of randomly stacked reduced graphene oxide 2D nanosheets, whose chemical and geometrical properties can be controlled independently, permitting to explore percolated networks ranging from a single nanosheet to some billions with room-temperature resistivity spanning from 10^-5 to 10^-1 Ω·m. We systematically observe a clear transition between two different regimes at a critical temperature T*: Efros-Shklovskii variable-range hopping (ES-VRH) below T* and power law behavior above. First, we demonstrate that the two regimes are strongly correlated with each other, both depending on the charge localization length ξ, calculated by the ES-VRH model, which corresponds to the characteristic size of overlapping sp² domains belonging to different nanosheets. Thus, we propose a microscopic model describing the charge transport as a geometrical phase transition, given by the metal-insulator transition associated with the percolation of quasi-one-dimensional nanofillers with length ξ, showing that the charge transport behavior of the networks is valid for all geometries and defects of the nanosheets, ultimately suggesting a generalized description on vdW and disordered thin films.

Applying Marcus theory to describe the carrier transports in organic semiconductors: Limitations and beyond

Marcus theory has been successfully applied to molecular design for organic semiconductors with the aid of quantum chemistry calculations for the molecular parameters: the intermolecular electronic coupling V and the intramolecular charge reorganization energy λ. The assumption behind this is the localized nature of the electronic state for representing the charge carriers, being holes or electrons. As far as the quantitative description of carrier mobility is concerned, the direct application of Marcus semiclassical theory usually led to underestimation of the experimental data. A number of effects going beyond such a semiclassical description will be introduced here, including the quantum nuclear effect, dynamic disorder, and delocalization effects. The recently developed quantum dynamics simulation at the time-dependent density matrix renormalization group theory is briefly discussed. The latter was shown to be a quickly emerging efficient quantum dynamics method for the complex system.

Apparent Power Law Scaling of Variable Range Hopping Conduction in Carbonized Polymer Nanofibers

We induce dramatic changes in the structure of conducting polymer nanofibers by carbonization at 800 °C and compare charge transport properties between carbonized and pristine nanofibers. Despite the profound structural differences, both types of systems display power law dependence of current with voltage and temperature, and all measurements can be scaled into a single universal curve. We analyze our experimental data in the framework of variable range hopping and argue that this mechanism can explain transport properties of pristine polymer nanofibers as well.

Effective Temperature and Universal Conductivity Scaling in Organic Semiconductors

We investigate the scalability of the temperature- and electric field-dependence of the conductivity of disordered organic semiconductors to ‘universal’ curves by two different but commonly employed methods; by so-called universal scaling and by using the effective temperature concept. Experimentally both scaling methods were found to be equally applicable to the out-of-plane charge transport in PEDOT:PSS thin films of various compositions. Both methods are shown to be equivalent in terms of functional dependence and to have identical limiting behavior. The experimentally observed scaling behavior can be reproduced by a numerical nearest-neighbor hopping model, accounting for the Coulomb interaction, the high charge carrier concentration and the energetic disorder. The underlying physics can be captured in a simple empirical model, describing the effective temperature of the charge carrier distribution as the outcome of a heat balance between Joule heating and (effective) temperature-dependent energy loss to the lattice.

Coulomb Blockade in a Two-Dimensional Conductive Polymer Monolayer

Electronic transport was investigated in poly(3-hexylthiophene-2,5-diyl) monolayers. At low temperatures, nonlinear behavior was observed in the current-voltage characteristics, and a nonzero threshold voltage appeared that increased with decreasing temperature. The current-voltage characteristics could be best fitted using a power law. These results suggest that the nonlinear conductivity can be explained using a Coulomb blockade (CB) mechanism. A model is proposed in which an isotropic extended charge state exists, as predicted by quantum calculations, and percolative charge transport occurs within an array of small conductive islands. Using quantitatively evaluated capacitance values for the islands, this model was found to be capable of explaining the observed experimental data. It is, therefore, suggested that percolative charge transport based on the CB effect is a significant factor giving rise to nonlinear conductivity in organic materials.

Negative isotope effect for charge transport in acenes and derivatives--a theoretical conclusion

The isotope effect (IE) on charge transport in polyacenes was proposed in 1970 to judge the transport mechanism. However, there had not been a definitive answer for more than 40 years as to whether such an IE is positive or negative, both theoretically and experimentally, because either theory was too approximate or the experimental estimate was too rough to make a judgment. Employing the quantum nuclear tunneling model for organic semiconductors, we investigate the IE on both hole and electron transport for acenes and their derivatives. We show that both (13)C-substitution and deuteration lead to a negative IE. By introducing phenyl, chlorine, or alkyl side-chains into acenes, the IE becomes more remarkable, especially for hole transport. The vibrational relaxation processes involving in-plane bending of ring or alkyl side-chain motions are found to be responsible for the IE.

Multi-barrier field-emission behavior in PBTTT thin films at low temperatures

We investigated the low-temperature transport mechanism for poly[2,5-bis(3-alkylthiophen-2-yl)thieno(3,2-b)thiophene] (PBTTT). The temperature-dependent transport behavior was studied by varying the drain–source electric field and gate bias. The results suggest that low-temperature charge transport is dominated by direct tunneling at low electric fields, while field emission is prevailing for high electric fields with high carrier densities. However, the obtained barrier heights are remarkably greater than expected in a conventional field emission. We propose a simplified model of field emission through quasi-one-dimensional path with multiple barriers which shows good agreement with the results more clearly. Field emission across the domain boundaries may assist in overcoming the transport barriers induced by the interchain disorder, which results in the weak temperature dependence of conductivities and nonlinear current–voltage relation at low temperatures.

Theoretical Prediction of Isotope Effects on Charge Transport in Organic Semiconductors

We suggest that the nuclear tunneling effect is important in organic semiconductors, which we showed is absent in both the widely employed Marcus theory and the band-like transport as described by the deformation potential theory. Because the quantum nuclear tunneling tends to favor electron transfer while heavier nuclei decrease the quantum effect, there should occur an isotope effect for carrier mobility. For N,N'-n-bis(n-hexyl)-naphthalene diimide, electron mobility of all-deuteration on alkyls and all (13)C-substitution on the backbone decrease ∼18 and 7%, respectively. Similar isotope effects are found in the N,N'-n-bis(n-octyl)-perylene diimide. However, there is nearly no isotope effect for all-deuterated rubrene or tetracene. We have found that the isotopic effect only occurs when the substituted nuclei contribute actively to vibrations with appreciable charge reorganization energy and coupling with carrier motion. Thus, this prediction can shed light on the current dispute over the hopping versus band-like mechanisms in organic semiconductors.

Polaron hopping mediated by nuclear tunnelling in semiconducting polymers at high carrier density

The transition rate for a single hop of a charge carrier in a semiconducting polymer is assumed to be thermally activated. As the temperature approaches absolute zero, the predicted conductivity becomes infinitesimal in contrast to the measured finite conductivity. Here we present a uniform description of charge transport in semiconducting polymers, including the existence of absolute-zero ground-state oscillations that allow nuclear tunnelling through classical barriers. The resulting expression for the macroscopic current shows a power-law dependence on both temperature and voltage. To suppress the omnipresent disorder, the predictions are experimentally verified in semiconducting polymers at high carrier density using chemically doped in-plane diodes and ferroelectric field-effect transistors. The renormalized current-voltage characteristics of various polymers and devices at all temperatures collapse on a single universal curve, thereby demonstrating the relevance of nuclear tunnelling for organic electronic devices.

Local spectral properties of Luttinger liquids: scaling versus nonuniversal energy scales

Motivated by recent scanning tunneling and photoemission spectroscopy measurements on self-organized gold chains on a germanium surface, we reinvestigate the local single-particle spectral properties of Luttinger liquids. In the first part we use the bosonization approach to exactly compute the local spectral function of a simplified field theoretical low-energy model and take a closer look at scaling properties as a function of the ratio of energy and temperature. Translational-invariant Luttinger liquids as well as those with an open boundary (cut chain geometry) are considered. We explicitly show that the scaling functions of both set-ups have the same analytical form. The scaling behavior suggests a variety of consistency checks which can be performed on measured data to experimentally verify Luttinger liquid behavior. In the second part we approximately compute the local spectral function of a microscopic lattice model-the extended Hubbard model-close to an open boundary using the functional renormalization group. We show that it follows the field theoretical prediction in the low-energy regime as a function of energy and temperature, and point out the importance of nonuniversal energy scales inherent to any microscopic model. The spatial dependence of this spectral function is characterized by oscillatory behavior and an envelope function which follows a power law in accordance with the field theoretical continuum model. Interestingly, for the lattice model we find a phase shift which is proportional to the two-particle interaction and not accounted for in the standard bosonization approach to Luttinger liquids with an open boundary. We briefly comment on the effects of several one-dimensional branches cutting the Fermi energy and Rashba spin-orbit interaction.

Insulating state and breakdown of Fermi liquid description in molecular-scale single-crystalline wires of gold

Electrical transport measurements on ultrathin single-crystalline Au nanowires, synthesized via a wet chemical route, show an unexpected insulating behavior. The linear response electrical resistance exhibits a power-law dependence on temperature. In addition, the variation of current over a wide range of temperature and voltage obeys a universal scaling relation that provides compelling evidence for a non-Fermi liquid behavior. Our results demonstrate that the quantum ground state in ultrathin nanowires of simple metallic systems can be radically different from their bulk counterparts and can be described in terms of a Tomonaga-Luttinger liquid (TLL), in the presence of remarkably strong electron-electron interactions.