Numerical studies of variable-range hopping in one-dimensional systems

Родин, Александр; Fogler, M. M.

doi:10.1103/physrevb.80.155435

Cited by 13 publications

(5 citation statements)

References 57 publications

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“…The total voltage drop V across the sample is the sum of voltage drops η i − η j on the links. One can determine the optimal path by finding the sequence of sites that gives the smallest V for a given I [30].…”

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confidence: 99%

“…To find the optimal path, we use a modified Dijkstra algorithm [30], in which the "cost" of reaching site j starting from the source equals −η j . The latter is calculated recurrently using Eq.…”

mentioning

confidence: 99%

“…1. They are obtained numerically following the approach used in our previous work [30], with some improvements. In the inset of Fig.…”

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confidence: 99%

“…We treat all ε i as constants, independent of the applied current. This is justified if electron interactions are weak [30]. The x-spacing between the sites is taken to be unity, so that the density of states is g = 1/∆ = 1/3.…”

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confidence: 99%

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Apparent Power-Law Behavior of Conductance in Disordered Quasi-One-Dimensional Systems

Родин¹,

Fogler²

2010

Phys. Rev. Lett.

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“…1. They are obtained numerically following the approach used in our previous work [30], with some improvements. In the inset of Fig.…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Apparent Power-Law Behavior of Conductance in Disordered Quasi-One-Dimensional Systems

Родин¹,

Fogler²

2010

Phys. Rev. Lett.

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“…Note that the geometrical constraint due to reducing dimensionality generally enhances fluctuations (see Ref. [19] and references therein), and leads ultimately to large non-self-averaging fluctuations in 1D [21].…”

Section: Reveals a Reentrance To Activated Behavior At Low T As The Amentioning

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Activated hopping transport in anisotropic systems at low temperatures

Ihnatsenka

2016

Phys. Rev. B

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Numerical calculations of anisotropic hopping transport based on the resistor network model are presented. Conductivity is shown to follow the stretched exponential dependence on temperature with exponents increasing from 1 4 to 1 as the wave functions become anisotropic and their localization length in the direction of charge transport decreases. For sufficiently strong anisotropy, this results in nearest-neighbor hopping at low temperatures due to the formation of a single conduction path, which adjusts in the planes where the wave functions overlap strongly. In the perpendicular direction, charge transport follows variable-range hopping, a behavior that agrees with experimental data on organic semiconductors.

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

Ruit

Cohen

Bollen

et al. 2013

Adv Funct Materials

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The 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.

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Numerical studies of variable-range hopping in one-dimensional systems

Cited by 13 publications

References 57 publications

Apparent Power-Law Behavior of Conductance in Disordered Quasi-One-Dimensional Systems

Apparent Power-Law Behavior of Conductance in Disordered Quasi-One-Dimensional Systems

Activated hopping transport in anisotropic systems at low temperatures

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

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