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Khondaker, Saiful I.; Shlimak, I.; Nicholls, J.E.; Pepper, M.; Ritchie, D. A.

doi:10.1103/physrevb.59.4580

Cited by 95 publications

(96 citation statements)

References 15 publications

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“…The difference between the Mott and ES-VRH is in the details of their localization parameters, density of states (DOS) and interactions that manifest in the temperature dependence of resistance (R). [33][34][35][36][37][38][39][40] In general, the VRH can be characterized as…”

Section: Introductionmentioning

confidence: 99%

Efros-Shklovskii variable-range hopping in reduced graphene oxide sheets of varying carbonsp2fraction

2012

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We investigate the low temperature electron transport properties of chemically reduced graphene oxide (RGO) sheets with different carbon sp 2 fractions of 55 to 80 %. We show that in the low bias (Ohmic) regime, the temperature (T) dependent resistance (R) of all the devices follow Efros-Shklovskii variable range hopping (with T ES decreasing from 30976 to 4225 K and electron localization length increasing from 0.46 to 3.21 nm with increasing sp 2 fraction. From our data, we predict that for the temperature range used in our study, Mott-VRH may not be observed even at 100 % sp 2 fraction samples due to residual topological defects and structural disorders. From the localization length, we calculate a bandgap variation of our RGO from 1.43 to 0.21 eV with increasing sp 2 fraction from 55 to 80 % which agrees remarkably well with theoretical prediction. We also show that, in the high bias regime, the hopping is field driven and the data follow R ~ exp[(E 0 /E)

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Section: Introductionmentioning

confidence: 99%

Efros-Shklovskii variable-range hopping in reduced graphene oxide sheets of varying carbonsp2fraction

2012

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“…This idea was widely used for interpretation of experimental [8,10] and numerical [11] results on 2D systems. Further, Ref.…”

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confidence: 99%

“…Our purpose here is to solve this long-standing fundamental problem, which is also of direct experimental relevance; see, e.g., Refs. [6] and [7,8], where the crossover from WL to SL with lowering T was studied for 1D and 2D systems, respectively. For definiteness, we concentrate on the case of a many-channel 1D system with a short-range interaction.…”

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confidence: 99%

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Interacting Electrons in Disordered Wires: Anderson Localization and Low-TTransport

2005

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We study transport of interacting electrons in a low-dimensional disordered system at low temperature T . In view of localization by disorder, the conductivity σ(T ) may only be non-zero due to electron-electron scattering. For weak interactions, the weak-localization regime crosses over with lowering T into a dephasing-induced "power-law hopping". As T is further decreased, the Anderson localization in Fock space crucially affects σ(T ), inducing a transition at T = Tc, so that σ(T < Tc) = 0. The critical behavior of σ(T ) above Tc is ln σ(T ) ∝ −(T − Tc) −1/2 . The mechanism of transport in the critical regime is many-particle transitions between distant states in Fock space. 72.15.Rn, 71.30.+h, In a pathbreaking paper [1] Anderson demonstrated that a quantum particle may become localized by a random potential. In particular, in non-interacting systems of one-dimensional (1D) or two-dimensional (2D) geometry even weak disorder localizes all electronic states [2], thus leading to the exactly zero conductivity, σ(T ) = 0, whatever temperature T . A non-zero σ(T ) in such systems may only occur due to inelastic scattering processes leading to dephasing of electrons. Two qualitatively different sources of dephasing are possible: (i) scattering of electrons by external excitations (in practice, phonons) and (ii) electron-electron (e-e) scattering. In either case, at sufficiently high temperatures, the dephasing rate τ −1 φ is high, so that the localization effects are reduced to a weak-localization (WL) correction to the Drude conductivity. This correction behaves as ln τ φ in 2D and as τ 1/2 φ in quasi-1D (many-channel wire) systems [3], and thus diverges with lowering T , signaling the occurrence of the strong localization (SL) regime. This prompts a question as to how the system conducts at low T .For the case of electron-phonon scattering the answer is well known. The conductivity is then governed by Mott's variable-range hopping (VRH) [4], yielding σ(T ) ∝ exp{−(T 0 /T ) µ } with µ = 1/(d+1), where d is the spatial dimensionality. In the presence of a long-range Coulomb interaction, the Coulomb gap in the tunneling density of states modifies the VRH exponent, µ = 1 2 [5]. But what is the low-T behavior of σ(T ) if the electronphonon coupling is negligibly weak and the only source of the inelastic scattering is the e-e interaction? Our purpose here is to solve this long-standing fundamental problem, which is also of direct experimental relevance; see, e.g., Refs.[6] and [7,8], where the crossover from WL to SL with lowering T was studied for 1D and 2D systems, respectively. For definiteness, we concentrate on the case of a many-channel 1D system with a short-range interaction. Our results are, however, more general (including single-channel wires, 2D systems, Coulomb interaction), as we discuss in the end of the paper.It was proposed in [9] that the e-e interaction by itself is sufficient to induce VRH at low T . This idea was widely used for interpretation of experimental [8,10] and numerical [11] results on ...

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“…Typically in GaAs heterostructures the localization length has been measured to be between 10 and 200 nm 18,23,24 and depends on carrier concentration and details of potential disorder. In a point contact geometry as used in this work, the electron depletion extending out from the point contact is not uniform.…”

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confidence: 99%