Electronic transport in two-dimensional high dielectric constant nanosystems

Abstract

There has been remarkable recent progress in engineering high-dielectric constant two dimensional (2D) materials, which are being actively pursued for applications in nanoelectronics in capacitor and memory devices, energy storage, and high-frequency modulation in communication devices. Yet many of the unique properties of these systems are poorly understood and remain unexplored. Here we report a numerical study of hopping conductivity of the lateral network of capacitors, which models two-dimensional insulators, and demonstrate that 2D long-range Coulomb interactions lead to peculiar size effects. We find that the characteristic energy governing electronic transport scales logarithmically with either system size or electrostatic screening length depending on which one is shorter. Our results are relevant well beyond their immediate context, explaining, for example, recent experimental observations of logarithmic size dependence of electric conductivity of thin superconducting films in the critical vicinity of superconductor-insulator transition where a giant dielectric constant develops. Our findings mark a radical departure from the orthodox view of conductivity in 2D systems as a local characteristic of materials and establish its macroscopic global character as a generic property of high-dielectric constant 2D nanomaterials.

Charging of highly resistive granular metal films

“…We consider a network model that consists on N sites at random on a square sample of size L × L = N and capacitors in the links joining nearest neighbor sites. Each site corresponds to a metallic grain (or set of metallic grains as explained bellow) and each capacitor to the capacitance between nearest neighbor grains 19 . A scheme of the network model is shown in Fig.…”

“…It is convenient to define the following charge vector of dimension N + 2 (see Ref. 19 for details of the model)…”

“…We measure samples that are qualitatively similar to those previously studied by some of us in the context of slow relaxation in the conductivity, but that have been grown with the appropriate resistance for this experiment, that is, with a resistance high enough to ensure that the charging processes take place in the scale from milliseconds to hours. As our experimental results are difficult to understand with a model of homogeneous conductivity, we have constructed a more general network resistance-capacitance model able to handle strong inhomogeneities 19 .…”

Density of states of two-dimensional systems with long-range logarithmic interactions

“…On the fundamental side the interest is motivated by the challenge of understanding the behavior of a 2D Coulomb glass, a highly frustrated strongly correlated system whose properties are governed by the intertwined effects of disorder and the long-range LI [26]. An impor-tant step has been done in our previous publication [27] where hopping conductivity of a 2D Coulomb glass was investigated via a first-principle numerical study. We demonstrated that hopping transport is controlled by the characteristic energy that scales as E a ∝ lnL with L = min{L, Λ}.…”

New Concepts for Production of Scalable Single Layer Oxidized Regions by Local Anodic Oxidation of Graphene

“…. Recent investigations by Ortuño et al on the electronic transport in 2D layers with high dielectric constants, reveal the existence of a nonlocal conductivity, σ, with a dependence on distance L as σ = σ 0 exp (γ/ L ). In any case, we note that whatever the model, the transport current is expected to decay rapidly with the radius of the spot, until it becomes irrelevant, as concluded previously from the analysis of Q ( t ) in Figure .…”