# Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons

@article{Beneventano2013ChargeDA, title={Charge density and conductivity of disordered Berry-Mondragon graphene nanoribbons}, author={C G Beneventano and Ignat V. Fialkovsky and E M Santangelo and Dmitri Vassilevich}, journal={The European Physical Journal B}, year={2013}, volume={87}, pages={1-9} }

We consider gated graphene nanoribbons subject to Berry-Mondragon boundary conditions in the presence of weak impurities. Using field-theoretical methods, we calculate the density of charge carriers (and, thus, the quantum capacitance) as well as the optical and DC conductivities at zero temperature. We discuss in detail their dependence on the gate (chemical) potential, and reveal a non-linear behaviour induced by the quantization of the transversal momentum.

## 10 Citations

### Optical conductivity in an effective model for graphene: finite temperature corrections

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2019

In this article, we investigate the temperature and chemical potential dependence of the optical conductivity of graphene, within a field theoretical representation in the continuum approximation,…

### Optical conductivity and transparency in an effective model for graphene

- PhysicsPhysical Review B
- 2018

Motivated by experiments confirming that the optical transparency of graphene is defined through the fine structure constant and that it could be fully explained within the relativistic Dirac…

### Graphene through the looking glass of QFT

- Physics
- 2016

This paper is aimed to review and promote the main applications of the methods of Quantum Field Theory to description of quantum effects in graphene. We formulate the effective electromagnetic action…

### Zeros of combinations of Bessel functions and the mean charge of graphene nanodots

- Mathematics
- 2016

We establish some properties of the zeros of sums and differences of contiguous Bessel functions of the first kind. As a by-product, we also prove that the zeros of the derivatives of Bessel…

### Study of temperature Green’s functions of graphene-like systems in a half-space

- Physics
- 2017

We consider the formalism of temperature Green’s functions to study the electronic properties of a semiinfinite two-dimensional graphene lattice at a given temperature. Under most general assumptions…

### Spectral Gaps of Dirac Operators Describing Graphene Quantum Dots

- Physics
- 2016

The two-dimensional Dirac operator describes low-energy excitations in graphene. Different choices for the boundary conditions give rise to qualitative differences in the spectrum of the resulting…

### Chiral magnetic effect at finite temperature in a field-theoretic approach

- PhysicsJournal of Physics A: Mathematical and Theoretical
- 2020

We investigate the existence (or lack thereof) of the chiral magnetic effect (CME) in the framework of finite temperature field theory, studied through the path integral approach and regularized via…

### Self-Adjointness of Two-Dimensional Dirac Operators on Domains

- Mathematics
- 2017

We consider Dirac operators defined on planar domains. For a large class of boundary conditions, we give a direct proof of their self-adjointness in the Sobolev space $$H^1$$H1.

### Self-Adjointness of Two-Dimensional Dirac Operators on Domains

- MathematicsAnnales Henri Poincaré
- 2017

We consider Dirac operators defined on planar domains. For a large class of boundary conditions, we give a direct proof of their self-adjointness in the Sobolev space H1\documentclass[12pt]{minimal}…

## References

SHOWING 1-10 OF 73 REFERENCES

### Conductance quantization and transport gaps in disordered graphene nanoribbons

- Physics
- 2009

We study numerically the effects of edge and bulk disorder on the conductance of graphene nanoribbons. We compute the conductance suppression due to Anderson localization induced by edge scattering…

### Electron transport in disordered graphene nanoribbons.

- PhysicsPhysical review letters
- 2010

An electron transport study of lithographically fabricated graphene nanoribbons of various widths and lengths finds that charging effects constitute a significant portion of the activation energy.

### Electronic structure of gated graphene and graphene ribbons

- Physics
- 2007

We study the electronic structure of gated graphene sheets. We consider both infinite graphene and finite width ribbons. The effect of Coulomb interactions between the electrically injected carriers…

### Transport in disordered graphene nanoribbons

- Physics
- 2009

We study electronic transport in graphene nanoribbons with rough edges. We first consider a model of weak disorder that corresponds to an armchair ribbon whose width randomly changes by a single unit…

### Conductance quantization in graphene nanoribbons: adiabatic approximation

- Physics
- 2007

Abstract.A theory of electron states for graphene nanoribbons
with a smoothly varying width is developed. It is demonstrated
that the standard adiabatic approximation allowing to neglect the
mixing…

### Edge scattering of electrons in graphene: Boltzmann equation approach to the transport in graphene nanoribbons and nanodisks

- Physics
- 2013

We discuss the contribution of edge scattering to the conductance of graphene nanoribbons and nanoflakes. Using different possible types of the boundary conditions for the electron wave function at…

### Coulomb blockade in graphene nanoribbons.

- PhysicsPhysical review letters
- 2007

It is proposed that recent transport experiments revealing the existence of an energy gap in graphene nanoribbons may be understood in terms of Coulomb blockade, and theory shows good agreement with the experimental data.

### Carrier statistics and quantum capacitance of graphene sheets and ribbons

- Physics
- 2007

In this work, fundamental results for carrier statistics in graphene two-dimensional sheets and nanoscale ribbons are derived. Though the behavior of intrinsic carrier densities in two-dimennsional…

### Faraday rotation in graphene

- Physics
- 2012

We study magneto-optical properties of monolayer graphene by means of quantum field theory methods in the framework of the Dirac model. We reveal a good agreement between the Dirac model and a recent…

### Transport of Dirac quasiparticles in graphene: Hall and optical conductivities

- Physics
- 2006

The analytical expressions for both diagonal and off-diagonal ac and dc conductivities of graphene placed in an external magnetic field are derived. These conductivities exhibit rather unusual…