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# Anisotropic Friedel oscillations in graphene-like materials: The Dirac point approximation in wave-number dependent quantities revisited

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### Abstract

Friedel oscillations of the graphene-like materials are investigated theoretically beyond the Dirac point-approximation. Numerical calculations have been performed within the random phase approximation (RPA). For intra-valley transitions it was demonstrated that the contribution of the different Dirac points in the wave-number dependent quantities, such as dielectric function $$\epsilon(q)$$, has been determined by the orientation of the wave-number with respect to the Dirac point position vector in $$k$$-space. Therefore identical contribution of the different Dirac points is not automatically guaranteed by the degeneracy of the Hamiltonian at these points. Meanwhile it was shown that the contribution of the inter-valley transitions is always anisotropic even when the Dirac points coincide with the Fermi level ($$E_F=0$$). This means that the Dirac point approximation based studies give the correct physics only at high wave length limit. The anisotropy of the static dielectric function reveals different contribution of the each Dirac point. Additionally, the anisotropic $$k$$-space dielectric function results in anisotropic Friedel oscillations in graphene-like materials. Calculations have also been performed in the presence of the Rashba interaction. It was shown that increasing the Rashba interaction strength slightly modifies the Friedel oscillations in graphene-like materials. Therefore the anisotropic dielectric function in $$k$$-space is the clear manifestation of band anisotropy in the graphene-like systems.

### Most cited references31

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(2007)
We report a naturally-occurring two-dimensional material (graphene that can be viewed as a gigantic flat fullerene molecule, describe its electronic properties and demonstrate all-metallic field-effect transistor, which uniquely exhibits ballistic transport at submicron distances even at room temperature.
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### The rise of graphene

(2007)
Graphene is a rapidly rising star on the horizon of materials science and condensed matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed matter physics, where quantum relativistic phenomena, some of which are unobservable in high energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.
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### Graphene Photonics and Optoelectronics

(2010)
The richness of optical and electronic properties of graphene attracts enormous interest. Graphene has high mobility and optical transparency, in addition to flexibility, robustness and environmental stability. So far, the main focus has been on fundamental physics and electronic devices. However, we believe its true potential to be in photonics and optoelectronics, where the combination of its unique optical and electronic properties can be fully exploited, even in the absence of a bandgap, and the linear dispersion of the Dirac electrons enables ultra-wide-band tunability. The rise of graphene in photonics and optoelectronics is shown by several recent results, ranging from solar cells and light emitting devices, to touch screens, photodetectors and ultrafast lasers. Here we review the state of the art in this emerging field.
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### Author and article information

###### Journal
1601.06061

Nanophysics