Electron Spectrum and Tunneling Current of the Toroidal and Helical Graphene Nanoribbon-Quantum Dots Contact

Mikhail B Belonenko,Nikolay G Lebedev,Alexander V Zhukov,Natalia N Yanyushkina

doi:10.5402/2011/161849

Abstract

We study the electron spectrum and the density of states of long-wave electrons in the curved graphene nanoribbon based on the Dirac equation in a curved space-time. The current-voltage characteristics for the contact of nanoribbon-quantum dot have been revealed. We also analyze the dependence of the specimen properties on its geometry.

Highlights

The problem of modified graphene properties attracts a considerable attention of researchers [1, 2] because the “pure” graphene has no energy gap in the band structure and, the creation of different structures is extremely difficult
We study the electron spectrum and the density of states of long-wave electrons in the curved graphene nanoribbon based on the Dirac equation in a curved space-time
We consider the modified graphene, for example, graphene nanoribbon, which have quantized electron energy spectrum due to the limited space in one dimension, which in turn can lead to the formation of the energy gap

Summary

Introduction

The problem of modified graphene properties attracts a considerable attention of researchers [1, 2] because the “pure” graphene has no energy gap in the band structure and, the creation of different structures (e.g., analogs of transistors) is extremely difficult. The long-wave approximation, which is widely used to describe the properties of electrons in graphene, leads to an analog of the Dirac equation, which in turn makes it easy to produce generalization to the case when the graphene surface is curved. Note that in this case the degeneracy in the Dirac points is removed and it becomes possible to create various structures with different band gaps. Quantum dots are still rather “young” objects of study, but their use in various fields of science and technology is obviously extremely promising (from the design of lasers and new generation displays to building qubits) [8]

Basic Equations and Spectrum of Electrons

L r2 4R2

Tunneling Characteristics

Conclusion