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Register a new userAbnormal Electronic Transport in Disordered Graphene Nanoribbon
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We investigate the conductivity $sigma$ of graphene nanoribbons with zigzag edges as a function of Fermi energy $E_F$ in the presence of the impurities with different potential range. The dependence of $sigma(E_F)$ displays four different types of behavior, classified to different regimes of length scales decided by the impurity potential range and its density. Particularly, low density of long range impurities results in an extremely low conductance compared to the ballistic value, a linear dependence of $sigma(E_F)$ and a wide dip near the Dirac point, due to the special properties of long range potential and edge states. These behaviors agree well with the results from a recent experiment by Miao emph{et al.} (to appear in Science).
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We investigate the electronic band structure of an undoped graphene armchair nanoribbon. We demonstrate that such nanoribbon always has a gap in its electronic spectrum. Indeed, even in the situations where simple single-electron calculations predict a metallic dispersion, the system is unstable with respect to the deformation of the carbon-carbon bonds dangling at the edges of the armchair nanoribbon. The edge bonds deformation couples electron and hole states with equal momentum. This coupling opens a gap at the Fermi level. In a realistic sample, however, it is unlikely that this instability could be observed in its pure form. Namely, since chemical properties of the dangling carbon atoms are different from chemical properties of the atoms inside the sample (for example, the atoms at the edge have only two neighbours, besides additional non-carbon atoms might be attached to passivate unpaired covalent carbon bonds), it is very probable that the bonds at the edge are deformed due to chemical interactions. This chemically-induced modification of the nanoribbons edges can be viewed as an effective field biasing our predicted instability in a particular direction. Yet by disordering this field (e.g., through random substitution of the radicals attached to the edges) we may tune the system back to the critical regime and vary the electronic properties of the system. For example, we show that electrical transport through a nanoribbon is strongly affected by such disorder.
We study charge transport in one-dimensional graphene superlattices created by applying layered periodic and disordered potentials. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the direction perpendicular to the layers, the eigenstates in a disordered sample are delocalized for all energies and provide a minimal non-zero conductivity, which cannot be destroyed by disorder, no matter how strong this is. However, along with extended states, there exist discrete sets of angles and energies with exponentially localized eigenfunctions (disorder-induced resonances). It is shown that, depending on the type of the unperturbed system, the disorder could either suppress or enhance the transmission. Most remarkable properties of the transmission have been found in graphene systems built of alternating p-n and n-p junctions. This transmission has anomalously narrow angular spectrum and, surprisingly, in some range of directions it is practically independent of the amplitude of fluctuations of the potential. Owing to these features, such samples could be used as building blocks in tunable electronic circuits. To better understand the physical implications of the results presented here, most of our results have been contrasted with those for analogous wave systems. Along with similarities, a number of quite surprising differences have been found.
We report measurements of disordered graphene probed by both a high electric field and a high magnetic field. By apply a high source-drain voltage Vsd, we are able to study the current-voltage relation I-Vsd of our device. With increasing Vsd, a crossover from the linear I-Vsd regime to the non-linear one, and eventually to activationless-hopping transport occurs. In the activationless-hopping regime, the importance of Coulomb interactions between charged carriers is demonstrated. Moreover, we show that delocalization of carriers which are strongly localized at low T and at small Vsd occurs with the presence of high electric field and perpendicular magnetic field..
Graphene nanoribbons provide an opportunity to integrate phase-coherent transport phenomena with nanoelectromechanical systems (NEMS). Due to the strain induced by a deflection in a graphene nanoribbon resonator, coherent electron transport and mechanical deformations couple. As the electrons in graphene have a Fermi wavelength lambda ~ a_0 = 1.4 {AA}, this coupling can be used for sensitive displacement detection in both armchair and zigzag graphene nanoribbon NEMS. Here it is shown that for ordered as well as disordered ribbon systems of length L, a strain epsilon ~ (w/L)^2 due to a deflection w leads to a relative change in conductance delta G/G ~ (w^2/a_0L).
We study two lattice models, the honeycomb lattice (HCL) and a special square lattice (SQL), both reducing to the Dirac equation in the continuum limit. In the presence of disorder (gaussian potential disorder and random vector potential), we investigate the behaviour of the density of states (DOS) numerically and analytically. While an upper bound can be derived for the DOS on the SQL at the Dirac point, which is also confirmed by numerical calculations, no such upper limit exists for the HCL in the presence of random vector potential. A careful investigation of the lowest eigenvalues indeed indicate, that the DOS can possibly be divergent at the Dirac point on the HCL. In spite of sharing a common continuum limit, these lattice models exhibit different behaviour.
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