A novel choice of the graphene unit vectors, useful in zone-folding computations

The dispersion relations of carbon nanotubes are often obtained cross-sectioning those of graphene (zone-folding technique) in a rectangular region of the reciprocal space, where it is easier to fold the resulting relations into the nanotube Brillouin zone. We propose a particular choice of the unit vectors for the graphene lattice, which consists of the symmetry vector and the translational vector of the considered carbon nanotube. Due to the properties of the corresponding unit vectors in the reciprocal space, this choice is particularly useful for understanding the relationship between the rectangular region where the folding procedure is most easily applied and the overall graphene reciprocal space. Such a choice allows one to find, from any graphene wave vector, the equivalent one inside the rectangular region in a computationally inexpensive way. As an example, we show how the use of these unit vectors makes it easy to limit the computation to the bands nearest to the energy maxima and minima when determining the nanotube dispersion relations from those of graphene with the zone-folding technique.Comment: 16 pages, 3 figure

The k.p method and its application to graphene, carbon nanotubes and graphene nanoribbons: the Dirac equation

The k.p method is a semi-empirical approach which allows to extrapolate the band structure of materials from the knowledge of a restricted set of parameters evaluated in correspondence of a single point of the reciprocal space. In the first part of this review article we give a general description of this method, both in the case of homogeneous crystals (where we consider a formulation based on the standard perturbation theory, and Kane's approach) and in the case of non-periodic systems (where, following Luttinger and Kohn, we describe the single-band and multi-band envelope function method and its application to heterostructures). The following part of our review is completely devoted to the application of the k.p method to graphene and graphene-related materials. Following Ando's approach, we show how the application of this method to graphene results in a description of its properties in terms of the Dirac equation. Then we find general expressions for the probability density and the probability current density in graphene and we compare this formulation with alternative existing representations. Finally, applying proper boundary conditions, we extend the treatment to carbon nanotubes and graphene nanoribbons, recovering their fundamental electronic properties.Comment: 96 pages, 14 figures, updated journal URL. Please cite as: P. Marconcini, M. Macucci, "The k.p method and its application to graphene, carbon nanotubes and graphene nanoribbons: the Dirac equation", Riv. Nuovo Cimento, Vol. 34, Issue N. 8-9, pp. 489-584 (2011), DOI: 10.1393/ncr/i2011-10068-1 . Downloadable also from Springer at https://link.springer.com/article/10.1393/ncr/i2011-10068-

Energy and Mode Filtering in a Graphene Channel With Unevenly Spaced Barriers with a Smooth Profile

We simulate the transport and shot noise behavior of graphene armchair ribbons with a series of parallel, unevenly spaced potential barriers with a smooth profile (which could result from the electrostatic effect of negatively biased gates). We analyze the effect of Klein tunneling and resonant tunneling on the individual modes propagating through the graphene channel, showing that this structure can behave as a mode and an energy filter for the charges injected from the contacts. Moreover, we study the different transport regimes (ballistic, strong localized, and diffusive) that can take place inside the graphene ribbon and the effect on the shot noise behavior of the device

Model for 1/f Noise in Graphene and in More Common Semiconductors

Measurements performed on several graphene samples have shown the presence of a minimum of the flicker noise power spectral density near the charge neutrality point. This behavior is anomalous with respect to what is observed in more usual semi-conductors. Here, we report our explanation for this difference. We simulate the 1/f noise behavior of devices made of graphene and of more common semiconductors, through a model based on the validity of the mass-action law and on the conservation of the charge neutrality. We conclude that the minimum of the flicker noise at the charge neutrality point can be observed only in very clean samples of materials with similar mobilities for electrons and holes

Effect of potential fluctuations on shot noise suppression in mesoscopic cavities

We perform a numerical investigation of the effect of the disorder associated with randomly located impurities on shot noise in mesoscopic cavities. We show that such a disorder becomes dominant in determining the noise behavior when the amplitude of the potential fluctuations is comparable to the value of the Fermi energy and for a large enough density of impurities. In contrast to existing conjectures, random potential fluctuations are shown not to contribute to achieving the chaotic regime whose signature is a Fano factor of 1/4, but, rather, to the diffusive behavior typical of disordered conductors. In particular, the 1/4 suppression factor expected for a symmetric cavity can be achieved only in high-quality material, with a very low density of impurities. As the disorder strength is increased, a relatively rapid transition of the suppression factor from 1/4 to values typical of diffusive or quasi-diffusive transport is observed. Finally, on the basis of a comparison between a hard-wall and a realistic model of the cavity, we conclude that the specific details of the confinement potential have a minor influence on noise.Comment: 8 pages, 10 figures. This is the final version published in AIP Advances. With respect to the previous arXiv version, there are some changes in the text (mainly in the introduction and in the references); the numerical results are unchange

Engineering interband tunneling in nanowires with diamond cubic or zincblende crystalline structure based on atomistic modeling

We present an investigation in the device parameter space of band-to-band tunneling in nanowires with a diamond cubic or zincblende crystalline structure. Results are obtained from quantum transport simulations based on Non-Equilibrium Green's functions with a tight-binding atomistic Hamiltonian. Interband tunneling is extremely sensitive to the longitudinal electric field, to the nanowire cross section, through the gap, and to the material. We have derived an approximate analytical expression for the transmission probability based on WKB theory and on a proper choice of the effective interband tunneling mass, which shows good agreement with results from atomistic quantum simulation.Comment: 4 pages, 3 figures. Final version, published in IEEE Trans. Nanotechnol. It differs from the previous arXiv version for the title and for some changes in the text and in the reference

Origin of shot noise in mesoscopic cavities

We discuss several aspects of shot noise suppression in mesoscopic cavities, focusing on the so-called "quantum to classical" crossover that can be induced by an increase of the width of the constrictions defining the cavity, an increase in the energy of the injected electrons or the application of a magnetic field. After reviewing the relevant literature, we present some results of our numerical simulations, and point out an alternative explanation of the observed shot noise suppression and the reasons why several statements that can be found in the literature are debatable. Overall, we point out how shot noise behavior in mesoscopic cavities can be explained without any need for classically chaotic dynamics and only on the basis of quantum chaos resulting from diffraction at the constrictions

Effects of A Magnetic Field on the Transport and Noise Properties of a Graphene Ribbon with Antidots

We perform a numerical simulation of the effects of an orthogonal magnetic field on charge transport and shot noise in an armchair graphene ribbon with a lattice of antidots. This study relies on our envelope-function based code, in which the presence of antidots is simulated through a nonzero mass term and the magnetic field is introduced with a proper choice of gauge for the vector potential. We observe that by increasing the magnetic field, the energy gap present with no magnetic field progressively disappears, together with features related to commensurability and quantum effects. In particular, we focus on the behavior for high values of the magnetic field: we notice that when it is sufficiently large, the effect of the antidots vanishes and shot noise disappears, as a consequence of the formation of edge states crawling along the boundaries of the structure without experiencing any interaction with the antidots

Theoretical Comparison between the Flicker Noise Behavior of Graphene and of Ordinary Semiconductors

Graphene is a material of particular interest for the implementation of sensors, and the ultimate performance of devices based on such a material is often determined by its flicker noise properties. Indeed, graphene exhibits, with respect to the vast majority of ordinary semiconductors, a peculiar behavior of the flicker noise power spectral density as a function of the charge carrier density. While in most materials flicker noise obeys the empirical Hooge law, with a power spectral density inversely proportional to the number of free charge carriers, in bilayer, and sometimes monolayer, graphene a counterintuitive behavior, with a minimum of flicker noise at the charge neutrality point, has been observed. We present an explanation for this stark difference, exploiting a model in which we enforce both the mass action law and the neutrality condition on the charge fluctuations deriving from trapping/detrapping phenomena. Here, in particular, we focus on the comparison between graphene and other semiconducting materials, concluding that a minimum of flicker noise at the charge neutrality point can appear only in the presence of a symmetric electron-hole behavior, a condition characteristic of graphene, but which is not found in the other commonly used semiconductors