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-

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

Asymmetry of the excess finite-frequency noise

We consider finite frequency noise in a mesoscopic system with arbitrary interactions, connected to many terminals kept at finite electrochemical potentials. We show that the excess noise, obtained by subtracting the noise at zero voltage from that at finite voltage, can be asymmetric with respect to positive/negative frequencies if the system is non-linear. This explains a recent experimental observation in Josephson junctions as well as strong asymmetry obtained in typical non-linear and strongly correlated systems described by the Luttinger liquid (LL): edge states in the fractional quantum Hall effect, quantum wires and carbon nanotubes. Another important problem where the LL model applies is that of a coherent conductor embedded in an ohmic environment.Comment: 4 pages, 1 figur

Thermal conductivity reduction in rough silicon nanomembranes

Nanostructured silicon is a promising material for thermoelectric conversion, because the thermal conductivity in silicon nanostructures can be strongly reduced with respect to that of bulk materials. We present thermal conductivity measurements, performed with the 3$\omega$ technique, of suspended monocrystalline silicon thin films (nanomembranes or nanoribbons) with smooth and rough surfaces. We find evidence for a significant effect of surface roughness on phonon propagation: the measured thermal conductivity for the rough structures is well below that predicted by theoretical models which take into account diffusive scattering on the nanostructure walls. Conversely, the electrical conductivity appears to be substantially unaffected by surface roughness: the measured resistance of smooth and rough nanostructures are comparable, if we take into account the geometrical factors. Nanomembranes are more easily integrable in large area devices with respect to nanowires and are mechanically stronger and able to handle much larger electrical currents (thus enabling the fabrication of thermoelectric devices that can supply higher power levels with respect to current existing solutions)

Poor qubits make for rich physics: noise-induced quantum Zeno effects and noise-induced Berry phases

We briefly review three ways that environmental noise can slow-down (or speed-up) quantum transitions; (i) Lamb shifts, (ii) over-damping and (iii) orthogonality catastrophe. We compare them with the quantum Zeno effect induced by observing the system. These effects are relevant to poor qubits (those strongly coupled to noise). We discuss Berry phases generated by the orthogonality catastrophe, and argue that noise may make it easier to observe Berry phases.Comment: 6 pages - Proceedings of International Conference on Noise and Fluctuations (Pisa, 14-19 June 2009) - Improved with respect to version in Conf. Pro

Fluctuation relations without micro-reversibility for two-terminal conductors

In linear transport, the fluctuation-dissipation theorem relates equilibrium current correlations to the linear conductance coefficient. Theory and experiment have shown that in small electrical conductors the non-linear I-V-characteristic of two-terminal conductor exhibits terms which are asymmetric in magnetic field and thus micro-reversibility is manifestly broken. We discuss a non-equilibrium fluctuation dissipation theorem which is not based on micro-reversibility. It connects the antisymmetric nonlinear conductance with the third cumulant of equilibrium current fluctuations and a noise term that is proportional to temperature, magnetic field and voltage.Comment: 6 pages, 2 figures, corrected typo

High-power thermoelectric generators based on nanostructured silicon

The low thermal conductivity of silicon nanowires and nanostructures opens interesting opportunities for energy harvesting through the direct, high-efficiency, conversion of waste heat into electrical power. We present solutions for the fabrication and interconnection of a high number of suspended silicon nanostructures, within CMOS compatible top-down processes. Mechanical stability and thermoelectric properties of these devices will be analysed by means of finite element simulations, and opportunities for practical applications will be discussed. It will be shown that, despite the reduced dimensions needed for a strong suppression of thermal conductivity, a considerable amount of electrical power can be delivered to the load as a result of the presence of many interconnected devices on the same chip

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