Comparing two different descriptions of the I-V characteristic of graphene: theory and experiment

The formalism of the nonperturbative description of transport phenomena in graphene in the framework of the quantum kinetic equation for the Schwinger-like process is compared with the description on the basis of Zener- Klein tunneling. The regime of ballistic conductivity in a constant electric field is considered. In the latter case the interaction of carriers with electric field is described in terms of the spatial dependence of their potential energy (x-representation). The presented kinetic formalism uses an alternative method of describing the interaction with a field through the introduction of a quasimomentum P = p – (e/c)A(t), where A(t) is the vector potential (t-representation). Both approaches should lead to the same physical characteristics of the described process. The measurement of the current in experiments is realized in static conditions determined by the potential difference between the electrodes and the distance between them. These parameters are native for the x-representation. On the contrary, in the approach based on the t-representation it is necessary to consider the situation in dynamics and introduce the effective lifetime of the generated carriers. In the ballistic regime this time depends on the distance between the electrodes. We give a detailed comparison of these two descriptions of the current and demonstrate a good coincidence with the experimental data of the alternative approach based on the t-representation. It provides a reliable foundation for the application of nonperturbative methods adopted from strong field QED, that allows one to include in the consideration more general models of the field (arbitrary polarization and time dependence) and extend the scope of the theory.

Optical conductivity of the R-Cd quasicrystals and approximants

Recently, a new family of R-Cd binary icosahedral quasicrystals has been discovered [1]. Using optical reflectance spectroscopy, we have examined the quasicrystal GdCd7.98and the approximants GdCd6and YCd6. To explain the unique behaviour of electrons in a quasiperiodic lattice Mayou [2] created a model of electron transport due to anomalous diffusion of wave packets scattering from the quasiperiodic lattice. We have determined the optical conductivity of the above-mentioned materials from 7.5 meV to 5.5 eV and have used Mayou's model of optical conductivity for approximants and quasicrystals, σ1∝ Re[ (1/(γ-iω))^(2β-1) ], to describe the low frequency behaviour. Despite the concern of Mayou of not being able to differentiate experimentally between normal metallic conductivity of ballistic electrons, β=1, and sub-ballistic conductivity, 1/2<β<1, we clearly see β≍3/4 in the intraband peak of the icosahedral approximants, which has not been observed before. Before this work, the only unambiguously Drude-like peak seen in any quasicrystal or their approximant occurred in the decagonal approximant γ-brass, which was fit with exactly β=1 [3]. However, unlike the approximants in our study, this sample of γ-brass was admittedly not a good approximant to a quasicrystal with its small lattice constant. In the GdCd7.98quasicrystal, we observe low frequency behaviour that lacks a Drude peak but is not nearly perfectly linear as seen by others. In this case, the low frequency behaviour is qualitatively similar to the diffusive regime, 0<β<1/2, that is often seen. However, it is not adequately modelled by Mayou's generalized Drude model. With these results, unlike in previous optical conductivity studies, we have a striking difference in the low frequency conductivity that suggests that there is a difference in the physics of the optical conductivity of periodic and quasiperiodic lattices that needs to be explored.

Resistance simulations for junctions of SW and MW carbon nanotubes with various metal substrates

This theoretical study focuses on junctions between the carbon nanotubes (CNTs) and contacting metallic elements of a nanocircuit. Numerical simulations on the conductance and resistance of these contacts have been performed using the multiple scattering theory and the effective media cluster approach. Two models for CNT-metal contacts have been considered in this paper: a) first principles “liquid metal” model and b) semi-empirical model of “effective bonds” based on Landauer notions on ballistic conductivity. Within the latter, which is a more adequate description of chirality effects, we have simulated both single-wall (SW) and multi-wall (MW) CNTs with different morphology. Results of calculations on resistance for different CNT-Me contacts look quantitatively realistic (from several to hundreds kOhm, depending on chirality, diameter and thickness of MW CNT). The inter-wall transparency coefficient for MW CNT has been also simulated, as an indicator of possible ‘radial current’ losses.