Two distinct ballistic processes in graphene

Physical Review B, 2011

The dynamical approach is applied to ballistic transport in mesoscopic graphene samples of length L and contact potential U. At times shorter than both relevant time scales, the flight time tL = L/vg (vg-Fermi velocity) and tU = /U , the major effect of the electric field is to create electron-hole pairs, i.e. causing interband transitions. In linear response this leads (for width W >> L) to conductivity σ2 = π/2 e 2 /h. On the other hand, at times lager than the two scales the mechanism and value are different. It is shown that the conductivity approaches its intraband value, equal to the one obtained within the Landauer-Bütticker approach resulting from evanescent waves. It is equal to σ1 = 4/π e 2 /h for W >> L and tU << tL. The interband transitions, within linear response, are unimportant in this limit. Between these extremes there is a crossover behaviour dependent on the ratio between the two time scales tL/tU. At strong electric fields (beyond linear reponse) the interband process dominates. The electron-hole mechanism is universal, namely does not depend on geometry (aspect ratio, topology of boundary conditions, properties of leads), while the evanescent modes mechanism depends on all of them. On basis of the results we determine, that while in absorption measurements and in DC transport in suspended graphene σ2 was measured, σ1 would appear in experiments on small ballistic graphene flakes on substrate.

Computer Physics Communications, 2011

We investigate the ballistic electron transport in a monolayer graphene with configurational averaged impurities, located between two clean graphene leads. It is shown that the electron transmission are strongly dependent on the concentration of impurities and the incident energy. In turn, the conductance computed using the Landauer formalism shows a similar behavior to those found in experimental works as a function of the applied voltage for different concentrations of impurities in the limit of low temperatures. In the limit of zero bias voltage, the conductance shows a minimum value which reduces to zero for high concentration of impurities which disentangle graphene sublattices. These results can be very helpful for exploring the tunneling mechanism of electrons through doped thermodynamically stable graphene.

Physical Review B, 2010

The process of coherent creation of particle -hole excitations by an electric field in graphene is quantitatively described beyond linear response. We calculate the evolution of current density, number of pairs and energy in ballistic regime for electric field E using the tight binding model. While for ballistic flight times smaller than t nl ∝ E −1/2 current is linear in E and independent of time, for larger ballistic times the current increases after t nl as J ∝ E 3/2 t and finally at yet larger times (t > tB ∝ E −1 ) Bloch oscillations set in. It is shown that the number of pairs follows the 2D generalization of the Schwinger's creation rate n ∝ E 3/2 only on certain time segments with a prefactor different from that obtained using the asymptotic formula.

2017

des akademischen Grades eines Doktors der Naturwissenschaften genehmigte Dissertation vorgelegt von Dipl.-Ing.

Condensed Matter Theories, 2008

Graphene is a fascinating material for exploring fundamental science questions as well as a potential building block for novel electronic applications. In order to realize the full potential of this material the fabrication techniques of graphene devices, still in their infancy, need to be refined to better isolate the graphene layer from the environment. We present results from a study on the influence of extrinsic factors on the quality of graphene devices including material defects, lithography, doping by metallic leads and the substrate. The main finding is that trapped Coulomb scatterers associated with the substrate are the primary factor reducing the quality of graphene devices. A fabrication scheme is proposed to produce high quality graphene devices dependably and reproducibly. In these devices, the transport properties approach theoretical predictions of ballistic transport.

Journal of Applied Physics, 2011

This manuscript deals with time flow in ballistic graphene devices. It is commonly believed that in the ballistic regime the traversal time of carriers in gated graphene at normal incidence is just the ratio of the length of the device and the Fermi velocity. However, we show that the traversal time is much slower if the influence of metallic contacts on graphene is considered. Even the transmission at normal incidence becomes smaller than 1, contradicting yet another common belief. These unexpected effects are due to the transformation of Schrödinger electrons in the metallic contact into Dirac electrons in graphene and vice versa. As a direct consequence of these transformations, the ultimate performance of gated ballistic devices are much lower than expected, in agreement with experimental results.

Physical Review B, 2013

We investigate the transport of electrons in disordered and clean graphene devices. We consider a geometry where the graphene flake is contacted by narrow metallic leads. Plotting the conductance as a function of the position of one of the leads, we can approximate the probability density function of the charge flow at the edge which is used to analyze the transport properties with increasing length of the device. Moreover, we simulate scanning probe microscopy (SPM) measurements for the same devices, which can be seen as a measure for the flow of charge inside the device, thus complementing the transport calculations. We compare our analysis to theory describing transport in clean and disordered systems.

Physical Review Letters, 2009

We investigate the temperature dependence of the conductivity in ballistic graphene using Landauer transport theory. We obtain results which are qualitatively in agreement with many features recently observed in transport measurements on high mobility suspended graphene. The conductivity σ at high temperature T and low density n grows linearly with T , while at high n we find σ ∼ p |n| with negative corrections at small T due to the T-dependence of the chemical potential. At moderate densities the conductivity is a non-monotonic function of T and n, exhibiting a minimum at T = 0.693 v p |n| where v is the Fermi velocity. We discuss two kinds of Fabry-Perot oscillations in short nanoribbons and their stability at finite temperatures.

Arxiv preprint arXiv:0806.4531, 2008

Based on a tight-binding approximation, we present analytical solutions for the wavefunction and propagation velocity of an electron in armchair graphene ribbons. The derived expressions are used for computing the transmission coefficients through step-like and barrier-like potentials. Our analytical solutions predict a new kind of transmission resonances for one-mode propagation in semiconducting ribbons. Contrary to the Klein paradox in graphene, this approach shows that backscattering for gapless mode is possible. In consistence with a higher order k · p method, the backscattering probabilities vary with the square of the applied potential in the low-energy limit. We also demonstrate that gapless-mode propagation through a potential step in armchair ribbons can be described by the same through-step relation as that for an undimerized 1D chain of identical atoms.