Reversal of Klein reflection in bilayer graphene

Whereas massless Dirac fermions in monolayer graphene exhibit Klein tunneling when passing through a potential barrier upon normal incidence, such a barrier totally reflects massive Dirac fermions in bilayer graphene due to difference in chirality. We show that, in the presence of magnetic barriers, such massive Dirac fermions can have transmission through even at normal incidence. The general consequence of this behaviour for multilayer graphene consisting of massless and massive modes are mentioned. We also briefly discuss the effect of a bias voltage on such magnetotransport.Comment: 10 double space single column latexed pages, 15 eps files in four figure

A Green's function approach to transmission of massless Dirac fermions in graphene through an array of random scatterers

We consider the transmission of massless Dirac fermions through an array of short range scatterers which are modeled as randomly positioned $\delta$- function like potentials along the x-axis. We particularly discuss the interplay between disorder-induced localization that is the hallmark of a non-relativistic system and two important properties of such massless Dirac fermions, namely, complete transmission at normal incidence and periodic dependence of transmission coefficient on the strength of the barrier that leads to a periodic resonant transmission. This leads to two different types of conductance behavior as a function of the system size at the resonant and the off-resonance strengths of the delta function potential. We explain this behavior of the conductance in terms of the transmission through a pair of such barriers using a Green's function based approach. The method helps to understand such disordered transport in terms of well known optical phenomena such as Fabry Perot resonances.Comment: 22 double spaced single column pages. 15 .eps figure

Caustical patterns in circular magnetic dots in graphene

The scattered wavefunction of an incoming plane wave of electrons due to a circular symmetric step-like potential shows an interference pattern which resembles that of ‘cup caustics’. The high intensity maximum located around caustics can be calculated from Snell’s law with negative refractive index. This paper investigates the wavefunction for a plane wave incident on a circular magnetic dot where the magnetic field is nonzero only in a finite, circular disc-like region of space in the presence of a commensurate scalar potential barrier and vanishes outside that region. By formulating the optical analogy, the caustical curves are described inside the scattering region in terms of geometrical optics and analyse the effect of magnetic field on it. The caustical curves obtained in the presence of weak magnetic field are found to be rotated as compared to the case in the absence of magnetic field. This theoretical formulation using geometrical optics also captures the features developed due to bending of classical trajectories in the presence of magnetic field

The energy spectra of the graphene-based quasi-periodic superlattice

The spectra of the Dirac quasi-electrons transmission through the Fibonacci quasi-periodical superlattice (SL) are calculated and analyzed in the continuum model with the help of the transfer matrix method. The one-dimensional SL based on a monolayer graphene modulated by the Fermi velocity barriers is studied. A new quasi-periodical factor is proposed to be considered. We show that the Fibonacci quasi-periodic modulation in graphene superlattices with the velocity barriers can be effectively realized by virtue of a difference in the velocity barrier values (no additional factor is needed and we keep in mind that not each factor can provide the quasi-periodicity). This fact is true for a case of normal incidence of quasi-electrons on a lattice. In contrast to the case of other types of the graphene SL spectra studied reveal the remarkable property, namely the periodic character over all the energy scale and the transmission coefficient doesn’t tend asymptotically to unity at rather large energies. Both the conductance (using the known Landauer–Buttiker formula) and the Fano factor for the structure considered are also calculated and analyzed. The dependence of spectra on the Fermi velocity magnitude and on the external electrostatic potential as well as on the SL geometrical parameters (width of barriers and quantum wells) is analyzed. Using the quasi-periodical SL one can control the transport properties of the graphene structures in a wide range. The obtained results can be used for applications in the graphene-based electronics.В континуальній моделі методом трансферних матриць розраховано та проаналізовано спектри трансмісії діраківських квазіелектронів крізь квазіперіодичну надгратку (НГ) Фібоначчі. Розглядається одновимірна НГ на основі моношарового графену, модульована бар’єрами швидкості Фермі. Запропоновано використати новий квазіперіодичний фактор. Показано, що квазіперіодична модуляція Фібоначчі в графенових надгратках із бар’єрами швидкості Фермі може бути ефективно реалізована завдяки різниці в значеннях бар’єрів цієї швидкості (додатковий фактор не потрібен, і слід зазначити, що не кожен фактор може забезпечити квазіперіодичну модуляцію). Цей факт справедливий для випадку нормального падіння квазіелектронів на гратку. На відміну від інших типів вивчених спектрів трансмісії в графенових НГ в даному випадку виявляється нетривіальна їх властивість — періодичність по всій шкалі енергії, так що коефіцієнт пропускання не наближається асимптотично до одиниці при достатньо високих енергіях. Розраховано та проаналізовано провідність (з використанням відомої формули Ландауера–Буттікера) та фактор Фано для даної структури. Проаналізовано залежність спектрів від величини швидкості Фермі та від зовнішнього електростатичного потенціалу, а також від геометричних параметрів НГ (ширин бар’єрів і квантових ям). Використовуючи розглянуті квазіперіодичні НГ, можна регулювати транспортні властивості графенових структур в широкому діапазоні їх параметрів. Отримані результати можуть бути використані для застосування в електроніці на основі графену

Field emission properties of highly ordered low-aspect ratio carbon nanocup arrays

Herein, we design and develop a field emission device utilizing highly porous carbon nanocup (CNC) films. These three-dimensional (3D) low-aspect ratio CNC structures were fabricated by a combination of anodization and chemical vapor deposition techniques. The low turn-on fields of 2.30 V mu m(-1) were observed to draw an emission current density of 1 mu A cm(-2) and a maximum emission current density of similar to 1.802 mA cm(-2) drawn at an applied field of similar to 4.20 V mu m(-1). The enhanced field emission behavior observed from the CNC films is attributed to an excellent field enhancement factor of 1645. The observed field emission properties of CNC arrays are attributed to a synergistic combination of high aspect ratio, nano-sized radius of curvature, highly organized distribution of the emitters over the whole area of specimen and lower screening effect of the CNC arrays. These observations shed light on the effect of the stacking carbon layers of CNC on their electronic properties and open up possibilities to integrate new morphologies of graphitic carbon in nanotechnology applications. Thus, the low turn on field, high emission current density and better emission current stability enable CNC based future field emission applications