The standard T-matrix method can be effectively used for studying the dynamics of Dirac electrons under one-dimensional potentials in graphene. The transmission probability expressed in terms of T-matrices and the corresponding ballistic current are derived for any smooth one-dimensional potential, taking into account the chirality of Dirac massless carriers. Numerical calculations are illustrated for the potential approximately describing graphene n-p junctions.

Using the non-equilibrium Green's functions formalism in a tight binding model, the spindependent transport in armchair graphene nanoribbon (GNR) structures controlled by a ferromagnetic gate is investigated. Beyond the oscillatory behavior of conductance and spin polarization with respect to the barrier height, which can be tuned by the gate voltage, we especially analyze the effect of width-dependent band gap and the nature of contacts. The oscillation of spin polarization in the GNRs with a large band gap is strong in comparison with 2D-graphene structures. Very high spin polarization (close to 100%) is observed in normal-conductor/graphene/normal-conductor junctions. Moreover, we find that the difference of electronic structure between normal conductor and graphene generates confined states in the device which have a strong influence on the transport quantities. It suggests that the device should be carefully designed to obtain high controllability of spin current.

We suggest a simple approach for studying the quasi-bound fermion states induced by one-dimensional potentials in graphene. Detailed calculations have been performed for symmetric double barrier structures and n-p-n junctions. Besides the crucial role of the transverse motion of carriers, we systematically examine the influence of different structure parameters such as the barrier width in double barrier structures or the potential slope in n-p-n junctions on the energy spectrum and, especially, on the resonant-level width and, therefore, the localization of quasi-bound states.Over the last 3 years, graphene and graphene-based nanostructures have attracted much attention both experimentally and theoretically. 1,2 This is due to the fact that the lowenergy excitations in these structures are massless chiral Dirac fermions, which behave in very unusual ways when compared to ordinary electrons in the conventional twodimensional ͑2D͒ electron gas realized in semiconductor heterostructures. One of particularly interesting features of Dirac fermions is their insensitivity to external electrostatic potentials due to the so-called Klein paradox. 3 It seems that Dirac electrons can propagate to the hole states across a steep potential barrier without any damping. 4 In this situation, the confinement of electrons becomes quite a challenging task, while it is very important for producing the basic building blocks of electronic devices such as resonant structures, electron waveguides, or quantum dots ͑QDs͒. 1,2,5,6 Graphene is a single layer of carbon atoms densely packed in a honeycomb lattice, which can be treated as two interpenetrating triangular sublattices often labeled by A and B. In the presence of an external electrostatic potential V, the low-energy quasi-particles of the system are formally described by the 2D Dirac-type Hamiltonian 7,8where v F Ϸ 10 6 ms −1 is the Fermi velocity, the pseudospin matrix ជ has components given by Pauli matrices, and p ជ = ͑p x , p y ͒ is the in-plane momentum. The term mv F 2 , representing the gap in the electronic spectrum, may arise from the spin-orbit interaction, 9 from the coupling between the graphene layer and the substrate, or from the effect of covering graphene by some appropriate materials. 10,11 Eigenstates of the Hamiltonian ͑1͒ are two-component pseudospinors ⌿ = ͓ A , B ͔ T , where A and B are envelope functions associated with the probabilities at respective sublattice sites of the graphene sheet.For one-dimensional ͑1D͒ potentials V = V͑x͒ it has been shown that the finite values of the momentum parallel to potential barrier, the transverse momentum p y , can suppress the Klein tunneling, giving rise to the electron confinement. 12 This discovery opens a way of confining electrons and, particularly, making graphene-based homojunctions and even QDs using only electrostatic gates. 13,14 Moreover, in difference from conventional semiconductor QDs, to form a graphene-strip-based QD a single barrier seems to be sufficient. 13 Thus, 1D potentials can produce in graphene ...

This work describes a simple single-step method for green synthesis of colloidal gold nanoparticles (AuNPs) using Litsea cubeba (LC) fruit extract as a reducing as well as stabilizing agent simultaneously. Major parameters affecting the formation of LC-AuNPs, including gold ion concentration, reaction time, and reaction temperature were optimized using ultraviolet-visible (UV-Vis) measurements at a characteristic maximum absorbance of 535 nm. The functional groups responsible for reducing gold ions and capping AuNPs were examined by Fourier-transform infrared (FTIR) spectroscopy. Powder X-ray diffraction (XRD) analysis revealed the crystalline nature of AuNPs. Transmission electron microscopy (TEM) measurements showed that the biosynthesized LC-AuNPs were mostly spherical with an average size of 8-18 nm. The nanoparticles also demonstrated excellent ultrarapid catalytic activity for the complete reduction of 4-nitrophenol to p-aminophenol in the presence of NaBH4 within 10 min with a reaction rate constant of 0.348 min-1.

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