Algebraic solution of a graphene layer in a transverse electric and perpendicular magnetic fields

We present an exact algebraic solution of a single graphene plane in transverse electric and perpendicular magnetic fields. The method presented gives both the eigen-values and the eigen-functions of the graphene plane. It is shown that the eigen-states of the problem can be casted in terms of coherent states, which appears in a natural way from the formalism.Comment: 11 pages, 5 figures, accepted for publication in Journal of Physics Condensed Matte

Bilayer graphene: gap tunability and edge properties

Bilayer graphene -- two coupled single graphene layers stacked as in graphite -- provides the only known semiconductor with a gap that can be tuned externally through electric field effect. Here we use a tight binding approach to study how the gap changes with the applied electric field. Within a parallel plate capacitor model and taking into account screening of the external field, we describe real back gated and/or chemically doped bilayer devices. We show that a gap between zero and midinfrared energies can be induced and externally tuned in these devices, making bilayer graphene very appealing from the point of view of applications. However, applications to nanotechnology require careful treatment of the effect of sample boundaries. This being particularly true in graphene, where the presence of edge states at zero energy -- the Fermi level of the undoped system -- has been extensively reported. Here we show that also bilayer graphene supports surface states localized at zigzag edges. The presence of two layers, however, allows for a new type of edge state which shows an enhanced penetration into the bulk and gives rise to band crossing phenomenon inside the gap of the biased bilayer system.Comment: 8 pages, 3 fugures, Proceedings of the International Conference on Theoretical Physics: Dubna-Nano200

Inducing energy gaps in graphene monolayer and bilayer

In this paper we propose a mechanism for the induction of energy gaps in the spectrum of graphene and its bilayer, when both these materials are covered with water and ammonia molecules. The energy gaps obtained are within the range 20-30 meV, values compatible to those found in experimental studies of graphene bilayer. We further show that the binding energies are large enough for the adsorption of the molecules to be maintained even at room temperature

Modeling non-thermal emission from stellar bow shocks

Runaway O- and early B-type stars passing throughout the interstellar medium at supersonic velocities and characterized by strong stellar winds may produce bow shocks that can serve as particle acceleration sites. Previous theoretical models predict the production of high energy photons by non-thermal radiative processes, but their efficiency is still debated. We aim to test and explain the possibility of emission from the bow shocks formed by runaway stars traveling through the interstellar medium by using previous theoretical models. We apply our model to AE Aurigae, the first reported star with an X-ray detected bow shock, to BD+43 3654, in which the observations failed in detecting high energy emission, and to the transition phase of a supergiant star in the late stages of its life.From our analysis, we confirm that the X-ray emission from the bow shock produced by AE Aurigae can be explained by inverse Compton processes involving the infrared photons of the heated dust. We also predict low high energy flux emission from the bow shock produced by BD+43 3654, and the possibility of high energy emission from the bow shock formed by a supergiant star during the transition phase from blue to red supergiant.Bow shock formed by different type of runaway stars are revealed as a new possible source of high energy photons in our neighbourhood

Variable exponent Sobolev spaces associated with Jacobi expansions

In this paper we define variable exponent Sobolev spaces associated with Jacobi expansions. We prove that our generalized Sobolev spaces can be characterized as variable exponent potential spaces and as variable exponent Triebel-Lizorkin type spaces.Comment: 30 pages, small typos corrected in the introductio

Localized states at zigzag edges of bilayer graphene

We report the existence of zero energy surface states localized at zigzag edges of bilayer graphene. Working within the tight-binding approximation we derive the analytic solution for the wavefunctions of these peculiar surface states. It is shown that zero energy edge states in bilayer graphene can be divided into two families: (i) states living only on a single plane, equivalent to surface states in monolayer graphene; (ii) states with finite amplitude over the two layers, with an enhanced penetration into the bulk. The bulk and surface (edge) electronic structure of bilayer graphene nanoribbons is also studied, both in the absence and in the presence of a bias voltage between planes.Comment: 4 pages, 5 figure