8 research outputs found

    Rashba and intrinsic spin-orbit interactions in biased bilayer graphene

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    We investigate the effect that the intrinsic spin-orbit and the inter- and intra-layer Rashba interactions have on the energy spectrum of either an unbiased or a biased graphene bilayer. We find that under certain conditions, a Dirac cone is formed out of a parabolic band and that it is possible to create a "Mexican hat"-like energy dispersion in an unbiased bilayer. In addition, in the presence of only an intralayer Rashba interaction, the K (K') point splits into four distinct ones, contrarily to the case in single-layer graphene, where the splitting also takes place, but the low-energy dispersion at these points remains identical.Comment: 10 pages, 10 figure

    Spin- and band-ferromagnetism in trilayer graphene

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    We study the ground state properties of an ABA-stacked trilayer graphene. The low energy band structure can be described by a combination of both a linear and a quadratic particle-hole symmetric dispersions, reminiscent of monolayer- and bilayer-graphene, respectively. The multi-band structure offers more channels for instability towards ferromagnetism when the Coulomb interaction is taken into account. Indeed, if one associates a pseudo-spin 1/2 degree of freedom to the bands (parabolic/linear), it is possible to realize also a band-ferromagnetic state, where there is a shift in the energy bands, since they fill up differently. By using a variational procedure, we compute the exchange energies for all possible variational ground states and identify the parameter space for the occurrence of spin- and band-ferromagnetic instabilities as a function of doping and interaction strength.Comment: 9 pages/ 8 figure

    Screening in multilayer graphene

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    Ferromagnetism in ABC-stacked trilayer graphene

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    In this article we study the ferromagnetic behavior of ABC-stacked trilayer graphene. This is done using a nearest-neighbor tight-binding model, in the presence of long-range Coulomb interactions. For a given electron-electron interaction g and doping level n, we determine whether the total energy is minimized for a paramagnetic or ferromagnetic configuration of our variational parameters. The g versus n phase diagram is first calculated for the unscreened case. We then include the effects of screening using a simplified expression for the fermion bubble diagram. We show that ferromagnetism in ABC-stacked trilayer graphene is more robust than in monolayer, in bilayer, and in ABA-stacked trilayer graphene. Although the screening reduces the ferromagnetic regime in ABC-stacked trilayer graphene, the critical doping level remains one order of magnitude larger than in unscreened bilayer graphene

    High resolution dynamic ocean topography in the Southern Ocean from GOCE

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    A mean dynamic ocean topography (MDT) has been computed using a high resolution GOCE (Gravity field and steady-state Ocean Circulation Explorer) gravity model and a new mean sea surface obtained from a combination of satellite altimetry covering the period 1992 October till 2010 April. The considered gravity model is GO-CONS-GCF-2-TIM-R3, which computes geoid using 12 months of GOCE gravity field data. The GOCE gravity data allow for more detailed and accurate estimates of MDT. This is illustrated in the Southern Ocean where the commission error is reduced from 20 to 5cm compared to the MDT computed using the GRACE gravity field model ITG-Grace2010. As a result of the more detailed and accurate MDT, the calculation of geostrophic velocities from the MDT is now possible with higher accuracy and spatial resolution, and the error estimate is about 7 cms−1 for the Southern Ocean

    Viral Disease of the Cornea and External Eye

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