90 research outputs found
Periodically rippled graphene: growth and spatially resolved electronic structure
We studied the growth of an epitaxial graphene monolayer on Ru(0001). The
graphene monolayer covers uniformly the Ru substrate over lateral distances
larger than several microns reproducing the structural defects of the Ru
substrate. The graphene is rippled with a periodicity dictated by the
difference in lattice parameter between C and Ru. The theoretical model predict
inhomogeneities in the electronic structure. This is confirmed by measurements
in real space by means of scanning tunnelling spectroscopy. We observe electron
pockets at the higher parts of the ripples.Comment: 5 page
Wigner formalism for a particle on an infinite lattice: dynamics and spin
The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Banuls MC and Perez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included
Periodically modulated geometric and electronic structure of graphene on Ru(0001)
We report here on a method to fabricate and characterize highly perfect,
periodically rippled graphene monolayers and islands, epitaxially grown on
single crystal metallic substrates under controlled UHV conditions. The
periodicity of the ripples is dictated by the difference in lattice parameters
of graphene and substrate, and, thus, it is adjustable. We characterize its
perfection at the atomic scale by means of STM and determine its electronic
structure in the real space by local tunnelling spectroscopy. There are
periodic variations in the geometric and electronic structure of the graphene
monolayer. We observe inhomogeneities in the charge distribution, i.e a larger
occupied Density Of States at the higher parts of the ripples. Periodically
rippled graphene might represent the physical realization of an ordered array
of coupled graphene quantum dots. The data show, however, that for rippled
graphene on Ru(0001) both the low and the high parts of the ripples are
metallic. The fabrication of periodically rippled graphene layers with
controllable characteristic length and different bonding interactions with the
substrate will allow a systematic experimental test of this fundamental
problem.Comment: 12 pages. Contribution to the topical issue on graphene of
Semiconductor Science and Technolog
Helium reflectivity and Debye temperature of graphene grown epitaxially on Ru(0001)
It is shown that the surface of an epitaxial graphene monolayer grown on Ru(0001) could be used as a quite efficient external mirror for He-atom microscopy, with a specular reflectivity of 20% of the incident beam. Furthermore, the system is stable up to 1150 K, and the He reflectivity remains almost unchanged after exposure to air. Additionally, the high reflectivity for H2 molecules (11%) opens up the development of a H2 microprobe suitable for lithography. The Debye temperature for this epitaxial graphene monolayer has been determined from a study of the temperature dependence of the He specular intensity as a function of incident parameters. A value of 1045 K has been obtained, which is much higher than the 590 K reported for graphite under similar conditions, and close to the value of 1287 K calculated for isolated grapheneThis work was supported by the Ministerio de EducaciĂłn y Ciencia through the program CONSOLIDER-INGENIO on Molecular Nanoscience (Project No. CSD 2007-00010), Project No. FIS2010-18847, and a Juan de la Cierva grant (A.P.), and by Comunidad de Madrid through the program NANOBIOMAGNE
Periodically modulated geometric and electronic structure of graphene on Ru(0001)
We report here on a method to fabricate and characterize highly perfect,
periodically rippled graphene monolayers and islands, epitaxially grown on
single crystal metallic substrates under controlled UHV conditions. The
periodicity of the ripples is dictated by the difference in lattice parameters
of graphene and substrate, and, thus, it is adjustable. We characterize its
perfection at the atomic scale by means of STM and determine its electronic
structure in the real space by local tunnelling spectroscopy. There are
periodic variations in the geometric and electronic structure of the graphene
monolayer. We observe inhomogeneities in the charge distribution, i.e a larger
occupied Density Of States at the higher parts of the ripples. Periodically
rippled graphene might represent the physical realization of an ordered array
of coupled graphene quantum dots. The data show, however, that for rippled
graphene on Ru(0001) both the low and the high parts of the ripples are
metallic. The fabrication of periodically rippled graphene layers with
controllable characteristic length and different bonding interactions with the
substrate will allow a systematic experimental test of this fundamental
problem.Comment: 12 pages. Contribution to the topical issue on graphene of
Semiconductor Science and Technolog
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