We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

http://ronald-wagner.de/diss/html/lit/share/surfsci411(98)186.pdf

The surface energy of metals

Electronic factors determining the reactivity of metal surfaces

The transfer matrix of a solid described by the stacking of principal layers is obtained by an iterative procedure which takes into account 2 layers after n iterations, in contrast to usual schemes where each iteration includes just one more layer. The Green function and density of states at the surface of the corresponding semi-infinite crystal are then given by well known formulae in terms of the transfer matrix. This method, especially convenient near singularities, is applied to the calculation of the spectral as well as the total densities of states for the (100) face of molybdenum. The Slater-Koster algorithm for the calculation of tight-binding parameters is used with a basis of nine orbitals per atom (4d, 5s, 5p). Surface states and resonances are first identified and then analysed into orbital components to find their dominant symmetry. Their evolution along the main symmetry lines of the two-dimensional Brillouin zone is given explicitly. The surface-state peak just below the Fermi level (Swanson hump) is not obtained. This is traced to the difficulty in placing an appropriate boundary condition at the surface with the tight-binding parameterisation scheme.

https://iopscience.iop.org/article/10.1088/0305-4608/14/5/016/pdf

Quick iterative scheme for the calculation of transfer matrices: application to Mo (100)

Surface plasmon polaritons (SPPs) are electromagnetic excitations existing at the interface between a metal and a dielectric material. Remarkable progress has been made in the field of SPPs in recent years. Control and manipulation of light using SPPs on the nanometre scale exhibit significant advantages in nanophotonics devices with very small elements, and SPPs open a promising way in areas involving environment, energy, biology and medicine. This paper presents an overview of current research activities on SPPs, including fundamental physics and applications. We first discuss the excitation of SPPs based on the SPP dispersion relation, coupling to SPPs by momentum matching between photons and SPPs, and propagation behaviour of SPPs. Based on the physical mechanism and the peculiar properties of SPPs, we demonstrate the major applications of SPPs, such as waveguides, sources, near-field optics, surface-enhanced Raman spectroscopy, data storage, solar cells, chemical sensors and biosensors.

https://iopscience.iop.org/article/10.1088/0022-3727/45/11/113001/pdf

Surface plasmon polaritons: physics and applications

Using the method of Chadi and Cohen, we present, for each of the two-dimensional lattice types, the mean-value point, the set of generating wave vectors, and the sets of special points in the two-dimensional Brillouin zone which are the most efficient in finding accurate averages of a periodic function over the Brillouin zone.

Special points in the two-dimensional Brillouin zone

We have solved Maxwell's equations for the fields localized near the surface of a doped semiconductor possessing either a depletion layer, an accumulation layer, or an inversion layer. We present the dispersion relation for the frequency of the surface plasmon polariton as a function of the wave vector parallel to the surface for each of the three cases. The effect of the space charge at the surface is taken into account by dividing the surface region into layers and assuming a linear position dependence for the free-carrier concentration and the local dielectric constant within each layer. We have found the solution for the fields within each layer and have satisfied the boundary conditions for the normal and tangential components of the fields at each interface between layers. We show that the features of the dispersion curve can be used to obtain information about the space-charge region. For illustration, we compare our calculations with measured dispersion curves of $n$-type InSb.

Effect of a charge layer on the surface-plasmon-polariton dispersion curve

Vibrational Edge Modes for Wedges with Arbitrary Interior Angles

Moss, Maradudin, and Cunningham recently calculated the velocities of long-wavelength acoustic phonons localized at the apex of a variable-angle semi-infinite elastic wedge. We present here a method by which more precise results may be obtained for small wedge angles.

Vibrational Edge Modes for Small-Angle Wedges

We propose a new mechanism which can lead to reconstruction in the surface region of a large class of materials. The mechanism is based on the fact that the dynamic effective charges present on the atoms near the surface can be different from those on the atoms in the bulk. The long-range interaction of these charges can cause the surface phonon to be lowered in frequency. We present numerical calculations of the normal-mode frequencies of a simple-cubic monatomic slab [(001) faces] of 15 layers when surface-induced dynamic effective charges are present near one of the surfaces. For reasonable values of the short-range atomic force constants, and for values of the dynamic effective charge on the surface layer of the order of 0.5e, the surface is unstable and recontruction occurs. Various patterns of reconstruction can be obtained depending upon the values of the short-range force constants.

S. L. Cunningham

Papers

Special points in the two-dimensional Brillouin zone

Effect of a charge layer on the surface-plasmon-polariton dispersion curve

Vibrational Edge Modes for Wedges with Arbitrary Interior Angles

Vibrational Edge Modes for Small-Angle Wedges

Soft Surface Phonons and Surface Reconstruction