We analyze in the framework of the space group theory the change of the dispersion law in grapenein the vicinity of the (former) Dirac points due to application of supercell potential with the $\sqrt{3}\times\sqrt{3}$ space periodicity and the same point symmetry as graphene.
Based on first principles density functional theory calculations we explore the energetics of the conversion of carbon mono and dioxide to methane over graphene oxide surfaces. Similar to the recently discovered hydration of various organic species over this catalyst, the transfer of hydrogen atoms from hydroxyl groups of graphene oxide provide a step by step transformation hydrogenation of carbon oxides. Estimated yields of modeled reactions at room temperature are about 0.01% for the carbon mono and dioxide. For the modeling of graphene oxide/metal oxide composites, calculations in the presence of MO_2 (where M = V, Cr, Mn, Fe) have been performed. Results of these calculations demonstrate significant decreases of the energy costs and increases of reaction yields to 0.07%, which is comparable to the efficiency of these reactions over platinum and ruthenium-based photocatalysts. Increasing the temperature to the value 100C should provide the total conversion of carbon mono and dioxides.
We present the results of the symmetry classification of the electron energy bands in graphene and silicene using group theory algebra and the tight--binding approximation. The analysis is performed both in the absence and in the presence of the spin-orbit coupling. We also discuss the bands merging in the Brillouin zone symmetry points and the conditions for the latter to become Dirac points.
Gradual localization of charge carriers was studied in a series of micro-size samples of monolayer graphene fabricated on the common large scale film and irradiated by different doses of C$^+$ ions with energy 35 keV. Measurements of the temperature dependence of conductivity and magnetoresistance in fields up to 4 T showed that at low disorder, the samples are in the regime of weak localization and antilocalization. Further increase of disorder leads to strong localization regime, when conductivity is described by the variable-range-hopping (VRH) mechanism. A crossover from the Mott regime to the Efros-Shklovskii regime of VRH is observed with decreasing temperature. Theoretical analysis of conductivity in both regimes showed a remarkably good agreement with experimental data.
In this chapter, semi-analytical models for the calculation of the quantum capacitance of both monolayer and bilayer graphene and its nanoribbons, are presented. Since electron-hole puddles are experimental facts in all graphene samples, they have been incorporated in our calculations. The temperature dependence of the quantum capacitance around the charge neutrality point is also investigated and the obtained results are in agreement with many features recently observed in quantum capacitance measurements on both monolayer and bilayer graphene devices. Furtheremore, the impact of finite-size and edge effects on the quantum capacitance of graphene nanoribbons is studied taking into account both the edge bond relaxation and third-nearest-neighbour interaction in the band structure of GNRs.
The development of selective high precision chemical functionalization strategies for device fabrication, in conjunction with associated techniques for patterning graphene wafers with atomic accuracy would provide the necessary basis for a post-CMOS manufacturing technology. This requires a thorough understanding of the principles governing the reactivity and patterning of graphene at the sub-nanometer length scale. This article reviews our quest to delineate the principles of graphene chemistry - that is, the chemistry at the Dirac point and beyond, and the effect of covalent chemistry on the electronic structure, electrical transport and magnetic properties of this low-dimensional material in order to enable the scalable production of graphene-based devices for low- and high-end technology applications.
In this book chapter, we introduce different schemes to create quantum states of matter in engineered graphene nanoribbons. We will focus on the emergence of controllable magnetic interactions, topological quantum magnets, and the interplay of magnetism and superconductivity. We comment on the experimental signatures of those states stemming from their electronic and spin excitations, that can be observed with atomic resolution using scanning probe techniques.
In this review we focus on the effect of the Dirac nature of graphene quasiparticles on two separate aspects. The first of these involves transport across superconducting graphene junctions with barriers of thickness $d_0$ and arbitrary gate voltages $V_0$ applied across the barrier region. The second aspect involves study of the presence of localized magnetic impurities in graphene and we show that Kondo effect in graphene is unconventional and can be tuned by gate voltage. We also discuss scanning tunneling conductance spectra phenomenon for both doped and undoped graphene. We show that the position of the impurity on or in graphene plays a subtle role and affects the underlying physics of STM spectra in doped graphene.
As conventional silicon technology is approaching its fundamental material and physical limits with continuous scaling, there is a growing push to look for new platform to design memory circuits for nanoelectronic applications. In this paper we explore new design concept of nonvolatile memory based on graphene nanotechnology. The investigation focuses on two forms of graphene based field effect transistor (FET) carbon nanotube FET (CNTFET) and graphene nanoribbon FET (GNRFET). The analysis reveals that GNRFET with a high trapping capable oxide layer is suitable for ultra high ensity nonvolatile memory.
We analyze the electrostatic interactions between a single graphene layer and a SiO$_2$ susbtrate, and other materials which may exist in its environment. We obtain that the leading effects arise from the polar modes at the SiO$_2$ surface, and water molecules, which may form layers between the graphene sheet and the substrate. The strength of the interactions implies that graphene is pinned to the substrate at distances greater than a few lattice spacings. The implications for graphene nanoelectromechanical systems, and for the interaction between graphene and a STM tip are also considered.
We present the electronic properties of massless Dirac fermions characterized by geometry and topology on a graphene sheet in this chapter. Topological effects can be elegantly illuminated by the Atiyah-Singer index theorem. It leads to a topological invariant under deformations on the Dirac operator and plays an essential role in formulating supersymmetric quantum mechanics over twisted Dolbeault complex caused by the topological deformation of the lattice in a graphene system. Making use of the G index theorem and a high degree of symmetry, we study deformed energy eigenvalues in graphene. The Dirac fermion results in SU(4) symmetry as a high degree of symmetry in the noninteracting Hamiltonian of the monolayer graphene. Under the topological deformation the zero-energy states emerge naturally without the Zeeman splitting at the Fermi points in the graphene sheet. In the case of nonzero energy, the up-spin and down-spin states have the exact high symmetries of spin, forming the pseudospin singlet pairing. We describe the peculiar and unconventional quantum Hall effects of the n = 0 Landau level in monolayer graphene on the basis of the G index theorem and the high degree of symme
Defects play a key role in the electronic structure of graphene layers flat or curved. Topological defects in which an hexagon is replaced by an n-sided polygon generate long range interactions that make them different from vacancies or other potential defects. In this work we review previous models for topological defects in graphene. A formalism is proposed to study the electronic and transport properties of graphene sheets with corrugations as the one recently synthesized. The formalism is based on coupling the Dirac equation that models the low energy electronic excitations of clean flat graphene samples to a curved space. A cosmic string analogy allows to treat an arbitrary number of topological defects located at arbitrary positions on the graphene plane. The usual defects that will always be present in any graphene sample as pentagon-heptagon pairs and Stone-Wales defects are studied as an example. The local density of states around the defects acquires characteristic modulations that could be observed in scanning tunnel and transmission electron microscopy.
The Diels-Alder surface modified top epitaxial graphene layer, with newly created pair of sp3 carbon centres, results in abrupt minimization of interlayer van der Waals interactions between two stacked graphene planes, and escapes the wafer during post-reaction manipulation stage, leaving the layer under it almost pristine-like. Above picture shows Diels-Alder functionalized sp2/sp3 graphene adduct leaves the parent wafer. In this communication we systematically address several fundamental questions in graphene surface chemistry, which are of extreme importance for device fabrication, and in successful implementation of covalently modified graphene in electronics industry.
Graphene is generally considered to be a strong candidate to succeed silicon as an electronic material. However, to date, it actually has not yet demonstrated capabilities that exceed standard semiconducting materials. Currently demonstrated viable graphene devices are essentially limited to micron size ultrahigh frequency analog field effect transistors and quantum Hall effect devices for metrology. Nanoscopically patterned graphene tends to have disordered edges that severely reduce mobilities thereby obviating its advantage over other materials. Here we show that graphene grown on structured silicon carbide surfaces overcomes the edge roughness and promises to provide an inroad into nanoscale patterning of graphene. We show that high quality ribbons and rings can be made using this technique. We also report on progress towards high mobility graphene monolayers on silicon carbide for device applications.
The interaction of graphene with neighboring materials and structures plays an important role in its behavior, both scientifically and technologically. The interactions are complicated due to the interplay between surface forces and possibly nonlinear elastic behavior. Here we review recent experimental and theoretical advances in the understanding of graphene adhesion. We organize our discussion into experimental and theoretical efforts directed toward: graphene conformation to a substrate, determination of adhesion energy, and applications where graphene adhesion plays an important role. We conclude with a brief prospectus outlining open issues.
The optical response of graphene micro-structures, such as micro-ribbons and disks, is dominated by the localized plasmon resonance in the far infrared (IR) spectral range. An ensemble of such structures is usually involved and the effect of the coupling between the individual structures is expected to play an important role. In this paper, the plasmonic coupling of graphene microstructures in different configurations is investigated. While a relatively weak coupling between graphene disks on the same plane is observed, the coupling between vertically stacked graphene disks is strong and a drastic increase of the resonance frequency is demonstrated. The plasmons in a more complex structure can be treated as the hybridization of plasmons from more elementary structures. As an example, the plasmon resonances of graphene micro-rings are presented, in conjunction with their response in a magnetic field. Finally, the coupling of the plasmon and the surface polar phonons of SiO2 substrate is demonstrated by the observation of a new hybrid resonance peak around 500cm-1.
We review the classification of all the 36 possible gap-opening instabilities in graphene, i.e., the 36 relativistic masses of the two-dimensional Dirac Hamiltonian when the spin, valley, and superconducting channels are included. We then show that in graphene it is possible to realize an odd number of Majorana fermions attached to vortices in superconducting order parameters if a proper hierarchy of mass scales is in place.
Graphene-oxide hybrid structures offer the opportunity to combine the versatile functionalities of oxides with the excellent electronic transport in graphene. Understanding and controlling how the dielectric environment affects the intrinsic properties of graphene is also critical to fundamental studies and technological development of graphene. Here we review our recent effort on understanding the transport properties of graphene interfaced with ferroelectric Pb(Zr,Ti)O_3 (PZT) and high-k HfO_2. Graphene field effect devices prepared on high-quality single crystal PZT substrates exhibit up to tenfold increases in mobility compared to SiO_2-gated devices. An unusual and robust resistance hysteresis is observed in these samples, which is attributed to the complex surface chemistry of the ferroelectric. Surface polar optical phonons of oxides in graphene transistors play an important role in the device performance. We review their effects on mobility and the high source-drain bias saturation current of graphene, which are crucial for developing graphene-based room temperature high-speed amplifiers. Oxides also introduce scattering sources that limit the low temperature electron mobil
Graphene supports surface plasmon polaritons (SPPs) with extreme field confinement and electrical tunability, but these waves are typically short-lived due to ohmic loss in the sheet. We show that embedding graphene in an active dielectric can counteract this loss and we derive closed-form design rules to do so, based on gain-assisted plasmonics and plasmonic amplification concepts. Specifically, from the full Maxwell model of a conductive sheet we obtain (i) the exact gain required for lossless plasmon propagation, and (ii) a second critical gain that marks the $\mathcal{PT}$-symmetric threshold, the exceptional point separating propagating and forbidden SPP regimes. The formulas are expressed directly in terms of the complex conductivity of graphene and the surrounding media, making them easy to evaluate and implement. We verify the theory with full-wave eigenmode calculations (COMSOL), showing dispersion and attenuation/amplification trends with and without gain for our plasmonic structures, finding a practical route to engineer long-range, tunable, lossless graphene plasmonics and to map/target non-Hermitian operating phases for device design in single- and double- layer graphe
We review chiral (Klein) tunneling in single-layer and bilayer graphene and present its semiclassical theory, including the Berry phase and the Maslov index. Peculiarities of the chiral tunneling are naturally explained in terms of classical phase space. In a one-dimensional geometry we reduced the original Dirac equation, describing the dynamics of charge carriers in the single layer graphene, to an effective Schrödinger equation with a complex potential. This allowed us to study tunneling in details and obtain analytic formulas. Our predictions are compared with numerical results. We have also demonstrated that, for the case of asymmetric n-p-n junction in single layer graphene, there is total transmission for normal incidence only, side resonances are suppressed.