Session U30: Electronic Properties of Graphene and Related Structures IV

Ab-initio study of polarization in graphene films

We present an ab-initio analysis of polarization of multilayer graphene systems under applied electric fields. The effects of applied electric fields are calculated using a Berry phase approach with a plane-wave density functional formalism. We have determine polarizability values for graphene films and carbon nanotubes and find that the polarizability of graphene films follows a linear relationship with the number of layers. We also examined changes in the induced charge distribution as a function of graphene layers. We focus in particular on bilayer graphene and find that the induced charge accumulates primarily on the B sublattice sites. This induced charge distribution was also confirmed by a separate tight-binding Green's function calculation.   

Large-Scale Self-Consistent Simulation of Multilayered Graphene Devices

We use the Density Functional Theory-based Self-Consistent Environment-Dependent Tight-Binding (SC-EDTB) and self-consistent Non-equilibrium Green function formalism (NEGF) to test the {\it all-graphene} multilayer circuit concept. The key element of multi-layered circuits, which are expected to become available through press-print technology, is the heavily perforated graphene layer. The latter serves as an electrical insulator due to its relatively large band gap, and poor ballistic coupling to the conductive parts of the circuit. High bias $I-V$ characteristics for various normally-ON and normally-OFF transistor configurations were simulated, and transistor tolerance to manufacturing defects and imperfections was tested. The usage of SC-EDTB-NEGF makes it possible to model quantum transport through {\em realistic} devices composed of large number of carbon atoms ($\sim 10000$), which are within the reach of presently available processing techniques. Other circuit elements, such as electric interconnects between different layers, wire crossings, and electric interconnects within the same layer are also considered.   

Energy bands of multilayer graphenes

The energy bands of L-layer graphenes have been obtained using first-principles calculations. We found that after the introduction of interlay coupling the linear valence and conduction bands of isolated layers can either remain or develop into parabolic bands or bands with a very flat top(bottom), depending on the stacking geometry. A theoretical explanation and some general rules have been developed based upon the tight-binding model with only the nearest-neighbor interactions.   

Effect of strain on the electronic structure of graphene

Graphene has been attracting interest due to its remarkable physical properties resulting from an electron spectrum resembling relativistic dynamics (Dirac fermions). Thus, is desirable to know methods for controling the charge carriers in graphene. In this work, we propose that the electronic properties of graphene can be modulated via isotropic and uniaxial strain. We have studied the electronic structure of graphene under mechanical deformation by means of first principles calculations. We present results for the charge distribution, electronic density of states, and band structure. We focus the analysis on the behavior of the Dirac cones and the number of the charge carriers as a function of strain. We find that an isotropic tensile strain increases the effective mass of carriers and an isotropic compression strain decrease it. Uniaxial tensile strain induce a similar behavior, as strain increase effective mass increase. Thus, our results show that strain allows controllable tuning of the graphene electronic properties. This research was supported by Consejo Nacional de Ciencia y Tecnolog\'{\i}a (Conacyt) under Grant No. 43830-F.   

Band-gap engineering in graphene systems for electronic applications

Ultrathin graphite films including monolayers, bilayers and graphene nanoribbons are intensely studied for the development of future electronic and optoelectronic devices. In this work we will present first principles electronic/phonon structure calculations to elucidate the role of geometry and interactions (electric field, edge functionalization, gating etc.) in the determination of the electronic properties of a wide variety of graphene systems (multi-layers, ribbons etc.). One preliminary objective of this task is to explore ways to accurately control the band gap through the careful design of the active graphitic systems. The coupling between electron and lattice dynamics will be analyzed via the evaluation of the electron-phonon coupling parameters and phonon dispersions calculations. We will discuss the growth of graphene layers on a preferred substrate e.g. SiC an Si. We will identify possible graphene-substrate geometries through first principles calculations and investigate the role of interfacial bonding in the modification and engineering of the band gap.   

Effect of Disorders in Graphene Nanoribbon Field-Effect Transistors

Recent progress on the graphene and graphene nanoribbon (GNR) has provoked strong interests in GNR field-effect transistors (FETs) for future digital and analog nanoelectronics applications. In this work, device characteristics of GNRFETs are calculated by solving the non-equilibrium Green's function (NEGF) transport equation in an atomistic p$_{Z}$ orbital basis set self-consistently with three-dimensional (3D) Poisson equation. The effects of a lattice vacancy, ionized impurity, and edge roughness on transistor performance and characteristics are examined by the atomistic simulations. We show that even a single disorder can have a significant effect on the device characteristics of GNRFETs due to the atomically thin and nanometer-wide channel geometry. For example, a single lattice vacancy can affect the on-current of a GNRFET by 40{\%}. Localized states in the GNR band gap energy range can be induced by the disorders, which affect quantum transport and self-consistent electrostatics. Significant variations between devices are expected due to disorders, but the GNRFETs still switch in the presence of moderate amount of disorders.   

Diluted Graphene Antiferromagnet

We study RKKY interactions between local magnetic moments for both doped and undoped graphene. We find in both cases that the interactions are primarily ferromagnetic for moments on the same sublattice, and antiferromagnetic for moments on opposite sublattices. This suggests that at sufficiently low temperatures dilute magnetic moments embedded in graphene can order into a state analogous to that of a dilute antiferromagnet. We find that in the undoped case one expects no net magnetic moment, and demonstrate numerically that this effect generalizes to ribbons where the magnetic response is strongest at the edge, suggesting the possibility of an unusual spin-transfer device. For doped graphene we find that moments at definite lattice sites interact over longer distances than those placed in interstitial sites of the lattice ($1/R^2$ vs. $1/R^3$) because the former support a Kohn anomaly that is suppressed in the latter due to the absence of backscattering.   

Magnetization measurement of highly oriented pyrolytic graphite surface with a spin-polarized metastable helium beam

Magnetic ordering in nanometerscale graphitic materials has attracted much interest in recent years. Some theoretical studies have predicted that the origin of ferromagnetism in these materials was attributed to defects in graphitic structures, such as edges and topological defects. Employing surface analytical technique is favorable for elucidation of these predictions by experimental studies, because there exist a number of pores and steps at the graphite surface and the structure not in an equilibrium phase might be realized at a surface state. In this work, we have successfully detected the magnetization in highly oriented pyrolytic graphite (HOPG) surface using a spin-polarized metastable helium (He*) beam under high magnetic field up to 5 T. The He* beam is an extremely surface-sensitive probe and the surface magnetization can be analyzed by measuring the asymmetry of sample current induced by the He* spin direction [1]. The observed value of the asymmetry shows a clear temperature dependence and is much larger than that of magnetic impurities measured by Auger electron spectroscopy. Thus, we could conclude that this surface magnetism is an intrinsic property of the HOPG itself other than the diamagnetism. \newline [1] M. Kurahashi and Y. Yamauchi Rev. Sci. Instrum. 77, 023904 (2006).   

Structural and electronic properties of few-layer graphenes from frist-principles

Using first-principles calculation method, it is found that the calculated layer spacing for the two-layer AB stacked FLG is only 2.725{\AA}, which is substantially reduced from the calculated value of 3.257{\AA} for bulk graphite. The average interlayer spacing for 2-, 3-, 4-, 5-, 6-, 7- and 8-layer FLG's are found to oscillate and approach that of the bulk graphite. The two-layer AA stacked FLG is found to remain metallic for the external electric potential up to 4.5Volts considered in this study. In contrast, the two-layer AB stacked FLG is found to exhibit a semi-metal-semiconductor transition under an external electric potential qualitatively in agreement with previous theoretical studies. However, the energy gap is not limited at 0.3eV as obtained in previous first-principles calculation due to the substantially reduced interlayer spacing. The threshold of the semi-metal-semiconductor transition is 0.04 Volts. The external electric potential also induced energy gaps in 3- and 4-layer AB stacked FLG's. However, in these two thicker FLG's, the induced energy gaps are small within 0.1eV. Based on this study, only the two-layer FLG is useful as a nanoscale electronic switch.   

Band structure engineering of graphene by strain

We have investigated the electronic structure of graphene under different planar strain distributions using the first principles pseudopotential planewave method and the tight-binding approach. We found that graphene with a symmetrical strain distribution is always a zero band gap semiconductor and its pseudogap decreases linearly with the strain strength in the elastic regime. However, asymmetrical strain distributions in graphene result in opening of band gaps at the Fermi level. For the graphene with a strain distribution parallel to C-C bonds, its band gap continuously increases to its maximum width of 0.486 eV as the strain increases. For the graphene with a strain distribution perpendicular to C-C bonds, its band gap continuously increases only to 0.170 eV. The anisotropic nature of graphene is also reflected by different Poisson ratios in different directions. We found that the Poisson ratio is 0.079 and 0.255 for the strain distributions parallel to or perpendicular to C-C bonds, respectively. These findings are important for understanding and controlling the transport properties of graphene systems.   

Electronic properties of nanotube-graphene composite carbon systems

Band structures of nanotube-graphene hybrid carbon systems are calculated by the tight-binding model. The Lennard-Jones potential is used to determine the optimal geometry for a single-walled carbon nanotube and a monolayer graphene. There exist many one-dimensional energy bands. The low energy bands are drastically changed by the interlayer atomic hoppings, such as the destruction of state degeneracy, alteration of Fermi-momentum states, creation of extra band-edge states, and modulation of energy gap. The composite systems are metals or semiconductors, which depends on the alignment and the geometry of carbon nanotube. The main characteristics of electronic structures are directly reflected in density of states. DOS exhibits a lot of asymmetric prominent peaks. The predicted results could be verified by the experimental measurements from the scanning tunneling spectroscopy.   

Edge states of zigzag bilayer graphite nanoribbons

Electronic structures of the zigzag bilayer graphite nanoribbons(Z-BGNR) with various ribbon width $N$ are studied within the tight binding approximation. Neglecting the small inter-layer hopping parameter $\gamma_4$, there exist two fixed Fermi points $\pm k^*$ independent of the ribbon width with the peculiar energy dispersion near $k^*$ as $\varepsilon (k) \sim \pm (k-k^*)^N$. By investigating the edge states of the Z-BGNR, we notice that the trigonal warping of the bilayer graphene sheets are reflected on in the edge state structure of the Z-BGNR. With the inclusion of $\gamma_4$, the above two Fermi points are not fixed, but drift toward the vicinity of the Dirac point with the increase of the width $N$ as shown by the finite scaling method and the peculiar dispersions change to the parabolic ones.