Band Structure Of Graphene Nanoribbons Research Articles

Semi-Empirical Pseudopotential Method for Graphene and Graphene Nanoribbons.

We implemented a semi-empirical pseudopotential (SEP) method for calculating the band structures of graphene and graphene nanoribbons. The basis functions adopted are two-dimensional plane waves multiplied by several B-spline functions along the perpendicular direction. The SEP includes both local and non-local terms, which were parametrized to fit relevant quantities obtained from the first-principles calculations based on the density-functional theory (DFT). With only a handful of parameters, we were able to reproduce the full band structure of graphene obtained by DFT with a negligible difference. Our method is simple to use and much more efficient than the DFT calculation. We then applied this SEP method to calculate the band structures of graphene nanoribbons. By adding a simple correction term to the local pseudopotentials on the edges of the nanoribbon (which mimics the effect caused by edge creation), we again obtained band structures of the armchair nanoribbon fairly close to the results obtained by DFT. Our approach allows the simulation of optical and transport properties of realistic nanodevices made of graphene nanoribbons with very little computation effort.

Transport model with atomistic band structure of graphene nanoribbon

The aim of the paper is to study the ballistic quantum transport in armchair graphene nanoribbon by developing a transport model followed by subsequent simulation. Electron transport in nanodevices can be studied by two different methods viz. wave function method and non-equilibrium Green function method. Here, we use the wave function method based transport mechanism with a view point on an atomistic quantum modeling of band structure. The interaction effects, unlike in Green function method, are included in a semi-empirical way where the resulting parameters are evaluated by fitting to experimental results. Interesting finding hitherto unknown to the graphene community, to the best belief of the authors, is that the current in armchair graphene nanoribbon starts to conduct only from a definite channel which is very much dimension-specific. As example, current conduction observed in the ribbon of dimension of seven atoms width starts only from the second channel. It is also noticed that a width dependent bandgap manifests the armchair ribbon to behave both as a semiconductor and semimetal depending on which family the ribbon belongs to. Further, the conductance of the ribbon is seen to have plateaus and current in it rises up in steps with increase of bias.

Interface Coupling as a Crucial Factor for Spatial Localization of Electronic States in a Heterojunction of Graphene Nanoribbons

The heterojunction (HJ) band structures of graphene nanoribbons (GNRs), generated by modulating ribbon width, are currently considered for use in tunnel field-effect transistors and optoelectronic applications, but interfacial states often exist and remove the band offsets. Here first-principles calculations show that these states are induced by C---C bonds at the interfacial edge, and can be eliminated by ``spare'' coupling of wide and narrow GNR segments, which is predicted to be stable at room temperature. Knowing how best to construct GNR HJs naturally will promote the technologies based on them.

Tuning the band structure of graphene nanoribbons through defect-interaction-driven edge patterning

We report a systematic analysis of pore-edge interactions in graphene nanoribbons (GNRs) and their outcomes based on first-principles calculations and classical molecular-dynamics simulations. We find a strong attractive interaction between nanopores and GNR edges that drives the pores to migrate toward and coalesce with the GNR edges, which can be exploited to form GNR edge patterns that impact the GNR electronic band structure and tune the GNR band gap. Our analysis introduces a viable physical processing strategy for modifying GNR properties by combining defect engineering and thermal annealing.

Computer simulation of edge-terminated carbon nanoribbons

In this paper, we present the results of ab initio simulation of edge-terminated carbon nanoribbons (CNRs). The calculations were performed using the electron density functional theory with the expansion of electron wave functions in plane waves in the Quantum Espresso software package [1]. The effect of various edge termination types on the band structure of graphene nanoribbons is studied. The data obtained showed that hydrogen and fluorine termination has a very weak effect on the structure. Sulfur or bromine termination causes a semiconductor-to-metal transition. The cause of the change in the conductivity type is the appearance of the electron dispersion curve crossing the nanoribbon band gap. At the same time, the dispersion dependences of the ribbon edge-terminated with alternating chlorine and hydrogen atoms do not exhibit such a change, and the curve mentioned above is not observed. The causes of the observed effects are analyzed.

Novel Strategy of Edge Saturation Hamiltonian for Graphene Nanoribbon Devices

Tight-binding (TB) Hamiltonian is widely used in the simulations of many low-dimensional devices, such as graphene nanoribbon (GNR)-based FETs, and usually, it is an empirical parameterized matrix. In this paper, we propose a novel strategy to construct the edge TB parameters of armchair GNR (a-GNR) under different edge saturations. Different from the traditional way’s only edge bonds analysis, this method also considers the diversity of three a-GNR families and the saturation atoms impact on the subedge bonds. The effects of several common elements or groups on the edge of GNRs are studied numerically and among them, hydrogen (H), fluorine (F), and hydroxyl group (OH) show better saturation properties. Through elaborate verifications of these three types of saturations, the TB fitting errors of the proposed new strategy are drastically reduced, in comparison with the traditional parameters. These verifications, which are subjected to the ab initio results, go from an energy-band level to a device-performance level. Simulation results also show that saturated by different atoms, the band structure of GNR obviously varies. Thus, edge saturation can be another effective method of tuning GNR device properties, such as bandgap, current on/off ratio, and carrier mobility.

Geometric phase at a graphene edge: Scattering phase shift of Dirac fermions

We study the scattering phase shift of Dirac fermions at graphene edge. We find that when a plane wave of a Dirac fermion is reflected at an edge of graphene, its reflection phase is shifted by the geometric phase resulting from the change of the pseudospin of the Dirac fermion in the reflection. The geometric phase is the Pancharatnam-Berry phase that equals the half of the solid angle on Bloch sphere determined by the propagation direction of the incident wave and also by the orientation angle of the graphene edge. The geometric phase is finite at the zigzag edge in general, while it always vanishes at the armchair edge because of intervalley mixing. To demonstrate its physical effects, we first connect the geometric phase with the energy band structure of graphene nanoribbon with the zigzag edge. The magnitude of the band gap of the nanoribbon, that opens in the presence of the staggered sublattice potential induced by edge magnetization, is related to the geometric phase. Second, we numerically study the effect of the geometric phase on the Veselago lens formed in a graphene nanoribbon. The interference pattern of the lens is distinguished between armchair and zigzag nanoribbons, which is useful for detecting the geometric phase.

Strain-Induced Pseudomagnetic Fields in Twisted Graphene Nanoribbons

We present, for the first time, an atomic-level and quantitative study of a strain-induced pseudomagnetic field in graphene nanoribbons with widths of hundreds of nanometers. We show that twisting strongly affects the band structures of graphene nanoribbons with arbitrary chirality and generates well-defined pseudo-Landau levels, which mimics the quantization of massive Dirac fermions in a magnetic field up to 160 T. Electrons are localized either at ribbon edges forming the edge current or at the ribbon center forming the snake orbit current, both being valley polarized. Our result paves the way for the design of new graphene-based nanoelectronics.

<I>Ab-Initio</I> Investigation of Band Structure of Graphene Nanoribbons Encapsulated in Single-Wall Carbon Nanotubes

<I>Ab-Initio</I> Investigation of Band Structure of Graphene Nanoribbons Encapsulated in Single-Wall Carbon Nanotubes

Analytical models of approximations for wave functions and energy dispersion in zigzag graphene nanoribbons

In this work, we present analytical solutions for the wave functions and energy dispersion of zigzag graphene nanoribbons. A nearest neighbor tight-binding model is employed to describe the electronic band structure of graphene nanoribbons. However, an exact analytical solution for the dispersion relation and the wave functions of zigzag nanoribbons cannot be obtained. We propose two approximations of the discrete energies, which are valid for a wide range of nanoribbon indices. Employing these models, selection rules for optical transitions and optical properties of zigzag graphene nanoribbons are studied.

Electronic band structures of graphene nanoribbons with self-passivating edgereconstructions

Using the nearest-neighbor tight-binding approach we study the electronic band structuresof graphene nanoribbons with self-passivating edge reconstructions. For zigzag ribbons theedge reconstruction moves both the Fermi energy and the flat band down by severalhundred meV, and the flat band is always found to be below the Fermi energy. The statesfeatured by the flat band are shown to be mainly localized at the atoms belonging toseveral lattice lines closest to the edges. For armchair ribbons the edge reconstructionstrongly modifies the band structure in the region close to the Fermi energy, leading to theappearance of a band gap even for ribbons which were predicted to be metallic inthe model of standard armchair edges. The gap widths are, however, stronglydifferent in magnitude and behave in different ways regarding the ribbon width.

Intrinsic Spin-Orbit Coupling in Zigzag and Armchair Graphene Nanoribbons

Starting from a tight-binding model, we derive the energy gaps induced by intrinsic spin-orbit (ISO) coupling in the low-energy band structures of graphene nanoribbons. The armchair graphene nanoribbons may be either semiconducting or metallic, depending on their widths in the absence of ISO interactions. For the metallic ones, the gaps induced by ISO coupling decrease with increasing ribbon widths. For the ISO interactions, we find that zigzag graphene nanoribbons with odd chains still have no band gaps while those with even chains have gaps with a monotonic decreasing dependence on the widths. First-principles calculations have also been carried out, verifying the results of the tight-binding approximation. Our paper reveals that the ISO interaction of graphene nanoribbons is governed by their geometrical parameters.

Properties of graphene: a theoretical perspective

In this review, we provide an in-depth description of the physics of monolayer and bilayer graphene from a theorist's perspective. We discuss the physical properties of graphene in an external magnetic field, reflecting the chiral nature of the quasiparticles near the Dirac point with a Landau level at zero energy. We address the unique integer quantum Hall effects, the role of electron correlations, and the recent observation of the fractional quantum Hall effect in the monolayer graphene. The quantum Hall effect in bilayer graphene is fundamentally different from that of a monolayer, reflecting the unique band structure of this system. The theory of transport in the absence of an external magnetic field is discussed in detail, along with the role of disorder studied in various theoretical models. We highlight the differences and similarities between monolayer and bilayer graphene, and focus on thermodynamic properties such as the compressibility, the plasmon spectra, the weak localization correction, quantum Hall effect, and optical properties. Confinement of electrons in graphene is nontrivial due to Klein tunneling. We review various theoretical and experimental studies of quantum confined structures made from graphene. The band structure of graphene nanoribbons and the role of the sublattice symmetry, edge geometry and the size of the nanoribbon on the electronic and magnetic properties are very active areas of research, and a detailed review of these topics is presented. Also, the effects of substrate interactions, adsorbed atoms, lattice defects and doping on the band structure of finite-sized graphene systems are discussed. We also include a brief description of graphane -- gapped material obtained from graphene by attaching hydrogen atoms to each carbon atom in the lattice.

Novel Band Structures and Transport Properties from Graphene Nanoribbons with Armchair Edges

Using an empirical linear combination of atomic orbitals method (LCAO) based on the sp3 tight-binding scheme, we studied the band structures of graphene nanoribbons with armchair edges terminated by H atoms and found that the band gap exhibits the size dependence and the ‘family’ behaviors, in which a metallic graphene nanoribbon and two semiconducting graphene nanoribbons coexist in a ‘family’. On the basis of Pichard’s transfer matrix technique, we calculated the conductance of the graphene nanoribbons and interestingly found that the steplike curves of conductance display conductance plateaus in the integer multiples of G0 = 2e2/h and the conductance gap emerges in the semiconducting graphene nanoribbon. Meanwhile, a side needle is located on the conductance curve at zero energy in the metallic graphene nanoribbon, which is attributed to degeneration of eigenstates at zero energy. Additionally, we showed that edge states do not have a notable contribution to the conductance because of the strong locali...