Origin of the spectrum of $π$ electrons that results from coupling of $N$ $\cal N$-long acenes via C-C covalent bonding have been traced with the use of the Green function formalism. Exact expressions of acene and graphene Green's functions, which are useful for analysis of electronic properties of these macromolecules, are obtained and advanced to the form suitable for instructive applications.
Closed expressions for the Green functions of the stationary two-dimensional two-component Schrodinger equation for an electron moving in monolayer and bilayer graphene in the presence of a magnetic field are obtained in terms of the Whittaker functions.
This work presents a novel approach to describe spectral properties of graphene layers with well defined edges. We microscopically analyze the boundary problem for the continuous Bogoliubov-de Gennes-Dirac (BdGD) equations and derive the Green functions for normal and superconducting graphene layers. Importing the idea used in tight-binding (TB) models of a microscopic hopping that couples different regions, we are able to set up and solve an algebraic Dyson's equation describing a graphene-superconductor junction. For this coupled system we analytically derive the Green functions and use them…
An accurate simulation of Green's function and self-energy function of non-interacting electrons in disordered graphenes are performed. Fundamental physical quantities such as the elastic relaxation time τe, the phase velocity vp, and the group velocity vg are evaluated. New features around the Dirac point are revealed, showing hints that multi-scattering induced hybridization of Bloch states plays an important role in the vicinity of the Dirac point.
We describe how to apply the recursive Green's function method to the computation of electronic transport properties of graphene sheets and nanoribbons in the linear response regime. This method allows for an amenable inclusion of several disorder mechanisms at the microscopic level, as well as inhomogeneous gating, finite temperature, and, to some extend, dephasing. We present algorithms for computing the conductance, density of states, and current densities for armchair and zigzag atomic edge alignments. Several numerical results are presented to illustrate the usefulness of the method.
The quantum Hall effect in Graphene nano-ribbons (GNR) is investigated with the non-equilibrium Green s function (NEGF) based quantum transport model in the ballistic regime. The nearest neighbor tight-binding model based on pz orbital constructs the device Hamiltonian. GNRs of different edge geometries (Zigzag and Armchair) are considered. The magnetic field is included in both the channels and contact through Peierls substitution. Efficient algorithms for calculating the surface Green function are used to save computation time while simulating realistically large dimensions comparable to tho…
The Green functions play a big role in the calculation of the local density of states of the carbon nanostructures. We investigate their nature for the variously oriented and disclinated graphene-like surface. Next, we investigate the case of a small perturbation generated by two heptagonal defects and from the character of the local density of states in the border sites of these defects we derive their minimal and maximal distance on the perturbed cylindrical surface. For this purpose, we transform the given surface into a chain using the Haydock recursion method. We will suppose only the nea…
Mode space approach has been used so far in NEGF to treat phonon scattering for computational efficiency. Here we perform a more rigorous quantum transport simulation in real space to consider interband scatterings as well. We show a seamless transition from ballistic to dissipative transport in graphene nanoribbon transistors by varying channel length. We find acoustic phonon (AP) scattering to be the dominant scattering mechanism within the relevant range of voltage bias. Optical phonon scattering is significant only when a large gate voltage is applied. In a longer channel device, the contr…
In this article we derive the lattice Green Functions (GFs) of graphene using a Tight Binding Hamiltonian incorporating both first and second nearest neighbour hoppings and allowing for a non-orthogonal electron wavefunction overlap. It is shown how the resulting GFs can be simplified from a double to a single integral form to aid computation, and that when considering off-diagonal GFs in the high symmetry directions of the lattice this single integral can be approximated very accurately by an algebraic expression. By comparing our results to the conventional first nearest neighbour model comm…
We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches', are connected using self energy terms which encode the information of the extended parts of the system. The calculation scheme uses a combination of analytic expressions for the Green's function of infinite pristine systems and an adaptive recursive Green's function technique for the patches. The method allows for an efficient calculation of both local electronic and transport properties,…
Bulk modes (BM) are basis solutions to the Schrödinger equation and they are useful in a number of physical problems. In the present work, we establish a complete set of BMs for graphene ribbons at arbitrary energy. We derive analytical expressions for these modes and systematically classify them into propagating or evanescent mode. We also demonstrate their uses in efficient electronic transport simulations of graphene-based electronic devices within both the mode-matching method and the Green's function framework. Explicit constructions of Green's functions for infinite and semi-infinite gra…
We study the exchange interaction $J$ between two magnetic impurities in graphene (the RKKY interaction) by directly computing the lattice Green's function for the tight-binding band structure for the honeycomb lattice. The method allows us to compute $J$ numerically for much larger distances than can be handled by finite-lattice calculations as well as for small distances. % avoids the use of a cutoff function often invoked in the literature to curtail the diverging contributions from the linear bands and yields results that are valid for all distances. In addition, we rederive the analytical…
Using the Green function formalism we calculate a current-induced spin polarization of weakly magnetized graphene with Rashba spin-orbit interaction. In a general case, all components of the current-induced spin polarization are nonzero, contrary to the nonmagnetic limit, where the only nonvanishing component of spin polarization is that in the graphene plane and normal to electric field. When the induced spin polarization is exchange-coupled to the magnetization, it exerts a spin-orbit torque on the latter. Using the Green function method we have derived some analytical formulas for the spin …
An exact solution is obtained for the electromagnetic field due to an electric current in the presence of a surface conductivity model of graphene. The graphene is represented by an infinitesimally-thin, local and isotropic two-sided conductivity surface. The field is obtained in terms of dyadic Green's functions represented as Sommerfeld integrals. The solution of plane-wave reflection and transmission is presented, and surface wave propagation along graphene is studied via the poles of the Sommerfeld integrals. For isolated graphene characterized by complex surface conductivity, a proper tra…
We describe the numerical modeling of current flow in graphene heterojunctions, within the Keldysh Landauer Non-equilibrium Green's function (NEGF) formalism. By implementing a $k$-space approach along the transverse modes, coupled with partial matrix inversion using the Recursive Green's function Algorithm (RGFA), we can simulate on an atomistic scale current flow across devices approaching experimental dimensions. We use the numerical platform to deconstruct current flow in graphene, compare with experimental results on conductance, conductivity and quantum Hall, and deconstruct the physics …
We discuss the renormalization of the polarizability of a nanoparticle in the presence of either (i) a continuous graphene sheet or (ii) a plasmonic graphene grating, taking into account retardation effects. Our analysis demonstrates that the excitation of surface plasmon-polaritons in graphene produces a large enhancement of the real and imaginary parts of the renormalized polarizability. We show that the imaginary part can be changed by a factor of up to 100 relatively to its value in the absence of graphene. We also show that the resonance in the case of the grating is narrower than in the …
A fluid-based method is demonstrated for preparing graphene nanomeshes (GNMs) directly from pristine graphite flakes by a one-step process. The high efficiency is attributed to the combination of fluid-assisted exfoliation and perforation of the graphene sheets. Atomic force microscopy shows that the as-produced GNMs are less than 1.5 nm thick. The total area of the pores within 1 um2 of the GNM sheet is estimated as ~0.15 um2 and the pore density as ~22 um-2, The yield of GNMs from pristine graphite powder and the power consumption for per gram GNM synthesis are evaluated as 5 wt% and 120 kWh…
An efficient method with no numerical diagonalization of a huge Hamiltonian matrix and calculation of a tedious Green's function is proposed to acquire the exact energy spectrum and dynamical conductivity in a gated AA-stacking $N$-layer Graphene (AANLG) with the intrinsic spin-orbital coupling (SOC). $2N \times 2N$ tight-binding Hamiltonian matrix, velocity operator and Green's function representation of an AANLG are simultaneously reduced to $N$ $2\times 2$ diagonal block matrices through a proper transformation matrix. A gated AANLG with intrinsic SOC is reduced to $N$ graphene-like layers.…
We calculate the electronic and thermal transport properties of devices based on finite graphene antidot lattices (GALs) connected to perfect graphene leads. We use an atomistic approach based on the $π$-tight-binding model, the Brenner potential, and employing recursive Green's functions. We consider the effect of random disorder on the electronic and thermal transport properties, and examine the potential gain of thermoelectric merit by tailoring of the disorder. We propose several routes to optimize the transport properties of the GAL systems. Finally, we illustrate how quantum thermal tran…
An analytical general analysis of the electromagnetic Dyadic Green's Function for two-dimensional sheet (or a very thin film) is presented, with an emphasis on on the case of graphene. A modified steepest descent treatment of the fields from a point dipole given in the form of Sommerfeld integrals is performed. We sequentially derive the expressions for both out-of-plane and in-plane fields of both polarizations. It is shown that the analytical approximation provided is very precise in a wide range of distances from a point source, down to a deep subwavelength region (1/100 of wavelength). We …
Dopants positioned near edges in nanostructured graphene behave differently from bulk dopants. Most notable, the amount of charge transferred to delocalized states (i.e. doping efficiency) depends on position as well as edge chirality. We apply a self-consistent tight-binding model to analyze this problem focusing on substitutional nitrogen and boron doping. Using a Greens function technique, very large structures can be studied and artificial interactions between dopants in periodically repeated simulations cells are avoided. We find pronounced signatures of edges in the local impurity densit…
van der Waals heterostructures assembled from atomically thin crystals are ideal model systems to study spin-orbital coupled transport because they exhibit a strong interplay between spin, lattice and valley degrees of freedom that can be manipulated by strain, electric bias and proximity effects. The recently predicted spin-helical regime in graphene on transition metal dichalcogenides, in which spin and pseudospin degrees of freedom are locked together [M. Offidani et al. Phys. Rev. Lett. 119, 196801 (2017)], suggests their potential application in spintronics. Here, by deriving an Eilenberg…
We present the complete formalism that describes scattering in graphene at low-energies. We begin by analyzing the real-space free Green's function matrix, and its analytical expansions at low-energy, carefully incorporating the discrete lattice structure, and arbitrary forms of the atomic-orbital wave function. We then compute the real-space Green's function in the presence of an impurity. We express our results both in 2X2 and 4X4 forms (for the two sublattices and the two inequivalent valleys of the first Brillouin zone). We compare this with the 4X4 formalism proposed in cond-mat/0608228 a…
We implement, optimize, and validate the linear-scaling Kubo-Greenwood quantum transport simulation on graphics processing units by examining resonant scattering in graphene. We consider two practical representations of the Kubo-Greenwood formula: a Green-Kubo formula based on the velocity auto-correlation and an Einstein formula based on the mean square displacement. The code is fully implemented on graphics processing units with a speedup factor of up to 16 (using double-precision) relative to our CPU implementation. We compare the kernel polynomial method and the Fourier transform method fo…
We describe a method and its implementation for calculating electronic structure and electron transport without approximating the structure using periodic super-cells. This effectively removes spurious periodic images and interference effects. Our method is based on already established methods readily available in the non-equilibrium Green function formalism and allows for non-equilibrium transport. We present examples of a N defect in graphene, finite voltage bias transport in a point-contact to graphene, and a graphene-nanoribbon junction. This method is less costly, in terms of CPU-hours, t…
The valley transport properties of a superlattice of out-of-plane Gaussians deformations are calculated using a Green's function and a Machine Learning approach. Our results show that periodicity significantly improves the valley filter capabilities of a single Gaussian deformation, these manifest themselves in the conductance as a sequence by valley filter plateaus. We establish that the physical effect behind the observed valley notch filter is the coupling between counter-propagating transverse modes; the complex relationship between the design parameters of the superlattice and the valley …
We study the electronic structure of graphene with a single substitutional vacancy using a combination of the density-functional, tight-binding, and impurity Green's function approaches. Density functional studies are performed with the all-electron spin-polarized linear augmented plane wave (LAPW) method. The three $sp^2 σ$ dangling bonds adjacent to the vacancy introduce localized states (V$σ$) in the mid-gap region, which split due to the crystal field and a Jahn-Teller distortion, while the $p_z π$ states introduce a sharp resonance state (V$π$) in the band structure. For a planar structur…
Despite the uniquely high thermal conductivity of graphene is well known, the exploitation of graphene into thermally conductive nanomaterials and devices is limited by the inefficiency of thermal contacts between the individual nanosheets. A fascinating yet experimentally challenging route to enhance thermal conductance at contacts between graphene nanosheets is through molecular junctions, allowing covalently connecting nanosheets otherwise interacting only via weak Van der Waals forces. Beside the bare existence of covalent connections, the choice of molecular structures to be used as therm…
We investigate polyethylene imine and diazonium salts as stable, complementary dopants on graphene. Transport in graphene devices doped with these molecules exhibits asymmetry in electron and hole conductance. The conductance of one carrier is preserved, while the conductance of the other carrier decreases. Simulations based on nonequilibrium Green's function formalism suggest that the origin of this asymmetry is imbalanced carrier injection from the graphene electrodes caused by misalignment of the electrode and channel neutrality points.
In this work the conducting properties of graphene lattice with a particular concentration of defect (5\% and 10\%) has been studied. The real space block recursion method introduced by Haydock et al. has been used in presence of the random distribution of defects in graphene. This Green function based method is found more powerful than the usual reciprocal based methods which need artificial periodicity. Different resonant states appear because of the presence of topological and local defects are studied within the framework of Green function.
We study the transport of charge carriers through finite graphene structures. The use of numerical exact kernel polynomial and Green function techniques allows us to treat actual sized samples beyond the Dirac-cone approximation. Particularly we investigate disordered nanoribbons, normal-conductor/graphene interfaces and normal-conductor/graphene/normal-conductor junctions with a focus on the behavior of the local density of states, single-particle spectral function, optical conductivity and conductance. We demonstrate that the contacts and bulk disorder will have a major impact on the electro…
Based on density functional theory (DFT), we have developed algorithms and a program code to investigate the electron transport characteristics for a variety of nanometer scaled devices in the presence of an external bias voltage. We employed basis sets comprised of linear combinations of numerical type atomic orbitals and k-point sampling for the realistic modeling of the bulk electrode. The scheme coupled with the matrix version of the non-equilibrium Green function method enables determination of the transmission coefficients at a given energy and voltage in a self-consistent manner, as wel…
Graphene and other nanostructures belong to the center of interest of today's physics research. The local density of states of the graphitic nanocone influenced by the spin-orbit interaction was calculated. Numerical calculations and the Green function approach were used to solve this problem. It was proven in the second case that the second order pproximation is not sufficient for this purpose.
The recent fabrication of graphene nanoribbon (GNR) field-effect transistors poses a challenge for first-principles modeling of carbon nanoelectronics due to many thousand atoms present in the device. The state of the art quantum transport algorithms, based on the nonequilibrium Green function formalism combined with the density functional theory (NEGF-DFT), were originally developed to calculate self-consistent electron density in equilibrium and at finite bias voltage (as a prerequisite to obtain conductance or current-voltage characteristics, respectively) for small molecules attached to me…
Electronic transport properties in armchair shaped edges graphene nanoribbons (AGNRs) doped various impurities have been simulated by the non-equilibrium Green's function approach combined with the first principle calculation based on the density functional theory. We have observed that impurity levels appear in electronic struc-tures, and that the quantization of transmission function is moderated for doped AGNRs. The I-V characteristic can be computed from the transmission function. Our simulation results show that AGNRs doped impurities have higher conductance than the non-doped one.
It is shown that apart from well-known factors, like temperature, substrate, and edge reconstruction effects, also the presence of external contacts is destructive for the formation of magnetic moments at the edges of graphene nanoribbons. The edge magnetism gradually decreases when graphene/electrode interfaces become more and more transparent for electrons. In addition to the graphene/electrode coupling strength, also the aspect ratio parameter, i.e. a width/length ratio of the graphene nanoribbon, is crucial for the suppression of edge magnetism. The present theory uses a tight-binding meth…
The optical conductivity of graphene strained uniaxially is studied within the Kubo-Greenwood formalism. Focusing on inter-band absorption, we analyze and quantify the breakdown of universal transparency in the visible region of the spectrum, and analytically characterize the transparency as a function of strain and polarization. Measuring transmittance as a function of incident polarization directly reflects the magnitude and direction of strain. Moreover, direction-dependent selection rules permit identification of the lattice orientation by monitoring the van-Hove transitions. These photoel…
We derive a semiclassical expression for the Green's function in graphene, in which the presence of a semiclassical phase is made apparent. The relationship between this semiclassical phase and the adiabatic Berry phase, usually referred to in this context, is discussed. These phases coincide for the perfectly linear Dirac dispersion relation. They differ however when a gap is opened at the Dirac point. We furthermore present several applications of our semiclassical formalism. In particular we provide, for various configurations, a semiclassical derivation of the electron's Landau levels, ill…
We theoretically study the electrical, thermal and thermoelectric transport properties of graphene nanoribbons under torsional deformations. The modelling follows a nonequilibrium Green's function approach in the ballistic transport regime, describing the electrical and phononic properties through \textit{ab-initio} density functional theory and empirical interatomic potentials, respectively. We consider two different types of deformations, a continuous twist of a given angle applied to the nanoribbon, and two consecutive twists applied in opposite angular directions. The numerical results are…
By using the real-space Green-Kubo formalism we study numerically the electron transport properties of low-fluorinated graphene. At low temperatures the diffuse transport regime is expected to be prevalent, and we found a pronounced electron-hole asymmetry in electrical conductivity as a result of quasi-resonant scattering on the localized states. For the finite temperatures in the variable-range hopping transport regime the interpretation of numerical results leads to the appearance of local minima and maxima of the resistance near the energies of the localized states. A comparison with the e…
The characteristics of energy band spectrum of armchair graphene nanoribbons in presence of line defect are analyzed within a simple non-interacting tight-binding framework. In metallic nanoribbons an energy gap may or may not appear in the band spectrum depending on the location of the defect line, while in semiconducting ribbons the gaps are customized, yielding the potential applicabilities of graphene nanoribbons in nanoscale electronic devices. With a more general model, we also investigate two-terminal electron transport using Green's function formalism.
In recent years, Chebyshev polynomial expansions of tight-binding Green's functions have been successfully applied to the study of a wide range of spectral and transport properties of materials. However, the application of the Chebyshev approach to the study of quantum transport properties of noninteracting mesoscopic systems with leads has been hampered by the lack of a suitable Chebyshev expansion of Landaeur's formula or one of its equivalent formulations in terms of Green's functions in Keldysh's perturbation theory. Here, we tackle this issue by means of a hybrid approach that combines th…
To achieve high thermal conductivity (k) of polymer graphene nanocomposites, it is critically important to achieve efficient thermal coupling between graphene and its surrounding polymers through effective functionalization schemes. In this work, we demonstrate that edge-functionalization of graphene nanoplatelets (GnPs) can enable a larger enhancement of effective thermal conductivity in polymer-graphene nanocomposites, relative to basal plane functionalization. Effective thermal conductivity for edge case is predicted, through molecular dynamics simulations, to be up to 48% higher relative t…
We perform a comparative study of the spin relaxation by spin-orbit coupling induced from adatoms (hydrogen and fluorine) in graphene. Two methods are applied, giving consistent results: a full quantum transport simulation of a graphene nanoribbon, and a T-matrix calculation using Green's functions for a single adatom in graphene. For hydrogenated graphene the dominant spin-orbit term for spin relaxation is PIA, the hitherto neglected interaction due to pseudospin inversion asymmetry. In contrast, in fluorinated graphene PIA and Rashba couplings destructively interfere, reducing the total spin…
Structure and coordinate dependence of the reflected wave, as well as boundary conditions for quasi-particles of graphene and the two dimensional electron gas in sheets with abrupt lattice edges are obtained and analyzed by the Green's function technique. In particular, the reflection wave function contains terms inversely proportional to the distance to the graphene lattice edge. The Dirac equation and the momentum dependence of the wave functions of the quasi-particles near the conical points are also found by the perturbation theory with degeneracy in terms of the Bloch functions taken at t…
The spin filter capability of a (0,8) armchair graphene nanoribbon with Fe atoms at substitutional sites is investigated by density functional theory in combination with the non-equilibrium Greens function technique. For specific arrangements, a high degree of spin polarization is achieved. These include a single substitution at an edge position or double substitution in the central sector of the transmission element. The possibility of switching between majority and minority spin polarization by changing the double substitution geometry is predicted. Including the bias dependence of the trans…
We theoretically predict, with the Keldysh Green's function combined with the Floquet method, that the AC electric field of a circularly polarized light should induce a Hall effect, in the absence of uniform magnetic fields, in graphene with a pair of Dirac dispersions. Although the Hall coefficient is not quantized, the dynamical gap generated by the AC field and the associated Hall effect bear a topological origin which can be traced back to the Dirac cones. We also study the dependence on boundary conditions. The required AC field strength is estimated to be realistic.
We propose a fast and versatile algorithm to calculate local and transport properties such as conductance, shot noise, local density of state or local currents in mesoscopic quantum systems. Within the non equilibrium Green function formalism, we generalize the recursive Green function technique to tackle multiterminal devices with arbitrary geometries. We apply our method to analyze two recent experiments: an electronic Mach-Zehnder interferometer in a 2D gas and a Hall bar made of graphene nanoribbons in quantum Hall regime. In the latter case, we find that the Landau edge state pinned to th…
The magneto- and Hall resistance of a locally gated cross shaped graphene Hall bar is calculated. The edge of the top gate is placed diagonally across the center of the Hall cross. Four-probe resistance is calculated using the Landauer-Büttiker formalism, while the transmission coefficients are obtained using the non-equilibrium Green's function approach. The interplay between transport due to edge channels and snake states is investigated. When two edge channels are occupied we predict oscillations in the Hall and the bend resistance as function of the magnetic field which are a consequence o…
We simulate electron transport through graphene nanoribbons of experimentally realizable size (length L up to 2 micrometer, width W approximately 40 nm) in the presence of scattering at rough edges. Our numerical approach is based on a modular recursive Green's function technique that features sub-linear scaling with L of the computational effort. We identify the influence of the broken A-B sublattice (or chiral) symmetry and of K-K' scattering by Fourier spectroscopy of individual scattering states. For long ribbons we find Anderson-localized scattering states with a well-defined exponential …
The quantum corrections to the conductivity and the thermopower in monolayer graphene are studied. We use the recursive Green's function method to calculate numerically the conductivity and the thermopower of graphene. We then analyze these weak localization corrections by fitting with the analytical theory as function of the impurity parameters and the gate potential. As a result of the quantum corrections to the thermopower, we find large magnetothermopower which is shown to provide a very sensitive measure of the size and strength of the impurities. We compare these analytical and numerical…
In our previous work (E. Kogan, Phys. Rev. B 84, 115119 (2011)) we presented calculation of RKKY interaction between two magnetic impurities in graphene based on Matsubara Green's functions (MGF) in the coordinate -- imaginary time representation. Now we present the calculation based on MGF in the coordinate -- frequency representation. We claim that both approaches have an important advantage over those based on zero temperature Green's functions (ZTGF), which are very briefly reviewed in the beginning of the present work. The MGF approaches, in distinction to the ZTGF approaches, operate onl…
The phonon Boltzmann transport equation (BTE) has been widely utilized to study thermal transport in solids. While for a number of materials the exact solution to the BTE has been obtained for a uniform heat flow, problems arising in micro/nanoscale heat transport have been analyzed within the relaxation time approximation (RTA). Since the RTA breaks down at temperatures low compared to the Debye temperature, this approximation prevents the study of an important class of high Debye temperature materials such as diamond, graphite, graphene and some other 2D materials. We present a full scatteri…
Using the recursive Green's function method, we study the problem of electron transport in a disordered single-layer graphene sheet. The conductivity is of order $e^2/h$ and its dependence on the carrier density has a scaling form that is controlled solely by the disorder strength and the ratio between the sample size and the correlation length of the disorder potential. The shot noise Fano factor is shown to have a narrow dip near the neutrality point for weak disorder and to develop a nearly doping independent behavior at strong disorder. Our results are in good qualitative and quantitative …
Intrinsic spin Hall effect in the AA-stacked bilayer graphene is studied theoretically. The low-energy electronic spectrum for states in the vicinity of the Dirac points is obtained from the corresponding $\mathbf{k}\cdot\mathbf{p}$ Hamiltonian. The spin Hall conductivity in the linear response regime is determined within the Green function formalism. Conditions for the existence of spin Hall insulator phase are also analyzed, and it is shown that the spin Hall insulator phase can exist for a sufficiently large spin-orbit coupling, which opens a gap in the spectrum. The electric field perpendi…
We use the non-equilibrium Green function (NEGF) method in the ballistic limit to provide a quantitative description of the conductance of graphene pn junctions - an important building block for graphene electronics devices. In this paper, recent experiments on graphene junctions are explained by a ballistic transport model, but only if the finite junction transition width, Dw, is accounted for. In particular, the experimentally observed anamolous increase in the resistance asymmetry between nn and np junctions under low source/drain charge density conditions is also quantitatively captured by…
We report an intriguing transition from the quantum spin Hall phase to the spin Hall effect upon segregation of thallium adatoms adsorbed onto a graphene surface. Landauer-Büttiker and Kubo-Greenwood simulations are used to access both edge and bulk transport physics in disordered thallium-functionalized graphene systems of realistic sizes. Our findings not only quantify the detrimental effects of adatom clustering in the formation of the topological state, but also provide evidence for the emergence of spin accumulation at opposite sample edges driven by spin-dependent scattering induced by t…
Using the Green's function method, we study the effect of an impurity potential on the electronic structure of the honeycomb lattice in the one-band tight-binding model that contains both the nearest neighbor ($t$) and the second neighbor ($t'$) interactions. The model is relevant to the case of the substitutional vacancy in graphene. If the second neighbor interaction is large enough ($t' > t /3$), then the linear Dirac bands no longer occur at the Fermi energy and the electronic structure is therefore fundamentally changed. With only the nearest neighbor interactions present, there is partic…
