Dirac Point Energy Research Articles

Modification on Flower Defects and Electronic Properties of Epitaxial Graphene by Erbium.

Manipulating the topological defects and electronic properties of graphene has been a subject of great interest. In this work, we have investigated the influence of Er predeposition on flower defects and electronic band structures of epitaxial graphene on SiC. It is shown that Er atoms grown on the SiC substrate actually work as an activator to induce flower defect formation with a density of 1.52 × 1012 cm-2 during the graphitization process when the Er coverage is 1.6 ML, about 5 times as much as that of pristine graphene. First-principles calculations demonstrate that Er greatly decreases the formation energy of the flower defect. We have discussed Er promoting effects on flower defect formation as well as its formation mechanism. Scanning tunneling microscopy (STM) and Raman and X-ray photoelectron spectroscopy (XPS) have been utilized to reveal the Er doping effect and its modification to electronic structures of graphene. N-doping enhancement and band gap opening can be observed by using angle-resolved photoemission spectroscopy (ARPES). With Er coverage increasing from 0 to 1.6 ML, the Dirac point energy decreases from -0.34 to -0.37 eV and the band gap gradually increases from 320 to 360 meV. The opening of the band gap is attributed to the synergistic effect of substitution doping of Er atoms and high-density flower defects.

Role of symmetry in quantum blocking of Andreev reflection in graphene nanoribbons side-terminated by superconductors

Andreev reflection can be forbidden by means of quantum interference when superconductors are attached at the side edges of graphene nanoribbons (GNRs). The blocking is restricted to single-mode nanoribbons having symmetric zigzag edges and is destroyed by the application of a magnetic field. These characteristics are shown to be the effects of the wavefunction parity on the Andreev retro and specular reflections. Not only the mirror symmetry of the GNRs but also symmetric coupling of the superconductors is required for the quantum blocking. The quasi-flat-band states around the Dirac point energy induced for armchair nanoribbons by adding carbon atoms at the nanoribbon edges do not cause the quantum blocking due to the lack of the mirror symmetry. Furthermore, the phase modulation by the superconductors is shown to be able to convert the quasi-flat dispersion for the edge states of zigzag nanoribbons to a quasi-vertical dispersion.

Stacking-induced Chern insulator

Graphene can be turned into a semimetal with broken time-reversal symmetry by adding a valley-dependent pseudo-scalar potential that shifts the Dirac point energies in opposite directions, as in the modified Haldane model. We consider a bilayer obtained by stacking two time-reversed copies of the modified Haldane model, where conduction and valence bands cross to give rise to a nodal line in each valleys. In the AB stacking, the interlayer hopping lifts the degeneracy of the nodal lines and induces a band repulsion, leading surprisingly to a chiral insulator with a Chern number $C=\pm2$. As a consequence a pair of chiral edge states appears at the boundaries of the ribbon bilayer geometry. In contrast, the AA stacking does not show nontrivial topological phases. We discuss possible experimental implementations of our results.

Spin-dependent transport and spin transfer torque in a system based on silagraghene nanoribbons

We theoretically investigate the spin-dependent transport and spin transfer torque ( S T T ) in a system composed of a silagraphene nanoribbon ( S L N R ) connected to two ferromagnetic ( F M ) leads with arbitrary relative magnetization direction, using the tight-binding model in the nearest neighbor approximation within the framework of the Green function’s technique and Landauer–Butticer formalism. We report numerical calculation results for conductance ( G ), magnetoresistance ( M R ), and spin transfer torque ( S T T ) in the F M / S L N R / F M junction for different strengths of ferromagnetic magnetization. It is found that the G and M R show oscillatory behavior around E F = 0 and more interestingly, the magnitude of the M R reaches up to % 100 , which can be effectively used for sensitive switchings. In addition, it is demonstrated that S T T versus Fermi energy shows noticeable peaks with moving away from Dirac point energy. The results show that the torques as a function of the angle between two magnetic electrodes ( θ ) show a s i n -like behavior and the G − θ curve demonstrates approximately a c o s i n e -like behavior, which is a function of M . Our results can provide valuable theoretical guidance to design future novel spintronic devices. • We report the spin-polarized transport in a system based on silagraphene. • Our system consists of a silagraphene nanoribbon connected to two ferromagnetic electrodes (FM/Silagraphene/FM). • We employ Green function’s technique and Landauer–Butticer formalism. • We consider the conductance, magnetoresistance and spin transfer torque in this system for different strengths of ferromagnetic magnetization. • Our results demonstrate that the G, MR and STT show oscillatory behavior around Dirac point. • We found the n-type impurity is more suitable for dopping the system.

Computationally Efficient Region-Wise Potential- Based Extremely Closed-Form Analytical Modeling of B/N Substitution Doped GFETs

A simplified region-wise potential-based analytical model is established for boron (B) or nitrogen (N) substitution doped graphene field-effect transistor (GFET). The closed-form direct analytical relation between graphene channel potential and applied bias condition is developed by imposing the effective approximation for Fermi–Dirac integral function in various regions of operation. The boundary for distinct GFET operating regime is separated based on the position of Dirac point and Fermi energy level with respect to applied bias condition. The semiclassical drift and diffusive transport model is utilized to obtain the drain current. In addition to that, the drift component, diffusion coefficient, and its corresponding current component for B and N substitution doped GFETs have been modeled individually and their influence on total current is discussed. The proposed region-potential-based analytical model has shown good agreement with numerically solved self-consistent model. Also, the physical insights in device design, such as threshold voltage and saturation drain potential model with respect to various doping/device parameters, have been examined.

Nonperturbative Green's function method to determine the electronic spectral function due to electron-phonon interactions: Application to a graphene model from weak to strong coupling

In solid state physics, the electron-phonon interaction (EPI) is central to many phenomena. The theory of the renormalization of electronic properties due to EPIs became well established with the theory of Allen-Heine-Cardona, usually applied to second order in perturbation theory (P2). However, this is only valid in the weak coupling regime, while strong EPIs have been reported in many materials. Although non-perturbative (NP) methods have started to arise in the last years, they are usually not well justified, and it is not clear to what degree they reproduce the exact theory. To address this issue, we present a stochastic approach for the evaluation of the non-perturbative interacting Green's function in the adiabatic limit, and show it is equivalent to the Feynman expansion to all orders in the perturbation. Also, by defining a self-energy, we can reduce the effect of broadening needed in numerical calculations, improving convergence in the supercell size. In addition, we clarify whether it is better to average the Green's function or self-energy. Then we apply the method to a graphene tight-binding model, and obtain several interesting results: (i) The Debye-Waller term, which is normally neglected, does affect the change of the Fermi velocity. (ii) The P2 and NP self-energies differ even at room temperature for some k-points, raising the question of how well P2 works in other materials. (iii) Close to the Dirac point, positive and negative energy peaks merge. (iv) In the strong coupling regime, a peak appears at energy E=0, which is consistent with previous works on disorder and localization in graphene. (v) The spectral function becomes more asymmetric at stronger coupling and higher temperatures. Finally, in the Appendix we show that the method has better convergent properties when the coupling is strong relative to when it is weak, and discuss other technical aspects.

Modulation of the electronic state of carbon thin films by inorganic substrates

The control of the electronic states of carbon-based materials is of great importance for the widespread use of carbon materials as electronic devices and catalysts. This article reports a novel method of controlling the electronic states of carbon-based materials by establishing covalent bonds between inorganic support materials and carbon thin films. Carbon thin films of 1 nm thickness were grown on inorganic substrates (Al2O3, AlN, and ZrO2) using chemical vapor deposition. Covalent bond formation was confirmed between the substrates and the carbon films. The investigations of field effect transistor characteristics and work function revealed the different relationships between the Dirac points and Fermi levels of carbon films depending on the type of substrate. The Fermi level of the films grown on Al2O3 or ZrO2 was found to be lower than the Dirac point energy level, with the ZrO2 sample exhibiting the lowest Fermi level. In contrast, the Fermi level of the film grown on AlN was located at a higher energy than the Dirac point. The Fermi level of the carbon film depends on the inorganic substrate, and the change in the Fermi level can be explained by the nature of the covalent bonds between the substrate and the film.

Дифференциальная туннельная проводимость в многокомпонентных твердых растворах Bi-=SUB=-2-x-=/SUB=-Sb-=SUB=-x-=/SUB=-Te-=SUB=-3-y-z-=/SUB=-Se-=SUB=-y-=/SUB=-S-=SUB=-z-=/SUB=-

Differential tunnel conductance of the interlayer van der Waals surface (0001) was investigated in n-Bi2-xSbxTe3-y-zSeySz multicomponent solid solutions at x = 0.2, y = z = 0.09, optimized for near room temperatures with a high power factor, and at x = 0.4, y = 0, z = 0.06 with optimal thermoelectric properties for low temperatures and a high Seebek coefficient. It is shown that the intensity of the fluctuations of the Dirac point energy, a shift the top of the valence band and presence of surface levels in the energy gap formed by impurity defects is determined with composition and thermoelectric properties of solid solutions. The contribution of the surface states of Dirac fermions increases in n-Bi1.8Sb0.2Te2.82Se0.09S0.09 solid solution with a high power factor due to significant decrease of the surface concentration near the charge neutrality point and the growth of fermion mobility.

Proximity effect in a superconductor–topological insulator heterostructure based on first principles

Superconductor-topological insulator (SC-TI) heterostructures were proposed to be a possible platform to realize and control Majorana zero-modes. Despite experimental signatures indicating their existence, univocal interpretation of the observed features demands theories including realistic electronic structures. To achieve this, we solve the Kohn-Sham-Dirac-Bogoliubov-de Gennes equations for ultrathin Bi$_2$Se$_3$ films on superconductor PdTe, within the fully relativistic Korringa-Kohn-Rostoker method, and investigate quasiparticle spectra as a function of chemical potential and film thickness. We find a strongly momentum-dependent proximity-induced gap feature where the gap sizes highly depend on characteristics of the TI states. The interface TI Dirac state is relevant to the induced gap only when the chemical potential is close to the Dirac-point energy. Otherwise, at a given chemical potential, the largest induced gap arises from the highest-energy quantum-well states, whereas the smallest gap arises from the TI topological surface state with its gap size depending on the TI pairing potential.

DFT-based Engineering of Dirac Surface States in Topological-insulator Multilayers

A highly insulating bulk state and a tunable Dirac cone surface state are required for future spintronics device applications of spin-polarized surface states in three-dimensional topological insulators. Here, a slab model with heterostructural Bi2Se3-related quintuple layers is employed to conduct first-principles simulations. The computational results show that the Dirac-point energy can be optimally tuned by the selection of an appropriate pair of materials, so that the work function of the surface quintuple layer is slightly different from that of the inner quintuple layers. The ideal surface state is obtained in a Bi2Te3/(Bi2Te2Se)4/Bi2Te3 slab, in which the Fermi lines show a significant warping effect and both in-plane and out-of-plane components of spin polarization emerge.

STM and STS studies of topological n-type (Bi, In)2(Te, Se, S)3 thermoelectrics

In topological n-type thermoelectrics based on Bi2Te3 with atomic substitutions Bi → In, Te → Se, S, the morphology and the surface states of Dirac fermions on the interlayer (0001) surface of van der Waals were studied by scanning tunneling microscopy and spectroscopy (STM/STS) techniques. By the STM method, the dark and light spots on the surface were found, which intensities depend on the composition and thermoelectric properties of solid solutions such as the Seebeck coefficient and thermoelectric power factor. The observed surface morphology features in the solid solutions are explained by distortions of surface electronic states originated from atomic substitutions, the influence of doping impurity, and formation mainly of substitutional impurity defects in thermoelectrics. The dips associated with substitutional impurities and antisite defects were found from the analysis of the height profiles obtained on the (0001) surface. Fast Fourier transform of the morphology STM images of the (0001) surface were used to obtain the interference patterns of the quasiparticles excitation caused by surface electrons scattering by defects. The Dirac point energy and its fluctuations, peak energies of surface defects, the positions of the valence and conduction band edges, and the energy gap were determined from an analysis of tunneling spectra. A correlation between the parameters of surface states of Dirac fermions and thermoelectric properties was found. Thus, a contribution of the fermions surface states increases with rise of the surface concentration in solid solutions with high power factor, and the largest concentration value was observed in the Bi1.98In0.02Te2.85Se0.15 composition. The dependences of Fermi energy on the wave vector for different solid solutions are described by a set of Dirac cone sections located within the limits of the fluctuations of the Dirac point energy that explained by weak changes of the Fermi velocity for studied atomic substitutions in sublattices of bismuth telluride.

Strong and Weak 3D Topological Insulators Probed by Surface Science Methods

The contributions of surface science methods to discover and improve 3D topological insulator materials are reviewed herein, illustrated with examples from the authors’ own work. In particular, it is demonstrated that spin‐polarized angular‐resolved photoelectron spectroscopy is instrumental to evidence the spin‐helical surface Dirac cone, to tune its Dirac point energy toward the Fermi level, and to discover novel types of topological insulators such as dual ones or switchable ones in phase change materials. Moreover, procedures are introduced to spatially map potential fluctuations by scanning tunneling spectroscopy and to identify topological edge states in weak topological insulators.

Characterization of edge states in perturbed honeycomb structures

This paper is a mathematical analysis of conduction effects at interfaces between insulators. Motivated by work of Haldane-Raghu , we continue the study of a linear PDE initiated in papers of Fefferman-Lee-Thorp-Weinstein. This PDE is induced by a continuous honeycomb Schrodinger operator with a line defect. This operator exhibits remarkable connections between topology and spectral theory. It has essential spectral gaps about the Dirac point energies of the honeycomb background. In a perturbative regime, Fefferman-Lee-Thorp-Weinstein construct edge states: time-harmonic waves propagating along the interface, localized transversely. At leading order, these edge states are adiabatic modulations of the Dirac point Bloch modes. Their envelops solve a Dirac equation that emerges from a multiscale procedure. We develop a scattering-oriented approach that derives all possible edge states, at arbitrary precision. The key component is a resolvent estimate connecting the Schrodinger operator to the emerging Dirac equation. We discuss topological implications via the computation of the spectral flow, or edge index.

Geometry and electronic structure of iridium adsorbed on graphene

We report investigation of the geometry and electronic structure of iridium atoms adsorbed onto graphene through a combined experimental and theoretical study. Ir atoms were deposited onto a flake of graphene on a Pt(111) surface and found to form clusters even at low temperatures. The areal density of the observed clusters on the graphene flake suggests the clusters are most likely pairs of Ir atoms. Theoretical ab initio density functional (DFT) calculations indicate that these Ir dimers are oriented horizontally, near neighboring ``bridge'' sites of the graphene lattice, as this configuration has the strongest adsorption energy of all high-symmetry configurations for the Ir dimer. A large peak in the local density of states (LDOS) at the Dirac point energy was measured via scanning tunneling spectroscopy, and this result is reproduced by a DFT calculation of the LDOS. The peak at the Dirac point energy is found to be from the Ir $s$ and $p$ states. The LDOS in the monomer case was also calculated, and is found to significantly differ from the experimentally determined data, further supporting the hypothesis of low-temperature clustering.

Floquet states of valley-polarized metal with one-way spin or charge transport in zigzag nanoribbons

Two-dimensional Floquet systems consisting of irradiated valley-polarized metal are investigated. For the corresponding static systems, we consider two graphene models of valley-polarized metal with either a staggered sublattice or uniform intrinsic spin-orbital coupling, whose Dirac point energies are different from the intrinsic Fermi level. If the frequency of irradiation is appropriately designed, the largest dynamical gap (first-order dynamical gap) opens around the intrinsic Fermi level. In the presence of the irradiation, two types of edge states appear at the zigzag edge of the semi-infinite sheet with energy within the first-order dynamical gap: the Floquet edge states and the strongly localized edge states. In narrow zigzag nanoribbons, the Floquet edge states are gapped out by the finite-size effect and the strongly localized edge states remain gapless. As a result, the conducting channels of the nanoribbons consist of the strongly localized edge states. Under the first and second model, the strongly localized edge states carry one-way spin-polarized and one-way charge current around the intrinsic Fermi level, respectively. Thus, the narrow zigzag nanoribbons of the first and second model have asymmetric spin and charge transmission rates, respectively. Quantum-transport calculations predict sizable pumped currents of charge and spin, which could be controlled by the Fermi level.

Numerical analysis of surface and edge states in slabs, stripes, rods and surface steps of topological insulators

By numerically solving the effective continuous model of a topological insulator with parameters corresponding to the band structure of the topological insulator Bi2Se3, we analyze possible appearance of one-dimensional states in various geometries. Massless Dirac fermions are found at the edges of thin ribbons with surface oriented not only along the van der Waals gap but also in the perpendicular direction. Thick rods and slabs with surface steps host massive modes localized on surface faces. We argue that the the origin of the massive modes is due to the difference in the Dirac point energy of adjacent faces. The absence of one-dimensional states near edges of a large rectangular rod and surface steps is demonstrated.

Pressure-induced topological insulator-to-metal transition and superconductivity in Sn-doped Bi1.1Sb0.9Te2S

Tetradymite-type topological insulator Sn-doped $\mathrm{B}{\mathrm{i}}_{1.1}\mathrm{S}{\mathrm{b}}_{0.9}\mathrm{T}{\mathrm{e}}_{2}\mathrm{S}$ (Sn-BSTS), with a surface state Dirac point energy well isolated from the bulk valence and conduction bands, is an ideal platform for studying the topological transport phenomena. Here, we present high-pressure transport studies on single-crystal Sn-BSTS, combined with Raman scattering and synchrotron x-ray diffraction measurements. Over the studied pressure range of 0.7--37.2 GPa, three critical pressure points can be observed: (i) At $\ensuremath{\sim}9$ GPa, a pressure-induced topological insulator-to-metal transition is revealed due to closure of the bulk band gap, which is accompanied by changes in slope of the Raman frequencies and a minimum in $c$/$a$ within the pristine rhombohedral structure ($R\text{\ensuremath{-}}3m$); (ii) at $\ensuremath{\sim}13$ GPa, superconductivity is observed to emerge, along with the $R\text{\ensuremath{-}}3m$ to a $C2$/$c$ (monoclinic) structural transition; (iii) at $\ensuremath{\sim}24$ GPa, the superconducting transition onset temperature ${T}_{\mathrm{C}}$ reaches a maximum of $\ensuremath{\sim}12\phantom{\rule{0.16em}{0ex}}\mathrm{K}$, accompanied by a second structural transition from the $C2$/$c$ to a body-centered cubic $Im\text{\ensuremath{-}}3m$ phase.

Landauer-Büttiker conductivity for spatially-dependent uniaxial strained armchair-terminated graphene nanoribbons

The Landauer-Büttiker conductivity of arbitrary uniaxial spatially dependent strain in an armchair graphene nanoribbon is studied. Due to the uniaxial character of the strain, the corresponding transfer matrix can be reduced to a product of 2 × 2 matrices. Then the conductivity and the Fano factor can be calculated from this product. As an example of the technique, sinusoidal space dependent strain fields are studied using two different strain wavelengths. For the bigger wavelength the conductivity is reduced when compared with the unstrained case, although both conductivities are almost the same in shape. Whereas, for the smaller wavelength case, the conductivity is strongly modified. In spite of this, for energies close to the Dirac point energy, the conductivity and the Fano factor are quite similar to their unstrained counterpart for the two strain wavelengths here studied.

Fermi surface map of large-scale single-orientation graphene on SiO2

Large scale tetraoctylammonium-assisted electrochemical transfer of graphene grown on single-crystalline Ir(1 1 1) films by chemical vapour deposition is reported. The transferred samples are characterized in air with optical microscopy, Raman spectroscopy and four point transport measurements, providing the sheet resistance and the Hall carrier concentration. In vacuum we apply low energy electron diffraction and photoelectron spectroscopy that indicate transferred large-scale single orientation graphene. Angular resolved photoemission reveals a Fermi surface and a Dirac point energy which are consistent with charge neutral graphene.

Gate-tunable valley currents, nonlocal resistances, and valley accumulation in bilayer graphene nanostructures

Using the B\"{u}ttiker-Landauer formulation of transport theory in the linear response regime, the valley currents and non-local resistances of bilayer graphene nanostructures with broken inversion symmetry are calculated. It is shown that broken inversion symmetry in bilayer graphene nanostructures leads to striking enhancement of the non-local 4-terminal resistance and to valley currents several times stronger than the conventional electric current when the Fermi energy is in the spectral gap close to the energy of Dirac point. The scaling relation between local and non-local resistances is investigated as the gate voltage varies at zero Fermi energy and a power-law is found to be satisfied. The valley velocity field and valley accumulation in four-terminal bilayer graphene nanostructures are evaluated in the presence of inversion symmetry breaking. The valley velocity and non-local resistance are found to scale differently with the applied gate voltage. The unit cell-averaged valley accumulation is found to exhibit a dipolar spatial distribution consistent with the accumulation arising from the valley currents. We define and calculate a {\em valley capacitance} that characterizes the valley accumulation response to voltages applied to the nanostructure's contacts.