Electronic States Of Graphene Research Articles

Analogous electronic states in graphene and planer metallic quantum dots

Graphene nanostructures offer wide range of applications due to their distinguished and tunable electronic properties. Recently, atomic and molecular graphene were modeled following simple free-electron scattering by periodic muffin tin potential leading to remarkable agreement with density functional theory. Here we extend the analogy of the π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pi$$\\end{document}-electronic structures and quantum effects between atomic graphene quantum dots (QDs) and homogeneous planer metallic counterparts of similar size and shape. Specifically, we show that at high binding energies, below the M¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overline{M}$$\\end{document}-point gap, graphene QDs enclose confined states and standing wave quasiparticle interference patterns analogous to those reported on coinage metal surfaces for nanoscale confining structures such as vacancy islands and quantum corrals. These confined and quantum corral-like states in graphene QDs can be resolved in tomography experiments using angle-resolved photoemission spectroscopy. Likewise, the shape of near-Fermi frontier orbitals in graphene quantum dots can be reproduced from electron confinement within homogeneous metal QDs of identical size and shape. Furthermore, confined states analogous to those found in metallic quantum stadiums can be realized in coupled QDs of graphene for reduced separation. The present study offer a simple fundamental understanding of graphene electronic structures and also open the way towards efficient modeling of novel graphene-based nanostructures.

Spintronic properties of 2D heterostructures from laterally connected graphene and hBN quantum dots

2D heterostructures based on graphene/hBN nanodots are investigated using DFT calculations. They have ferromagnetic spin ordering with spin directly proportional to the number and size of the graphene nanodots. The wide energy gap of hBN acts as confinement potential for graphene electronic states, thus the resultant system is type-I heterojunction. An applied electric field converts the type-I to type-II heterojunction. The prominent excitation of the UV–Vis spectrum, at ∼4 eV, is equally contributed by transitions between spin-up and spin-down orbitals. The spectrum is redshifted to a lower energy by the electric field with excitations contributed mostly by spin-down transitions.

Effect of the number of graphene layers on the electron transfer kinetics at metal/graphene heterostructures

We theoretically investigated the kinetics of outer-sphere electron transfer (ET) at graphene with different number of layers in the presence and absence of metal substrates using density functional theory (DFT) calculations. It is shown that the experimental data on the electrocatalytic activity of the metal substrate for few-layer graphene can be explained under the assumption of the nonadiabatic electron transfer. However, the electron transfer at the metal-supported single-layer graphene is likely adiabatic. The enhanced electron transfer in the presence of the metal substrate is explained by the hybridization of the metal and graphene electronic states, which provides more efficient interaction of the metal substrate with the reactant near the graphene surface.

Realizing One-Dimensional Electronic States in Graphene via Coupled Zeroth Pseudo-Landau Levels.

Strain-induced pseudomagnetic fields can mimic real magnetic fields to generate a zero-magnetic-field analog of the Landau levels (LLs), i.e., the pseudo-Landau levels (PLLs), in graphene. The distinct nature of the PLLs enables one to realize novel electronic states beyond what is feasible with real LLs. Here, we show that it is possible to realize exotic electronic states through the coupling of zeroth PLLs in strained graphene. In our experiment, nanoscale strained structures embedded with PLLs are generated along a one-dimensional (1D) channel of suspended graphene monolayer. Our results demonstrate that the zeroth PLLs of the strained structures are coupled together, exhibiting a serpentine pattern that snakes back and forth along the 1D suspended graphene monolayer. These results are verified theoretically by large-scale tight-binding calculations of the strained samples. Our result provides a new approach to realizing novel quantum states and to engineering the electronic properties of graphene by using localized PLLs as building blocks.

Imaging the Spatial Distribution of Electronic States in Graphene Using Electron Energy-Loss Spectroscopy: Prospect of Orbital Mapping.

The spatial distributions of antibonding π^{*} and σ^{*} states in epitaxial graphene multilayers are mapped using electron energy-loss spectroscopy in a scanning transmission electron microscope. Inelastic channeling simulations validate the interpretation of the spatially resolved signals in terms of electronic orbitals, and demonstrate the crucial effect of the material thickness on the experimental capability to resolve the distribution of unoccupied states. This work illustrates the current potential of core-level electron energy-loss spectroscopy towards the direct visualization of electronic orbitals in a wide range of materials, of huge interest to better understand chemical bonding among many other properties at interfaces and defects in solids.

Many-particle electron states in graphene.

Scanning tunneling microscopy probes ground state competition in a magnetic field.

Reversible Switching of Charge Transfer at the Graphene-Mica Interface with Intercalating Molecules.

Understanding and controlling charge transfer through molecular nanostructures at interfaces is of paramount importance, particularly for electronic devices but also for contact electrification or in bioelectronics. We investigate the influence of intercalation and exchange of molecularly thin layers of small molecules (water, ethanol, 2-propanol, and acetone) on charge transfer at the well-defined interface between an insulator (muscovite mica) and a conductor (graphene). Raman spectroscopy is used to probe the charge carriers in graphene. While a molecular layer of water blocks charge transfer between mica and graphene, a layer of the organic molecules allows for it. The exchange of molecular water layers with ethanol layers switches the charge transfer very efficiently from off to on and back. We propose a charge transfer model between occupied mica trap states and electronic states of graphene, offset by the electrostatic potentials produced by the molecular dipole layers, as supported by molecular dynamics simulations. Our work demonstrates how intercalation of molecules of volatile liquids can reversibly affect charge transfer at interfaces. This implies its strong impact on the function of hybrid inorganic-organic electronic devices in different ambients and potential applications, including sensors and actuators.

Optical properties of graphene quantum dots: the role of chiral symmetry

We analyse the electronic and optical properties of graphene quantum dots (GQD) using accurate ab initio many-body GW and Bethe-Salpeter calculations. We show that most pristine GQD, including structures with irregular shapes, are characterized by dark low energy singlet excitations that quench fluorescence. We rationalize this property by exploiting the chiral symmetry of the low energy electronic states in graphene. Edge sp3 functionalization is shown to efficiently brighten these low lying excitations by distorting the sp2 backbone planar symmetry. Such findings reveal an original indirect scenario for the influence of functionalization on the photoluminescence properties.

Influence of defects in graphene on electron transfer kinetics: The role of the surface electronic structure

The kinetics of an outer-sphere nonadiabatic electron transfer reaction at the defective graphene is theoretically investigated. Different intrinsic and extrinsic point defects were analyzed. The band structure from DFT, in combination with the Gerischer model, was used for the predictions. Calculations were done taking into account the quantum capacitance of the surface for the correct prediction of alignment and occupation of graphene electronic states upon contact with an electrolyte. We have shown that an electrochemical property of graphene largely depends on defect type due to differences in the electronic structure induced by defects. Due to small graphene quantum capacitance, the electron transfer kinetics can be modulated by changes in the double-layer capacitance. The deviations of the potential dependence of the rate constant from the Butler-Volmer kinetics are predicted.

Hydrogenated-Graphene-Encapsulated Graphene: A Versatile Material for Device Applications.

Graphene and its heterostructures exhibit interesting electronic properties and are explored for quantum spin Hall effect (QSHE) and magnetism-based device applications. In present work, we propose a heterostructure of graphene encapsulated by hydrogenated-graphene, which could be a promising candidate for a variety of device applications. We have carried out DFT calculations on this system to check its feasibility to be a versatile material. We found that electronic states of multilayer pristine graphene, especially the Dirac cone, an important feature to host QSHE, can be preserved by sandwiching it by fully hydrogenated graphene. The interference of electronic states of hydrogenated graphene was insignificant with those of graphene. States of graphene were also found to be stable upon application of an electric field up to ±2.5 V/nm. For device applications, multilayer graphene or its heterostructures are required to be deposited on a substrate, which interacts with the system opening up a gap at the Dirac cone making it less suitable for QSHE applications, and hydrogenated graphene can prevent it. Magnetization in these hydrogenated-graphene-sandwiched graphene systems may be induced by creating vacancies or distortions in hydrogenated graphene, which was found to have a minimal effect on graphene’s electronic states, thus providing an additional degree of manipulation. We also performed a set of calculations to explore its applicability for detecting some molecules. Our results on trilayer graphene encapsulated by hydrogenated graphene indicate that all these observations can be generalized for systems with a larger number of graphene layers, indicating that multilayer graphene sandwiched between two hydrogenated graphene is a versatile material that can be used in QSHE and sensor devices.

Lazy electrons in graphene

Within a tight-binding approximation, we numerically determine the time evolution of graphene electronic states in the presence of classically vibrating nuclei. There is no reliance on the Born-Oppenheimer approximation within the p-orbital tight-binding basis, although our approximation is "atomically adiabatic": the basis p-orbitals are taken to follow nuclear positions. Our calculations show that the strict adiabatic Born-Oppenheimer approximation fails badly. We find that a diabatic (lazy electrons responding weakly to nuclear distortions) Born-Oppenheimer model provides a much more accurate picture and suggests a generalized many-body Bloch orbital-nuclear basis set for describing electron-phonon interactions in graphene.

Observation of intercalation-driven zone folding in quasi-free-standing graphene energy bands

Two-photon photoemission measurements reveal a near-zero-dispersion empty electronic state, approximately 2.6 eV above the Fermi energy and near the Brillouin zone center, induced by oxygen intercalation at the graphene-Ir(111) interface. While oxygen intercalation leads to quasi-free-standing graphene, electron diffraction shows $2\ifmmode\times\else\texttimes\fi{}2$ periodicity due to the patterned intercalant. Near the zone center, large-wave-vector zone folding, driven by this $2\ifmmode\times\else\texttimes\fi{}2$ periodicity, replicates states from near the Dirac cone that have little dispersion due to trigonal warping, explaining the nearly flat band. The zone-folding mechanism is supported by results from angle-resolved photoemission measurements and from density-functional-theory-based calculations of the unfolded energy bands. These results demonstrate zone-folding effects in graphene on a wave vector and energy scale that has largely been unexplored, and may open new opportunities to engineer the graphene electronic states.

Phonon-induced linewidths of graphene electronic states

The linewidths of the electronic bands originating from the electron-phonon coupling in graphene are analyzed based on model tight-binding calculations and experimental angle-resolved photoemission spectroscopy (ARPES) data. Our calculations confirm the prediction that the high-energy optical phonons provide the most essential contribution to the phonon-induced linewidth of the two upper occupied $\sigma$ bands near the $\bar{\Gamma}$-point. For larger binding energies of these bands, as well as for the $\pi$ band, we find evidence for a substantial lifetime broadening from interband scattering $\pi \rightarrow \sigma$ and $\sigma \rightarrow \pi$, respectively, driven by the out-of-plane ZA acoustic phonons. The essential features of the calculated $\sigma$ band linewidths are in agreement with recent published ARPES data [F. Mazzola et al., Phys.~Rev.~B. 95, 075430 (2017)] and of the $\pi$ band linewidth with ARPES data presented here.

Topological phases and twisting of graphene on a dichalcogenide monolayer

Depositing monolayer graphene on a transition metal dichalcogenide (TMD) semiconductor substrate has been shown to change the dynamics of the electronic states in graphene, inducing spin orbit coupling (SOC) and staggered potential effects. Theoretical studies on commensurate supercells have demonstrated the appearance of interesting phases, as different materials and relative gate voltages are applied. Here we address the effects of the real incommensurability between lattices by implementing a continuum model approach that does not require small-period supercells. The approach allows us to study the role of possible relative twists of the layers, and verify that the SOC transfer is robust to twists, in agreement with observations. We characterize the nature of the different phases by studying an effective Hamiltonian that fully describes the graphene-TMD heterostructure. We find the system supports topologically non-trivial phases over a wide range of parameter ranges, which require the dominance of the intrinsic SOC over the staggered and Rashba potentials. This tantalizing result suggests the possible experimental realization of a tunable quantum spin Hall phase under suitable conditions. We estimate that most TMDs used to date likely result in weak intrinsic SOC that would not drive the heterostructure into topologically non-trivial phases. Additional means to induce a larger intrinsic SOC, such as strain fields or heavy metal intercalation may be required.

Narrow photoluminescence and Raman peaks of epitaxial MoS2 on graphene/Ir(1 1 1)

We report on the observation of photoluminescence (PL) with a narrow 18 meV peak width from molecular beam epitaxy grown on graphene/Ir(1 1 1). This observation is explained in terms of a weak graphene-MoS2 interaction that prevents PL quenching expected for a metallic substrate. The weak interaction of MoS2 with the graphene is highlighted by angle-resolved photoemission spectroscopy and temperature dependent Raman spectroscopy. These methods reveal that there is no hybridization between electronic states of graphene and MoS2 as well as a different thermal expansion of both materials. Molecular beam epitaxy grown MoS2 on graphene is therefore an important platform for optoelectronics which allows for large area growth with controlled properties.

Exact Solution of the Problem of Bound Electronic States in Graphene

In graphene with a gap in the electronic spectrum, the problem of bound states of an electron in the field of an impurity ion with the charge Z is considered. Parameter Z is the effective ion charge; it includes the permittivity of graphene. Analytical solution of the Schrodinger equation in the problem under consideration leads to a formula which contains two numbers determining the quantum state of the electron: the total pseudospin moment and the radial quantum number. The sign of the effective screening ion charge Z determines the positions of levels near the conduction or valence band of graphene. Accordingly, the energy levels can be interpreted as donor or acceptor electronic states in the gap.

Magnetic field-, strain-, and disorder-induced responses in an energy spectrum of graphene

We study numerically a role of the uniaxial tensile strains and disordered defects in their impact on electronic density of states (DOS) in graphene exposed to an external magnetic field. The DOS curves are calculated using the tight-binding Hamiltonian, where the perpendicular magnetic field and uniaxial tension are included via the relevant modifications of the hopping parameters. Observed non-equidistant Landau levels (LLs) in the energy spectrum of a defectless graphene undergo the displacement towards the non-shiftable zero-energy Landau level (LL), thus they get contraction as the uniaxial tension is applied independently on the stretching direction. The presence of both point and extended defects reduces LLs peaks, broadens, smears, and can even suppress the LLs depending on a degree of disorders, their strength, and largely effective ranges. Splitting of the zero-energy LL is observable in case of a short-range disorder. Alteration of the localized electronic states in graphene is sensitive to the axis of strain: the uniaxial tensile strains along armchair- and zigzag-edge directions can result to competing phenomena associated with enhancement and reduction of the DOS, respectively. Mutual action of the perpendicular magnetic field and uniaxial stress along the zigzag-edge direction in graphene contributes to the band gap observed in its energy spectrum: the gap becomes more pronounced and even wider as compared with that emerges in case of a zigzag strain effect only, i.e. beyond magnetic field effect.

Supersymmetric quantum electronic states in graphene under uniaxial strain

We study uniaxially strained graphene under the influence of non-uniform magnetic fields perpendicular to the material sample with a coordinate independent strain tensor. For that purpose, we solve the Dirac equation with anisotropic Fermi velocity and explore the conditions upon which such an equation possesses a supersymmetric structure in the quantum mechanical sense through examples. Working in a Laudau-like gauge, wave functions and energy eigenvalues are found analytically in terms of the magnetic field intensity, the anisotropy scales and other relevant parameters that shape the magnetic field profiles.

Electron–Electron and Electron–Phonon Interactions in Graphene on a Semiconductor Substrate: Simple Estimations

The problem of epitaxial graphene formed on a semiconductor substrate is considered in the context of the extended Hubbard and Holstein–Hubbard models for electron–electron and electron–phonon interactions. The Haldane–Anderson model is chosen for the density of states of the substrate. Three regions of the phase diagram, specifically, spin- and charge-density waves and a spin- and charge-homogeneous paramagnetic state are considered. For a number of special cases used as examples, the similarities and differences of the electron states of graphene on semiconductor and metal substrates are demonstrated. It is shown that the main difference arises, if the Dirac point of graphene lies within the band gap of the semiconductor. Numerical estimations are performed for a SiC substrate.

Spin Proximity Effects in Graphene/Topological Insulator Heterostructures.

Enhancing the spin-orbit interaction in graphene, via proximity effects with topological insulators, could create a novel 2D system that combines nontrivial spin textures with high electron mobility. To engineer practical spintronics applications with such graphene/topological insulator (Gr/TI) heterostructures, an understanding of the hybrid spin-dependent properties is essential. However, to date, despite the large number of experimental studies on Gr/TI heterostructures reporting a great variety of remarkable (spin) transport phenomena, little is known about the true nature of the spin texture of the interface states as well as their role on the measured properties. Here, we use ab initio simulations and tight-binding models to determine the precise spin texture of electronic states in graphene interfaced with a Bi2Se3 topological insulator. Our calculations predict the emergence of a giant spin lifetime anisotropy in the graphene layer, which should be a measurable hallmark of spin transport in Gr/TI heterostructures and suggest novel types of spin devices.