Dirac Point Of Graphene Research Articles

An ab initio study of the ferroelectric In2Se3/graphene heterostructure

Using ab initio calculations, we have investigated the electronic structure properties of the ferroelectric α-In2Se3/graphene heterostructure. The presence of an intrinsic polarization in In2Se3 shifts the Dirac point of graphene above the Fermi level, resulting in a p-type doping, the degree of doping being dependent on the direction of the dipole with respect to the graphene layer. Also, we found that an external electric field can be used to control not only the degree of doping but also the type of Schottky contact, as n-type, p-type or Ohmic.

Reversible Switching of the Dirac Point in Graphene Field-Effect Transistors Functionalized with Responsive Polymer Brushes.

The reversible control of the graphene Dirac point using external chemical stimuli is of major interest in the development of advanced electronic devices such as sensors and smart logic gates. Here, we report the coupling of chemoresponsive polymer brushes to reduced graphene oxide (rGO)-based field-effect transistors to modulate the graphene Dirac point in the presence of specific divalent cations. Poly[2-(methacryloyloxy)ethyl] phosphate (PMEP) brushes were grown on the transistor channel by atom transfer radical polymerization initiated from amine-pyrene linkers noncovalently attached to rGO surfaces. Our results show an increase in the Dirac point voltage due to electrostatic gating effects upon the specific binding of Ca2+ and Mg2+ to the PMEP brushes. We demonstrate that the electrostatic gating is reversibly controlled by the charge density of the polymer brushes, which depends on the divalent cation concentration. Moreover, a theoretical formalism based on the Grahame equation and a Langmuir-type binding isotherm is presented to obtain the PMEP-cation association constant from the experimental data.

Electron mobility in graphene without invoking the Dirac equation

The Dirac point and linear band structure in graphene bestow it with remarkable electronic and optical properties, a subject of intense ongoing research. Explanations of high electronic mobility in graphene often invoke the masslessness of electrons based on the effective relativistic Dirac-equation behavior, which are inaccessible to most undergraduate students and are not intuitive for non-physics researchers unfamiliar with relativity. Here, we show how to use only basic concepts from semiconductor theory and the linear band structure of graphene to explain its unusual effective mass and mobility, and compare them with conventional metals and semiconductors. We discuss the more intuitive concept of transverse effective mass, which emerges naturally from these basic derivations, and which approaches zero in the limit of undoped graphene at low temperature and is responsible for its extremely high mobility.

Twist-angle dependence of the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides

We theoretically study the proximity spin-orbit coupling in graphene on transition-metal dichalcogenides monolayer stacked with arbitrary twist angles. We find that the relative rotation greatly enhances the spin splitting of graphene, typically by a few to ten times compared to the non-rotated geometry,and the maximum splitting is achieved around $20^\circ$. The induced SOC can be changed from the Zeeman-type to the Rashba-type by rotation. The spin-splitting is also quite sensitive to the gate-induced potential, and it sharply rises when the graphene's Dirac point is shifted toward the TMDC band. The theoretical method does not need the exact lattice matching and it is applicable to any incommensurate bilayer systems. It is useful for the twist-angle engineering of a variety of van der Waals proximity effects.

Ultrafast Monolayer In/Gr-WS2-Gr Hybrid Photodetectors with High Gain.

One of the primary limitations of previously reported two-dimensional (2D) photodetectors is a low frequency response (≪ 1 Hz) for sensitive devices with gain. Yet, little efforts have been devoted to improve the temporal response of photodetectors while maintaining high gain and responsivity. Here, we demonstrate a gain of 6.3 × 103 electrons per photon and a responsivity of 2.6 × 103 A/W while simultaneously exhibiting an ultrafast response time of 40-65 μs in a hybrid photodetector that consists of graphene-WS2-graphene junctions covered with indium (In) adatoms atop. The resultant responsivity is 6 orders of magnitude higher than that of conventional photodetectors comprising solely of a Au-WS2-Au junction. The photogain is provided mainly by the adsorbed In adatoms, from which photogenerated electrons can be transferred to the WS2 channel, while holes remain trapped in In adatoms, leading to a photogating effect as electrons are recirculating during the residence of holes in In adatoms. At a gate voltage near the Dirac point of graphene, a detectivity of D* = 2.2 × 1012 Jones and an ON/OFF ratio of 104 are achieved. The enhanced performance of the device can be attributed partly to the transparent graphene/WS2 contact and partly to the strong capacitive coupling of the In adatoms with the WS2 channel, which enables ultrafast carrier dynamics.

Giant intrinsic photoresponse in pristine graphene.

When the Fermi level is aligned with the Dirac point of graphene, reduced charge screening greatly enhances electron-electron scattering1-5. In an optically excited system, the kinematics of electron-electron scattering in Dirac fermions is predicted to give rise to novel optoelectronic phenomena6-11. In this paper, we report on the observation of an intrinsic photocurrent in graphene, which occurs in a different parameter regime from all the previously observed photothermoelectric or photovoltaic photocurrents in graphene12-20: the photocurrent emerges exclusively at the charge neutrality point, requiring no finite doping. Unlike other photocurrent types that are enhanced near p-n or contact junctions, the photocurrent observed in our work arises near the edges/corners. By systematic data analyses, we show that the phenomenon stems from the unique electron-electron scattering kinematics in charge-neutral graphene. Our results not only highlight the intriguing electron dynamics in the optoelectronic response of Dirac fermions, but also offer a new scheme for photodetection and energy harvesting applications based on intrinsic, charge-neutral Dirac fermions.

The Role of the Charge State of Surface Atoms of a Metal Substrate in Doping of Quasi-Free-Standing Graphene

To determine the effect of a metal substrate on the electronic state of quasi-free-standing graphene, a simple model taking into account the presence of the double electric layer on the metal surface is proposed. The arising electrostatic field shifts the Dirac point of graphene, which leads to its doping. An analytical expression for the charge of graphene atoms is obtained. Numerical estimations are made for (111) faces of Cu, Ag, Au, and Pt. The agreement of the obtained estimations with the available results of numerical calculations is discussed.

Bandgap opening in graphene using alkali ions by first principles

Recently, bandgap opening at the Dirac point in graphene, formed on SiC(0001) surfaces, has been reported in different experiments, by deposition of positively charged alkali ions. This is clearly of great relevance for the countless practical applications of graphene in nano-electronic devices. By first principles calculations, based on the Density Functional Theory, the electronic band structure and the energetic properties are obtained for Na+, K+, and Cs+ ions interacting with graphene on SiC. We show that simple adsorption of alkali ions on intact graphene cannot give rise to a significant energy gap. An appreciable bandgap opening, similar to that observed in actual experiments, occurs instead due to the formation of Stone-Wales defects and substitutional defects (where positively charged alkali ions replace carbon atoms) that lead to a significant breaking of the charge symmetry among the carbon atoms of pristine graphene.

True spin and pseudo spin entanglement around Dirac Points in graphene with Rashba spin–orbit interaction

We analytically obtained the Schmidt decomposition of the entangled state between the pseudo spin and the true spin in graphene with Rashba spin–orbit coupling. The entangled state has the standard form of the Bell state, where the SU(2) spin symmetry is broken. These states can be explicitly expressed as the superposition of two nonorthogonal, but mirror symmetrical spin states entangled with the pseudo spin states. Because of the closely locking between the pseudo spin and the true spin, it is found that the orbit curve in the spin-polarization parameter space for the fixed equi-energy contour around Dirac points has the same shape as the δk→-contour. Due to the spin–orbit coupling that cause the topological transition in the local geometry of the dispersion relation, the new equi-energy contours around the new emergent Dirac Points can be obtained by squeezing the one around the original Dirac point. The spin texture in the momentum space around the Dirac points is analyzed under the Rashba spin–orbit interaction and it is found that the orientation of the spin polarization at each crystal momentum k→ is independent of the Rashba coupling strength.

(Anti-)de Sitter, Poincaré, Super symmetries, and the two Dirac points of graphene

We propose two different high-energy-theory correspondences with graphene (and related materials) scenarios, associated to grain boundaries, that are topological defects for which both Dirac points are necessary. The first correspondence points to a (3+1)-dimensional theory, with nonzero torsion, with spatiotemporal gauge group SO(3,1), locally isomorphic to the Lorentz group in (3+1) dimensions, or to the de Sitter group in (2+1) dimensions. The other correspondence treats the two Dirac fields as an internal symmetry doublet, and it is linked here with unconventional supersymmetry with SU(2) internal symmetry. Our results are suggestive, rather than conclusive, and pave the way to the inclusion of grain boundaries in the emergent field theory picture associated with these materials, whereas disclinations and dislocations have been already well explored.

The Interaction between Quantum Dots and Graphene: The Applications in Graphene‐Based Solar Cells and Photodetectors

AbstractGraphene with a series of neoteric electronic and optical properties is an intriguing building block for optoelectronic devices. Over the past decade, graphene‐based solar cells (SCs) and photodetectors (PDs) which can convert light signals to electrical signals have received burgeoning exploration. However, limited light absorption hampers the performance of these devices. Quantum dots (QDs) possess a strong confinement effect, a large exciton energy, and long exciton lifetime, enhancing the interaction between incident light and graphene. Especially, as the density of states near the Dirac point of graphene is ultralow, it is easy to modify the Fermi level of graphene by inserting quantum dots at the interface between graphene and light, thereby enhancing the performance of graphene‐based optoelectronic devices. The characteristics of QDs and crucial physical mechanisms of the interaction and energy transfer in QDs/graphene nanohybrids are systematically addressed. The factors influencing the efficiency of energy transfer are also analyzed quantitatively. Moreover, the experimental process of QD‐enhanced technologies for SCs, photoconductors, phototransistors, and photodiode PDs is reviewed. Eventually, a conclusion is given and the remaining challenges and future development for QDs/2D materials hybrid systems is discussed. Possible steps toward large‐scale commercial applications and integration into optoelectronic networks are suggested.

Deciphering the origin of nonlocal resistance in multiterminal graphene on hexagonal-boron-nitride with ab initio quantum transport: Fermi surface edge currents rather than Fermi sea topological valley currents

The recent observation (Gorbachev et al 2014 Science 346 448) of nonlocal resistance RNL near the Dirac point (DP) of multiterminal graphene on aligned hexagonal-boron nitride (G/hBN) has been interpreted as the consequence of topological valley Hall currents carried by the Fermi sea states just beneath the bulk gap Eg induced by inversion symmetry breaking. However, the corresponding valley Hall conductivity , quantized inside Eg, is not directly measurable. Conversely, the Landauer–Büttiker formula, as a numerically exact approach to observable nonlocal transport quantities, yields RNL ≡ 0 for the same simplistic Hamiltonian of gapped graphene that generates via the Kubo formula. We combine ab initio with quantum transport calculations to demonstrate that G/hBN wires with zigzag edges host dispersive edge states near the DP that are absent in theories based on the simplistic Hamiltonian. Although such edge states exist also in isolated zigzag graphene wires, aligned hBN is required to modify their energy–momentum dispersion and generate near the DP. The Fermi surface-determined edge currents carrying the nonlocal signal persist also in the presence of edge disorder and over long distances. Concurrently, they resolve the long-standing puzzle of why the highly insulating state of G/hBN is rarely observed. Thus, we conclude that the observed RNL is unrelated to Fermi sea topological valley currents conjectured for gapped Dirac spectra.

Very high open-circuit voltage in dual-gate graphene/silicon heterojunction solar cells

Two dimensional (2D) layered materials and their heterojunctions with other materials are attracted because of their remarkable electrical and optical properties. In particular, graphene/semiconductor Schottky heterojunction is used for high performance solar cells. Here, we demonstrated very high open circuit voltage (Voc) in graphene/silicon heterojunction solar cell by dual-gate electric field application. The low density of states near Dirac point in graphene allows large modulation of graphene Fermi-level and corresponding Schottky barrier in a graphene/silicon junction. The top and bottom gate electric fields independently adjust the built-in potentials of respective upper and lower silicon energy band to induce higher band bending (1.22 eV) than the bandgap (1.12 eV). As a result, a maximum Voc of 0.94 V is achieved at the − 8 V of top-gate voltage and 10 V of bottom-gate voltage, exceeding highest known Voc for previous graphene/silicon solar cell (Voc = 0.61 V) and the S-Q Limit (0.84 V) of conventional silicon solar cell – a thermodynamic limit for the energy conversion efficiency of solar cells with a single band gap energy. The ratio of output power gain to input gate power (ΔPG/ΔPC) is approximately 1012–1014 with negligible power consumption in the gate (PC = 1 fW/cm2–10 pW/cm2), resulting in the significant advances in the power generation (PG = 40 mW/cm2).

Ultrasensitive Heterojunctions of Graphene and 2D Perovskites Reveal Spontaneous Iodide Loss

Summary Despite the demonstrated high efficiency of perovskite solar cells and light-emitting devices, the understanding of the intrinsic stability of perovskites is far from complete. In this work, using an ultrasensitive, exfoliated 2D perovskite single-crystal sheet/graphene heterostructure device, we reveal spontaneous iodide loss as an important degradation pathway of 2D perovskite single crystals, which n-dopes the perovskite semiconductor by generating positively charged iodide vacancies. Furthermore, we show that covering perovskites with graphene can suppress the iodide loss, significantly improving perovskite stability. A perovskite phototransistor is demonstrated with a graphene/2D perovskite/graphene structure, which shows no degradation after 75 days. Our work not only provides important insights for future stable perovskite optoelectronic device development, but also demonstrates the potential of graphene as a promising sensitive diagnostic tool for device and material degradation studies.

How Do Contact and Channel Contribute to the Dirac Points in Graphene Field‐Effect Transistors?

AbstractThe Dirac point(s) in graphene field‐effect transistors (GFETs) are of great importance for electronic application. However, the lack of the effective means to distinguish the electrical properties of graphene at the contact and channel regions limits a clear understanding of their contributions to the Dirac point(s). A method, which can characterize the electrical properties of graphene under metal contact and in the channel, is developed, respectively. It is found that the Fermi levels of graphene at the contact and channel regions are quite different in the GFETs. The difference in Fermi levels results in the penetration of the doping effect under the contact into the channel with a length as long as 1 µm. The difference also causes the double Dirac point feature in the long‐channel GFET due to the combined graphene properties both in contact and channel. One of the two Dirac points diminished in short‐channel GFET due to the penetration of doping effect under the contact. The study demonstrates that the electrical behavior of short‐channel GFET is dominated by the contact region. This paces a way to deeply understand and further improve the performances of GFETs by controlling the Fermi levels in the whole devices.

Driving-laser ellipticity dependence of high-order harmonic generation in graphene

High-order harmonic generation in graphene driven by the elliptically polarized midinfrared driving pulse is theoretically investigated by solving the two-band semiconductor Bloch equation in the Houston basis under the tight-binding approximation. It is found that the maximal harmonic yield occurs at a specific driver ellipticity whose value is determined by relaxation processes, so that the proper choice of the dephasing time is key to quantitatively reproducing the recent experiment. We show that the ellipticity dependence mainly originates from the interband harmonic emission, and exhibits an almost stable behavior against the crystal orientation. Furthermore, we also demonstrate that both the large magnitude and the circular vortex structure of the transition dipole near the graphene Dirac point are responsible for forming the unique characteristics. These results demonstrate that high-harmonic generation by the elliptically polarized driving field carries significant information on the dephasing time and the electronic structure signature in the graphene.

Valley filters, accumulators, and switches induced in graphene quantum dots by lines of adsorbed hydrogen atoms

We present electronic structure and quantum transport calculations that predict conducting channels induced in graphene quantum dots by lines of adsorbed hydrogen atoms to function as highly efficient, experimentally realizable valley filters, accumulators and switches. The underlying physics is a novel property of graphene Dirac point resonances (DPRs) that is revealed here, namely, that an electric current passing through a DPR-mediated conducting channel in a given direction is carried by electrons of em only one of the two graphene valleys. Our predictions apply to lines of hydrogen atoms adsorbed on graphene quantum dots that are either free standing or supported on a hexagonal boron nitride substrate.

Dirac Points, Spinons, and Spin Liquid in Twisted Bilayer Graphene

Twisted bilayer graphene is an excellent example of highly correlated system demonstrating a nearly flat electron band, the Mott transition and probably a spin liquid state. Besides the one-electron picture, analysis of Dirac points is performed in terms of spinon Fermi surface in the limit of strong correlations. Application of gauge field theory to describe deconfined spin liquid phase is treated. Topological quantum transitions, including those from small to large Fermi surface in the presence of van Hove singularities, are discussed.

Imaging Bulk and Edge Transport near the Dirac Point in Graphene Moiré Superlattices.

Van der Waals structures formed by aligning monolayer graphene with insulating layers of hexagonal boron nitride exhibit a moiré superlattice that is expected to break sublattice symmetry. Despite an energy gap of several tens of millielectronvolts opening in the Dirac spectrum, electrical resistivity remains lower than expected at low temperature and varies between devices. While subgap states are likely to play a role in this behavior, their precise nature is unclear. We present a scanning gate microscopy study of moiré superlattice devices with comparable activation energy but with different charge disorder levels. In the device with higher charge impurity (∼1010 cm-2) and lower resistivity (∼10 kΩ) at the Dirac point we observe current flow along the graphene edges. Combined with simulations, our measurements suggest that enhanced edge doping is responsible for this effect. In addition, a device with low charge impurity (∼109 cm-2) and higher resistivity (∼100 kΩ) shows subgap states in the bulk, consistent with the absence of shunting by edge currents.

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.