We develop a microscopic theory of a strong electromagnetic field interaction with gated bilayer graphene. Quantum kinetic equations for density matrix are obtained using a tight binding approach within second quantized Hamiltonian in an intense laser field. We show that adiabatically changing the gate potentials with time may produce (at resonant photon energy) a full inversion of the electron population with high density between valence and conduction bands. In the linear regime, excitonic absorption of an electromagnetic radiation in a graphene monolayer with opened energy gap is also studied.
We demonstrate that single layer graphene exhibits the electronic structure of a bilayer when it is connected to two gated bilayers. The energy gap characteristic for gated bilayer is induced in the single layer and it persists for distances separating the bilayers up to 20 nm. Most importantly, we report on the appearance of topologically protected gapless state localized in a single graphene layer when the distant bilayers differ in the stacking order. The one-dimensional current in the topological state flows in a single layer graphene, and this finding suggests a new exploitation of graphe…
We discuss the physics of the tunable bandgap in bilayer graphene with the gate voltage and doping. A comparison with experimental data obtained by Kuzmenko et al [Phys. Rev. B \textbf{80}, 165406 (2009)] demonstrates the good agreement.
The possibility of modulation of mid-IR radiation by low voltage gated single/multilayer graphene on Pb(ZrxTi1-x)O3 (PZT) ferroelectric substrate was demonstrated theoretically. The depth of modulation for 5 layer graphene for the range of gate voltages, where thin PZT epitaxial film behaves as high-κ dielectric, can be of 10% order.
We investigate gated trilayer graphene partially devoid of outer layers and forming a system of two trilayers connected by a single layer of graphene. A difference in the stacking order of trilayers leads to the appearance of gapless states, one of which is mainly localized in the single graphene layer. We demonstrate that by changing the value of the gate voltage applied to the outer layers one can change the slope of E(k) of this state. As a consequence the direction of current flowing in the single layer graphene can also be changed, the effect that could be useful in practical applications…
The resistance of dual-gated bilayer graphene is measured as a function of temperature and gating electric fields in the Corbino geometry which precludes edge transport. The temperature-dependent resistance is quantitatively described by a two channel conductance model including parallel thermal activation and variable range hopping channels, which gives the electric-field-dependent band gap whose magnitude is found to be in good agreement with infrared absorption experiments. Low temperature transport is similar to previous studies of dual-gated bilayer graphene with edges, suggesting that ed…
Double-gated graphene devices provide an important platform for understanding electrical and optical properties of graphene. Here we present transport measurements of single layer, bilayer and trilayer graphene devices with suspended top gates. In zero magnetic fields, we observe formation of pnp junctions with tunable polarity and charge densities, as well as a tunable band gap in bilayer graphene and a tunable band overlap in trilayer graphene. In high magnetic fields, the devices' conductance are quantized at integer and fractional values of conductance quantum, and the data are in good agr…
We study the electronic structure of gated graphene sheets. We consider both infinite graphene and finite width ribbons. The effect of Coulomb interactions between the electrically injected carriers and the coupling to the external gate are computed self-consistently in the Hartree approximation. We compute the average density of extra carriers, $n_{2D}$, the number of occupied subbands and the density profiles as a function of the gate potential $V_g$. We discuss quantum corrections to the classical capacitance and we calculate the threshold $V_g$ above which semiconducting armchair ribbons c…
We present transport measurements on a bilayer graphene sheet with homogeneous back gate and split top gate. The electronic transport data indicates the capability to direct electron flow through graphene nanostructures purely defined by electrostatic gating. By comparing the transconductance data recorded for different top gate geometries - continuous barrier and split-gate - the observed transport features for the split-gate can be attributed to interference effects inside the narrow opening.
Epitaxial graphene films were formed on the Si-face of semi-insulating 4H-SiC substrates by a high temperature sublimation process. A high-k gate stack on epitaxial graphene is realized by inserting a fully oxidized nanometer thin aluminum film as a seeding layer followed by an atomic-layer deposition process. The electrical properties of epitaxial graphene films are sustained after gate stack formation without significant degradation. At low temperatures, the quantum-Hall effect in Hall resistance is observed along with pronounced Shubnikov-de Hass oscillations in diagonal magneto-resistance …
We have developed the combination of an etching and deposition technique that enables the fabrication of locally gated graphene nanostructures of arbitrary design. Employing this method, we have fabricated graphene nanoconstrictions with local tunable transmission and characterized their electronic properties. An order of magnitude enhanced gate efficiency is achieved adopting the local gate geometry with thin dielectric gate oxide. A complete turn off of the device is demonstrated as a function of the local gate voltage. Such strong suppression of device conductance was found to be due to bot…
Conductivity of monolayer and two-layer graphene is considered with due regard for mutual drag of band electrons and holes. Search of contribution of the drag in conductivity shows that this effect can sufficiently influence on mobility of carriers, which belong to different groups and have different drift velocities. In two-layer system the mutual drag can even change the di-rection of partial current in separate layer.
We present measurements on side gated graphene constrictions of different geometries. We characterize the transport gap by its width in back gate voltage and compare this to an analysis based on Coulomb blockade measurements of localized states. We study the effect of an applied side gate voltage on the transport gap and show that high side gate voltages lift the suppression of the conductance. Finally we study the effect of an applied magnetic field and demonstrate the presence of edge states in the constriction.
The electronic structure and optical response of electrically gated bilayer graphene are studied by first-principles approaches. We have obtained the induced band gap that is in good agreement with experiment when the applied electric field is less than 1.5 V/nm. The infrared optical absorbance is calculated within the single-particle excitation picture and its fine structures are presented. In addition, the calculated infrared optical absorbance is found to be strongly depending on stacking styles of bilayer graphene and the polarization direction of the incident light, which provides efficie…
The electronic structure of multilayer graphenes depends strongly on the number of layers as well as the stacking order. Here we explore the electronic transport of purely ABA-stacked trilayer graphenes in a dual-gated field-effect device configuration. We find that both the zero-magnetic-field transport and the quantum Hall effect at high magnetic fields are distinctly different from the monolayer and bilayer graphenes, and that they show electron-hole asymmetries that are strongly suggestive of a semimetallic band overlap. When the ABA trilayers are subjected to an electric field perpendicul…
We report on asymmetric electron-hole decoherence in epitaxial graphene gated by an ionic liquid. The observed negative magnetoresistance near zero magnetic field for different gate voltages, analyzed in the framework of weak localization, gives rise to distinct electron-hole decoherence. The hole decoherence rate increases prominently with decreasing negative gate voltage while the electron decoherence rate does not exhibit any substantial gate dependence. Quantitatively, the hole decoherence rate is as large as the electron decoherence rate by a factor of two. We discuss possible microscopic…
We study the electronic transport properties of dual-gated bilayer graphene devices. We focus on the regime of low temperatures and high electric displacement fields, where we observe a clear exponential dependence of the resistance as a function of displacement field and density, accompanied by a strong non-linear behavior in the transport characteristics. The effective transport gap is typically two orders of magnitude smaller than the optical band gaps reported by infrared spectroscopy studies. Detailed temperature dependence measurements shed light on the different transport mechanisms in …
Gated bilayer graphene exhibits spin-degenerate gapless states with a topological character localized at stacking domain walls. These states allow for one-dimensional currents along the domain walls. We herein demonstrate that these topologically protected currents are spin -polarized and locked in a single layer when bilayer graphene contains stacking domain walls decorated with magnetic defects. The magnetic defects, which we model as π-vacancies, perturb the topological states but also lift their spin degeneracy. One gapless state survives the perturbation of these defects, and its spin pol…
We report on transport properties in dual-gated hexagonal boron nitride (hBN)/bilayer-graphene (BLG) superlattices. Here, BLG is nontwisted, i.e., plain. This paper focuses on the charge neutrality point (CNP) for a plain BLG. Under a perpendicular magnetic field, transitions between two insulating phases at the CNP are detected by varying a displacement field with the study on the resistance-temperature characteristics and the magnetoresistance. This work opens avenues for exploring the global phase diagram of the hBN/BLG superlattices beyond the CNP.
We investigate the magnetoresistance of a side-gated ring structure etched out of single-layer graphene. We observe Aharonov-Bohm oscillations with about 5% visibility. We are able to change the relative phases of the wave functions in the interfering paths and induce phase jumps of pi in the Aharonov-Bohm oscillations by changing the voltage applied to the side gate or the back gate. The observed data can be well interpreted within existing models for 'dirty metals' giving a phase coherence length of the order of 1 micrometer at a temperature of 500mK.
A Raman study of a back gated bilayer graphene sample is presented. The changes in the Fermi level induced by charge transfer splits the Raman G-band, hardening its higher component and softening the lower one. These two components are associated with the symmetric (S) and anti-symmetric vibration (AS) of the atoms in the two layers, the later one becoming Raman active due to inversion symmetry breaking. The phonon hardening and softening are explained by considering the selective coupling of the S and AS phonons with interband and intraband electron-hole pairs.
We report simultaneous transport and scanning microwave impedance microscopy to examine the correlation between transport quantization and filling of the bulk Landau levels in the quantum Hall regime in gated graphene devices. Surprisingly, a comparison of these measurements reveals that quantized transport typically occurs below the complete filling of bulk Landau levels, when the bulk is still conductive. This result points to a revised understanding of transport quantization when carriers are accumulated by gating. We discuss the implications on transport study of the quantum Hall effect in…
Gated trilayer graphene exhibits energy gap in its most stable ABC stacking. Here we show that when the stacking order changes from ABC to CBA, three gapless states appear in each valley. The states are topologically protected and their number is related to the change of the valley Chern number across the stacking boundary. The stacking change is achieved by corrugation or delamination in the top and bottom layers, which simultaneously yields two AB/BA stacking domain walls in the pairs of adjacent layers (in bilayers). This in turn causes that for some gate voltages two pairs of topological r…
Four-terminal resistances, both longitudinal and diagonal, of a locally gated graphene device are measured in the quantum-Hall (QH) regime. In sharp distinction from previous two-terminal studies [J. R. Williams \textit{et al.}, Science {\bf 317}, 638 (2007); B. Özyilmaz \textit{et al.}, Phys. Rev. Lett. {\bf 99}, 166804 (2007)], asymmetric QH resistances are observed, which provide information on reflection as well as transmission of the QH edge states. Most quantized values of resistances are well analyzed by the assumption that all edge states are equally populated. Contrary to the expectat…
We present a fabrication process for high quality suspended and double gated trilayer graphene devices. The electrical transport measurements in these transistors reveal a high charge carrier mobility (higher than 20000 cm^2/Vs) and ballistic electric transport on a scale larger than 200nm. We report a particularly large on/off ratio of the current in ABC-stacked trilayers, up to 250 for an average electric displacement of -0.08 V/nm, compatible with an electric field induced energy gap. The high quality of these devices is also demonstrated by the appearance of quantum Hall plateaus at magnet…
We show simultaneous p and n type carrier injection in bilayer graphene channel by varying the longitudinal bias across the channel and the top gate voltage. The top gate is applied electrochemically using solid polymer electrolyte and the gate capacitance is measured to be 1.5 $μF/cm^2$, a value about 125 times higher than the conventional SiO$_2$ back gate capacitance. Unlike the single layer graphene, the drain-source current does not saturate on varying the drain-source bias voltage. The energy gap opened between the valence and conduction bands using top and back gate geometry is estimate…
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.…
Galvanomagnetic effects in graphene Magnetoresistivity and Hole-effect were theoretically investigated for neutral and gated graphene. It is shown that in neutral graphene Hall-effect is totally absent. In gated, exactly monopolar graphene effect of magnetoresistivity vanishes; here Hall-constant does not involve any relaxation characteristic in contrast to result obtained for popular method of relaxation time approximation.
We study the effect of electron-electron interactions in the optical conductivity of graphene under applied bias and derive a generalization of Elliot's formula, commonly used for semiconductors, for the optical intensity. We show that {\it excitonic resonances} are responsible for several features of the experimentally measured mid-infrared response of graphene such as the increase of the conductivity beyond the "universal" value above the Fermi blocked regime, the broadening of the absorption at the threshold, and the decrease of the optical conductivity at higher frequencies. Our results ar…
The photovoltaic and bolometric photoresponse in gapped bilayer graphene was investigated by optical and transport measurements. A pulse coincidence technique at 1.5 um was used to measure the response times as a function of temperature. The bolometric and photovoltaic response times were found to be identical implying that the photovoltaic response is also governed by hot electron thermal relaxation. Response times of tau ~ 100 - 20 ps were found for temperatures from 3 - 100 K. Above 10 K, the relaxation time was observed to be tau = 25 +/- 5 ps, independent of temperature within noise.
Graphene field-effect transistors are widely used for development of biosensors. However, certain fundamental questions about details of their functioning are not fully understood yet. One of these questions is the presence of gate (leakage) currents in the electrolyte-gated configuration. Here, we report our observations considering causes of this phenomena on chemical vapor deposition (CVD) grown graphene. We observed that gate currents reflect currents that occur on the transistor surface similarly to a working electrode - counter electrode pair currents in an electrochemical cell. Gate cur…
Quantum dynamics and kinetics of electrically gated graphene ribbons with lateral n-p and e-n-p junctions under magnetic field are investigated. It is shown that the snake-like states of quasiparticles skipping along the n-p interface do not manifest themselve in the main semiclassical part of the ribbon conductance. Giant oscillations of the conductance of a ribbon with an n-p-n junction are predicted and analytically calculated. Depending on the number of junctions inside the ribbon its magnetoresistance may be controllably changed by 50% - 90% by an extremely small change of the magnetic fi…
Mechanism of transient population inversion in graphene with multi-splitted (interdigitated) top-gate and grounded back gate is suggested and examined for the mid-infrared (mid-IR) spectral region. Efficient stimulated emission after fast lateral spreading of carriers due to drift-diffusion processes is found for the case of a slow electron-hole recombination in the passive region. We show that with the large gate-to-graphene distance the drift process always precedes the diffusion process, due to the ineffective screening of the inplane electric field by the gates. Conditions for lasing with …
We demonstrate top-gated field effect transistor made of reduced graphene oxide (RGO) monolayer (graphene) by dielectrophoresis. Raman spectrum of RGO flakes of typical size of 5μm x 5μm show a single 2D band at 2687 cm-1, characteristic of a single layer graphene. The two probe current - voltage measurements of RGO flakes, deposited in between the patterned electrodes with a gap of 2.5 μm using a.c. dielectrophoresis show ohmic behavior with a resistance of ~ 37kΩ. The temperature dependence of the resistance (R) of RGO measured between temperatures 305 K to 393 K yields temperature coefficie…
Coherent spin-dependent transport through a junction containing of Normal/Ferromagnetic/Normal bilayer graphene nanoribbon with zigzag edges is investigated by using Landauer formalism. In a more realistic set-up, the exchange field is induced by two ferromagnetic insulator strips deposited on the ribbon edges while a perpendicular electric field is applied by the top gated electrodes. Our results show that, for antiparallel configuration, a band gap is opened giving rise a semiconducting behavior, while for parallel configuration, the band structure has no band gap. As a result, a giant magne…
We present a novel measurement approach which combines the electrical characterization of solution-gated field effect transistors based on epitaxial bilayer graphene on 4H-SiC (0001) with simultaneous Raman spectroscopy. By changing the gate voltage, we observed Raman signatures related to the resonant electron-phonon coupling. An analysis of these Raman bands enabled the extraction of the geometrical capacitance of the system and an accurate calculation of the Fermi levels for bilayer graphene. An intentional application of higher gate voltages allowed us to trigger electrochemical reactions,…
We report on quantum-interference measurements in top-gated Hall bars of monolayer graphene epitaxially grown on the Si face of SiC, in which the transition from negative to positive magnetoresistance was achieved varying temperature and charge density. We perform a systematic study of the quantum corrections to the magnetoresistance due to quantum interference of quasiparticles and electron-electron interaction. We analyze the contribution of the different scattering mechanisms affecting the magnetotransport in the $-2.0 \times 10^{10}$ cm$^{-2}$ to $3.75 \times 10^{11}$ cm$^{-2}$ density reg…
Metal-semiconductor interfaces, known as Schottky junctions, have long been hindered by defects and impurities. Such imperfections dominate the electrical characteristics of the junction by pinning the metal Fermi energy. We report measurements on a boron nitride encapsulated graphene-tungsten diselenide (WSe$_2$) Schottky junction which exhibits ideal diode characteristics and a complete lack of Fermi-level pinning. The Schottky barrier height of the device is rigidly tuned by electrostatic gating of the WSe$_2$, enabling experimental verification of the Schottky-Mott limit in a single device…
Graphene/silicon (G/Si) heterojunction based devices have been demonstrated as high responsivity photodetectors that are potentially compatible with semiconductor technology. Such G/Si Schottky junction diodes are typically in parallel with gated G/silicon dioxide (SiO$_2$)/Si areas, where the graphene is contacted. Here, we utilize scanning photocurrent measurements to investigate the spatial distribution and explain the physical origin of photocurrent generation in these devices. We observe distinctly higher photocurrents underneath the isolating region of graphene on SiO$_2$ adjacent to the…
Detection of infrared light is central to diverse applications in security, medicine, astronomy, materials science, and biology. Often different materials and detection mechanisms are employed to optimize performance in different spectral ranges. Graphene is a unique material with strong, nearly frequency-independent light-matter interaction from far infrared to ultraviolet, with potential for broadband photonics applications. Moreover, graphene's small electron-phonon coupling suggests that hot-electron effects may be exploited at relatively high temperatures for fast and highly sensitive det…
We describe the results of a theoretical study of transport through gated metallic graphene nanoribbons using a non-equilibrium Green function method. Although analogies with quantum field theory predict perfect transmission of chiral fermions through gated regions in one dimension, we find \emph{perfect reflection} of chiral fermions in armchair ribbons for specific configurations of the gate. This effect should be measurable in narrow graphene constrictions gated by a charged carbon nanotube.
We study the effect of local modulation of charge density and carrier type in graphene field effect transistors using a double top gate geometry. The two top gates lead to the formation of multiple \emph{p-n} junctions. Electron transport measurements at low temperature and in the presence of magnetic field show various integer and fractionally quantized conductance plateaus. We explain these results based on the mixing of the edge channels and find that inhomogeneity plays an important role in defining the exact quantization of these plateaus, an issue critical for the metrology applications …
We investigate the effects of homogeneous and inhomogeneous deformations and edge disorder on the conductance of gated graphene nanoribbons. Under increasing homogeneous strain the conductance of such devices initially decreases before it acquires a resonance structure, and finally becomes completely suppressed at larger strain. Edge disorder induces mode mixing in the contact regions, which can restore the conductance to its ballistic value. The valley-antisymmetric pseudo-magnetic field induced by inhomogeneous deformations leads to the formation of additional resonance states, which either …
The fate of the low-temperature conductance at the charge-neutrality (Dirac) point in a single sheet of graphene is investigated down to 20 mK. As the temperature is lowered, the peak resistivity diverges with a power-law behavior and becomes as high as several Megohms per square at the lowest temperature, in contrast with the commonly observed saturation of the conductivity. As a perpendicular magnetic field is applied, our device remains insulating and directly transitions to the broken-valley-symmetry, nu=0 quantum Hall state, indicating that the insulating behavior we observe at zero magne…
We compare the conductance of an undoped graphene sheet with a small region subject to an electrostatic gate potential for the cases that the dynamics in the gated region is regular (disc-shaped region) and classically chaotic (stadium). For the disc, we find sharp resonances that narrow upon reducing the area fraction of the gated region. We relate this observation to the existence of confined electronic states. For the stadium, the conductance looses its dependence on the gate voltage upon reducing the area fraction of the gated region, which signals the lack of confinement of Dirac quasipar…
We have fabricated a centimeter-size single-layer graphene device, with a gate electrode, which can modulate the transmission of terahertz and infrared waves. Using time-domain terahertz spectroscopy and Fourier-transform infrared spectroscopy in a wide frequency range (10-10000 cm^{-1}), we measured the dynamic conductivity change induced by electrical gating and thermal annealing. Both methods were able to effectively tune the Fermi energy, E_F, which in turn modified the Drude-like intraband absorption in the terahertz as well as the '2E_F onset' for interband absorption in the mid-infrared…
In this work we study the behavior of the optical phonon modes in bilayer graphene devices by applying top gate voltage, using Raman scattering. We observe the splitting of the Raman G band as we tune the Fermi level of the sample, which is explained in terms of mixing of the Raman (Eg) and infrared (Eu) phonon modes, due to different doping in the two layers. We theoretically analyze our data in terms of the bilayer graphene phonon self-energy which includes non-homogeneous charge carrier doping between the graphene layers. We show that the comparison between the experiment and theoretical mo…
Electric transport of double gated bilayer graphene devices is studied as a function of charge density and bandgap. A top gate electrode can be used to control locally the Fermi level to create a pn junction between the double-gated and single-gated region. These bilayer graphene pn diodes are characterized by non-linear currents and directional current rectification, and we show the rectified direction of the source-drain voltage can be controlled by using gate voltages. A systematic study of the pn junction characteristics allows to extract a gate-dependent bandgap value which ranges from 0 …
The effects of Coulomb interactions on the electronic properties of bilayer graphene nanoribbons (BGNs) covered by a gate electrode are studied theoretically. The electron density distribution and the potential profile are calculated self-consistently within the Hartree approximation. A comparison to their single-particle counterparts reveals the effects of interactions and screening. Due to the finite width of the nanoribbon in combination with electronic repulsion, the gate-induced electrons tend to accumulate along the BGN edges where the potential assumes a sharp triangular shape. This has…
We investigate the conductivity of graphene sheet deformed over a gate. The effect of the deformation on the conductivity is twofold: The lattice distortion can be represented as pseudovector potential in the Dirac equation formalism, whereas the gate causes inhomogeneous density redistribution. We use the elasticity theory to find the profile of the graphene sheet and then evaluate the conductivity by means of the transfer matrix approach. We find that the two effects provide functionally different contributions to the conductivity. For small deformations and not too high residual stress the …
We demonstrate that the carrier concentration of epitaxial graphene devices grown on the C-face of a SiC substrate is efficiently modulated by a buried gate. The gate is fabricated via the implantation of nitrogen atoms in the SiC crystal, 200 nm below the surface, and works well at intermediate temperatures: 40K-80K. The Dirac point is observed at moderate gate voltages (1-20V) depending upon the surface preparation. For temperatures below 40K, the gate is inefficient as the buried channel is frozen out. However, the carrier concentration in graphene remains very close to the value set at T\s…
Understanding the origin of hysteresis in the channel resistance from top gated graphene transistors is important for transistor applications. Capacitance - voltage measurements across the gate oxide on top gated bilayer graphene show hysteresis with a charging and discharging time constant of ~100 μs. However, the measured capacitance across the graphene channel does not show any hysteresis, but shows an abrupt jump at a high channel voltage due to the emergence of an order, indicating that the origin of hysteresis between gate and source is due to charge traps present in the gate oxide and g…
Graphene-based heterostructures display a variety of phenomena that are strongly tunable by electrostatic local gates. Monolayer graphene (MLG) exhibits tunable surface plasmon polaritons, as revealed by scanning nano-infrared experiments. In bilayer graphene (BLG), an electronic gap is induced by a perpendicular displacement field. Gapped BLG is predicted to display unusual effects such as plasmon amplification and domain wall plasmons with significantly larger lifetime than MLG. Furthermore, a variety of correlated electronic phases highly sensitive to displacement fields have been observed …
Electronic current densities can reach extreme values in highly conducting nanostructures where constrictions limit current. For bias voltages on the 1 volt scale, the highly non-equilibrium situation can influence the electronic density between atoms, leading to significant inter-atomic forces. An easy interpretation of the non-equilibrium forces is currently not available. In this work, we present an ab-initio study based on density functional theory of bias-induced atomic forces in gated graphene nanoconstrictions consisting of junctions between graphene electrodes and graphene nano-ribbons…
The non-interacting energy spectrum of graphene and its bilayer counterpart consists of multiple degeneracies owing to the inherent spin, valley and layer symmetries. Interactions among charge carriers are expected to spontaneously break these symmetries, leading to gapped ordered states. In the quantum Hall regime these states are predicted to be ferromagnetic in nature whereby the system becomes spin polarized, layer polarized or both. In bilayer graphene, due to its parabolic dispersion, interaction-induced symmetry breaking is already expected at zero magnetic field. In this work, the unde…
Based on the standard tight-binding model of the graphene $π$-band electronic structure, the extended Hückel model for the adsorbate and graphene carbon atoms, and spin splittings estimated from density functional theory (DFT), the Dirac point resonances due to a single cobalt atom on graphene are studied. The relaxed geometry of the magnetic adsorbate and the graphene is calculated using DFT. The system shows strong spin polarization in the vicinity of the graphene Dirac point energy for all values of the gate voltage, due to the spin-splitting of Co 3d orbitals. We also model the differentia…
We analyze the response of bilayer graphene to an external transverse electric field using a variational method. A previous attempt to do so in a recent paper by Falkovsky [Phys. Rev. B 80, 113413 (2009)] is shown to be flawed. Our calculation reaffirms the original results obtained by one of us [E. McCann, Phys. Rev. B 74, 161403(R) (2006)] by a different method. Finally, we generalize these original results to describe a dual-gated bilayer graphene device.
