Gapless Graphene Research Articles

Surface acoustic wave amplification by drifting electrons in semiconducting epitaxial graphene on silicon carbide

Abstract A theory is presented for the amplification of a surface acoustic wave (SAW) due to its interaction with conduction electrons in gate-controlled epitaxial graphene (epigraphene) on a SiC substrate. It is assumed that the SAW is launched onto the substrate in the direction of an external dc electric field applied to the graphene sample and causing the conduction electrons to drift at a speed greater than the speed of the SAW. The wavelength of the SAW is assumed to be shorter than the mean free path of the electrons, so that the quantum regime of interaction of those electrons with the SAW is realized. The Green’s function method is used to calculate the SAW gain as a function of the electron concentration in epigraphene and the external dc electric field strength. It is shown that the substrate-induced band gap in the electronic spectrum of epigraphene leads to a significant (at least an order of magnitude) increase in the SAW gain as compared to the case of gapless graphene. In addition, the opening of the band gap results in a non-monotonic dependence of the SAW gain on the electron concentration, controlled by the gate voltage applied to the graphene sample. This dependence is characterized by the presence of a distinct maximum at a certain value of electron concentration (of about 2 × 10 12 cm−2 for typical values of the other parameters involved), which distinguishes it from the monotonic concentration dependence of the SAW gain in gapless graphene.

Al/Si dopants effect on the electronic and optical behaviors of graphene mono-layers useful for infrared detector devices

Two-dimensional (2D) graphene with different forms is a prosperous class of materials beneficial in nano-electronics, and infrared-detector devices. Herein, we analyze the electronic and optical behaviours of electron acceptor (Al)- and isovalent (Si) inserted into graphene sheets, which are computed by utilizing ab-initio simulations. We find that the individual doping impurities of Al or Si atoms onto monolayer graphene result in p-type and semiconducting behaviours, respectively, attributed to the contribution of the valence electrons number of these atoms to the host 2D honeycomb lattice of graphene. Even though the Al atom contributing one less electron to the host lattice, both individual impurities of the Al- or Si-doped materials are found to cause a splitting in the valence states and conduction states at the K-point, leading to the opening of the Dirac cone. In monolayer graphene, doping two Al atoms into the nearest neighbour sites creates a trivial metallic system, while doping two Si atoms into the nearest neighbour sites causes the Dirac cone to re-emerge. Owing to the stark difference in the electronic structure results of mono- and double-atom substitution of Al/Si in graphene single-layers, we find different optical behaviours in these doped systems. Additionally, X-ray absorption spectroscopy simulations are employed to inspect the core-level spectra of pure and substitutional doped graphene single layers. Accordingly, the optical spectral features of graphene single-layers substituted with foreign impurities, such as Al/Si have revealed the tailoring of optical absorption from the infrared to the visible windows. Due to the outstanding characteristics of this 2D dimensional gapless graphene, our simulated results could provide a guidance for future experimental investigations into the fabrication of doped graphene sheets suitable for infrared detectors, photonics, and modern optoelectronic devices integrated into advanced technologies.

Dirac electron in gapped graphene under exponentially decaying magnetic field

In this work, we present a Dirac electron in gapped graphene under the exponentially decaying magnetic field. Solving Dirac-Weyl equations, we obtain exact expressions of the eigenfunctions and their corresponding eigenvalues. The probability density and current distributions are also investigated in detail. The results are compared to those in the gapless graphene as well as in the gapped graphene in the presence of a uniform magnetic field.

First Principles Study and Experimental Investigation of Graphene-Molybdenum Disulphide Nanocomposites Based Passive Saturable Absorber

Research on hybrid graphene with other two-dimensional materials has gained considerable attention owing to their potential applications beyond single components. Through our first principles analysis via density functional theory, graphene-molybdenum disulphide (MoS2) demonstrated a band gap opening by 2 meV, from gapless graphene when MoS2 layer is introduced into the structure. The simulated graphene-MoS2 has a direct band gap situated at K point of Brillouin zone with preserved Dirac properties of graphene. The experimental studies on graphene-MoS2 also have been performed by preparing graphene-MoS2-chitin nanocomposite through facile liquid-phase exfoliation method. Apart from energy gap using Tauc relation, the physical morphology and nonlinear properties of the material were systematically characterized. Graphene-MoS2-chitin exhibits a modulation depth of 10.5%, which is lower than individual graphene but higher than individual MoS2. Further investigation on the material’s performance was done by integrating the fabricated film into Erbium-doped fiber laser. Stable nanosecond pulse laser operation was realized with graphene-MoS2-chitin hybrid saturable absorber. The pulse width was measured to be 156.4 ns with repetition rate of 1.89 MHz, corresponding to a peak power of 56.13 mW and pulse energy of 8.78 nJ.

Analog and Digital Performance of Graphene-Germanene-Graphene Heterojunction Based Field Effect Transistor

In this study, by taking the advantage of electrical properties of graphene, silicene and germanene sheets we propose and analyze a heterojunction based field effect transistor. It is comprised of germanene sheet in the channel and gapless graphene in the source/drain regions. We investigate and compare the performances of proposed device from two points of view comprised of analog and digital applications. A comparative study is carried out with three other simulated devices including gapless graphene, germanene and graphene-silicene-graphene heterojunction based field effect transistors. Our theoretical analysis show that for digital applications, Ion/Ioff ratio in the proposed graphene-germanene-graphene (G-Ge-G) heterojunction based field effect transistor shows a significant better value than other counterpart simulated devices and reaches to 106. However for the analog applications, the output characteristic curves show different behavior for the simulated devices under study. The output characteristic of (G-Ge-G) heterojunction based field effect transistor displays a very good saturation which owes to improved pinch-off in the channel.

Phonon anharmonicities in 7-armchair graphene nanoribbons

Graphene nanoribbons (GNRs) provide a potential alternative to overcome the shortcoming of gapless graphene and have been applied into next-generation nanoelectronic devices like FETs. The phonon anharmonicities in functional materials usually play a key role in the device performance. Here, temperature dependent Raman scattering measurements on high quality 7-armchair GNRs (7-AGNRs) on Au(111) synthesized by on-surface method were conducted in the temperature range from 80 to 520 K. The frequency of optical phonon G mode (collective acoustic phonon RBLM mode) linearly (nonlinearly) downshifts with temperature. The first-order temperature coefficient of G mode of 7-AGNR is calculated to be −0.026 cm−1K−1, almost twice that of freestanding graphene of −0.015 cm−1K−1 and half of that of CVD grown single layer graphene on Cu foils of −0.056 cm−1K−1. For RBLM, the anharmonicity is much weaker and attributed to the intrinsic quartic-phonon decay processes rather than the cubic-phonon ones. Our findings make a first step to the thermal properties of atomically precise GNRs.

Effect of interlayer coupling on the electron spectra of vertical superlattice

By use of the Green's function method analytical expressions for the dispersion lows of superlattice (SL) consists of two alternating 2D layers are obtained. Weak interlayer coupling regime is analized thoroughly. As the examples, the SLs graphene --- h-BN ( 1), AlN --- GaN ( 2), Gr --- Ni ( 3) and h-BN --- Ni ( 4) are considered and analytical electron spectrum characteristics for the corresponding 2D layers are given. It is shown that 1) electron effective masses become havier for the h-BN, AlN, GaN, and Ni layers in all SLs; 2) Fermi velocity becomes lower for the gapless graphene layer in the SL ( 1) and remains constant in the SL ( 3); 3) energy gaps become narrower for the h-BN, AlN and GaN layers in the SLs (1) and ( 2) and wider for h-BN layer in the SL (4). Keywords: dispersion low, Fermi velocity, effective mass, graphene-like compound, two-dimensional ferromagnetic metal.

Plasmon modes in N-layer silicene structures

We investigate the plasmon properties in N-layer silicene systems consisting of N, up to 6, parallel single-layer silicene (SLS) under the application of an out-of-plane electric field, taking into account the spin–orbit coupling within the random-phase approximation. Numerical calculations demonstrate that N undamped plasmon modes, including one in-phase optical (Op) and (N − 1) out-of-phase acoustic (Ac) modes, continue mainly outside the single-particle excitation area of the system. As the number of layers increases, the frequencies of plasmonic collective excitations increase and can become much larger than that in SLS, more significant for high-frequency modes. The Op (Ac) plasmon mode(s) noticeably (slightly) decreases with the increase in the bandgap and weakly depends on the number of layers. We observe that the phase transition of the system weakly affects the plasmon properties, and as the bandgap caused by the spin–orbit coupling equal that caused by the external electric field, the plasmonic collective excitations and their broadening function in multilayer silicene behave similarly to those in multilayer gapless graphene structures. Our investigations show that plasmon curves in the system move toward that in SLS as the separation increases, and the impacts of this factor can be raised by a large number of layers in the system. Finally, we find that the imbalanced carrier density between silicene layers significantly decreases plasmon frequencies, depending on the number of layers.

Robust wavefront dislocations of Friedel oscillations in gapped graphene

Friedel oscillation is a well-known wave phenomenon, which represents the oscillatory response of electron waves to imperfection. By utilizing the pseudospin-momentum locking in gapless graphene, two recent experiments demonstrate the measurement of the topological Berry phase by corresponding to the unique number of wavefront dislocations in Friedel oscillations. Here, we study the Friedel oscillations in gapped graphene, in which the pseudospin-momentum locking is broken. Unusually, the wavefront dislocations do occur as that in gapless graphene, which expects the immediate verification in the current experimental condition. The number of wavefront dislocations is ascribed to the invariant pseudospin winding number in gaped and gapless graphene. This study deepens the understanding of correspondence between topological quantity and wavefront dislocations in Friedel oscillations, and implies the possibility to observe the wavefront dislocations of Friedel oscillations in intrinsic gapped two-dimensional materials, e.g., transition metal dichalcogenides.

On the electronic structure of a recently synthesized graphene-like BCN monolayer from bis-BN cyclohexane with single-atom vacancies: a DFT study

Since the rising of graphene, boron nitride monolayers have been deeply studied due to their structural similarity with the former. A hexagonal graphene-like boron–carbon–nitrogen (h-BCN) monolayer was synthesized recently using bis-BN cyclohexane (B2N2C2H12) as a precursor molecule. Herein, we investigated the electronic and structural properties of this novel BCN material, in the presence of single-atom (boron, carbon, or nitrogen) vacancies, by employing density functional theory calculations. The stability of these vacancy-endowed structures is verified from cohesion energy calculations. Results showed that a carbon atom vacancy strongly distorts the lattice leading to breaking on its planarity and bond reconstructions. The single-atom vacancies induce the appearance of flat midgap states. A significant degree of charge localization takes place in the vicinity of these defects. It was observed a spontaneous magnetization only for the boron-vacancy case, with a magnetic dipole moment about 0.87 μ B .Our calculations predicted a direct electronic bandgap value of about 1.14 eV. Importantly, this bandgap value is intermediate between gapless graphene and insulating hexagonal boron nitride.

Two-Dimensional Silicon Carbide: Emerging Direct Band Gap Semiconductor.

As a direct wide bandgap semiconducting material, two-dimensional, 2D, silicon carbide has the potential to bring revolutionary advances into optoelectronic and electronic devices. It can overcome current limitations with silicon, bulk SiC, and gapless graphene. In addition to SiC, which is the most stable form of monolayer silicon carbide, other compositions, i.e., are also predicted to be energetically favorable. Depending on the stoichiometry and bonding, monolayer may behave as a semiconductor, semimetal or topological insulator. With different Si/C ratios, the emerging 2D silicon carbide materials could attain novel electronic, optical, magnetic, mechanical, and chemical properties that go beyond those of graphene, silicene, and already discovered 2D semiconducting materials. This paper summarizes key findings in 2D SiC and provides insight into how changing the arrangement of silicon and carbon atoms in SiC will unlock incredible electronic, magnetic, and optical properties. It also highlights the significance of these properties for electronics, optoelectronics, magnetic, and energy devices. Finally, it will discuss potential synthesis approaches that can be used to grow 2D silicon carbide.

Growth mechanism of graphene/h-BN intra-layer interface

Graphene has received many attentions from the scientist due to its outstanding properties since it was mechanically exfoliated. The rise of graphene has stimulated immense research on analogous two-dimensional (2D) materials, such as the hexagonal boron nitride (h-BN), monolayer transition metal dichalcogenides, black phosphorene, silicene, borophene and germanene. However, as a semimetal, gapless graphene has been limited in the application like semiconducting electronics. Previous theoretical calculations predict that a small bandgap will arise when the graphene is placed onto an h-BN substrate. Then graphene/h-BN (G/h-BN) lateral heterostructures have been fabricated by many research groups on metal substrates. Comparing vertical vdW layer assembling, the atomic G/h-BN system combining both the high carrier mobility and tunable bandgap can build in-plane integrated circuit directly. However, to reduce the interface scattering, a sharp atomic interface between graphene and h-BN is required. To date, some experiments have built high quality G/h-BN heterostructures with sharp atomic interfaces, while many others did not. The underlying growth mechanism is crucial to control the size and shapes of the G/h-BN heterostructures of high quality. In this review, we first review the growth mechanism of graphene, mainly focusing on the nucleating process, which plays a vital role to reduce the grain boundary in the overall growth. The nucleation behavior of graphene is influenced by the growth temperature, substrate, carbon source partial pressure and hydrogen partial pressure. We review the structure and energy evaluation of clusters in the graphene nucleation stage on the Ir(111) and Ni(111) surface. Moreover, the nucleation barrier and size can also be obtained by combing the first-principles calculations and classical nucleation theory. Secondly, we present an overview on experimental fabrication of G/h-BN heterojunctions. Up to now, lateral G/h-BN heterojunctions has been produced on some metal substrates such as Cu foil, Ru(0001), Rh(111), Ni(111), Ir(111) and Pt(111). There are several methods to construct G/h-BN heterojunctions in experiments which can be classified into two kinds: Batch chemical vapor deposition and two/multi-step growth. In the earlier period, the large area randomly hybridized h-BN and graphene are fabricated by this method through supplying C precursors and NH3-BH3 at the same time. Another routine is two/multi-step growth technique in which G/h-BN is deposited on a metal surface beforehand as seeds of the second step of growth. And afterwards, by alternating the type of source supply, in plane heterojunctions with the predeposited grains will be formed. The growth sequence is proved to be a crucial factor that determines the quality of heterostructures. For multistep growth, lithographically technology and etching process are introduced to get spatially controlled heterostructures. Then, we introduce recent studies on the growth mechanism of G/h-BN lateral heterostructure both by atomistic first-principles calculations and experimental observations. The heteroepitaxial growth of graphene along the predeposited h-BN domains is systematically investigated by classical nucleation theory. At the initial stage, C atoms tend to attach linearly along the B/N-edges rather than perpendicular to the edges which resemble the graphene growth on the metal surface. When the carbon concentration is low, the nucleation barriers of graphene at B/N-edges are lower compared to the case of a Cu terrace. Nevertheless, under high carbon concentration, the nucleation barriers and nucleation rates in the two cases become comparable. Therefore, the chemical potential of the carbon source should be controlled within a suitable range to produce high quality G/h-BN lateral heterostructures with sharply and continuously atomic interface. Finally, we give a prospect on this rising field.

Plasmon modes in double-layer gapped graphene

Abstract We calculate plasmon frequencies and decay rates of plasma oscillations in double layer gapped graphene (DLGG) made of two parallel monolayer gapped graphene sheets, separated by a dielectric spacer. The results are compared to those in double layer gapless graphene with the same parameters. Numerical calculations show that, as in other double-layer systems, two plasmon modes exist in DLGG, corresponding to in-phase and out-of-phase oscillations of carriers in two sheets of the system. The energy loss of acoustic plasmon mode in DLGG is remarkably different from that in DLG caused by a separation of intra- and inter-band single-particle excitation regions of DLGG. In addition, the increase in band gap leads to a significant decrease in DLGG plasmon frequencies. Finally, the temperature dependence of plasmon properties in DLGG differs remarkably from that in DLG, and the effect of the band gap on plasmon characters decreases notably with increasing temperature.

Recent progress in devices and circuits based on wafer-scale transition metal dichalcogenides

Two-dimensional layered materials (2DLMs) have triggered a broad researchthrust over the last decade worldwide. Different from the gapless graphene,transition metal dichalcogenides (TMDs) exhibit versatile bandstructure, withbandgap sizes ranging from semi-metallic to over 2 eV. Therefore, 2D-TMDscan be utilized in various applications from logic to optoelectronicdevices. In this review we first introduce the latest developments of thewafer-scale synthesis of continuous TMD films, then we present recentadvances in large scale devices and circuits based on TMD films, includinglogic, memory, optoelectronic and analog devices. We also provide aperspective and a look at the future device applications based onwafer-scale 2D-TMDs.

Tuning the supercritical effective charge in gapless graphene via Fermi velocity modifying through the mechanical stretching

We present a theoretical study of the stretched graphene containing the Coulomb impurity. The cases of uniaxial armchair/zigzag and biaxial symmetry stretching are considered. For the uniaxial stretching, we found the gap opening with the non-monotonic dependence between the gap value and the strain. For the biaxial stretching, we observe a monotonic decreasing of Fermi velocity without the gap opening. Non-relativistic ab initio calculations of graphene electronic structure are combined with the analytical solution of relativistic Dirac equation. We found that the sheet stretching could provide a smooth fitting of Fermi velocity and, therefore, the smooth transformation of subcritical Coulomb impurity to the supercritical one.

Topological resonance and single-optical-cycle valley polarization in gapped graphene

For gapped graphene, we predict that an intense ultrashort (single-oscillation) circularly-polarized optical pulse can induce a large population of the conduction band and a large valley polarization. With an increase in the bandgap, the magnitude of the valley polarization gradually increases from zero (for the native gapless graphene) to a value on the order of unity. The energy bandwidth of the electrons excited into the conduction band can be very large ($\gtrsim 10$ eV for a reasonable pulse amplitude of $\sim 0.5$ $\mathrm{V/\AA}$). These phenomena are due to the effect of topological resonance: the matching of the topological (geometric) phase and the dynamic phase. Gapped graphene with tunable bandgap can be used as a convenient generic model of two-dimensional semiconductors with honeycomb generic lattice structures and broken inversion symmetry, such as transition metal dichalcogenides.

Hall viscosity and nonlocal conductivity of gapped graphene

We calculate the Hall viscosity and the nonlocal (i.e., dependent on wave vector $\bm q$) Hall conductivity of "gapped graphene" (a non-topological insulator with two valleys) in the presence of a strong perpendicular magnetic field. Using the linear-response theory at zero temperature within the Dirac approximation for the Landau levels, we present analytical expressions for both valley and total Hall viscosity and conductivity up to $\bm q^2$ at all frequencies. Although the final formulas for total Hall viscosity and conductivity are similar to the ones previously obtained for gapless graphene, the derivation reveals a significant difference between the two systems. First of all, both the Hall viscosity and the Hall conductivity vanish when the Fermi level lies in the gap that separates the lowest Landau level in the conduction band from the highest Landau level in the valence band. It is only when the Fermi level {\it is not} in the gap that the familiar formulas of gapless graphene are recovered. Second, in the case of gapped graphene, it is not possible (at least within our present approach) to define a single-valley Hall viscosity: this quantity diverges with a strength proportional to the magnitude of the gap. It is only when both valleys are included that the diverging terms, having opposite signs in the two valleys, cancel out and the familiar result is recovered. In contrast to this, the nonlocal Hall conductivity is finite in each valley. These results indicate that the Hoyos-Son formula connecting the Hall viscosity to the coefficient of $q^2$ in the small-$q$ expansion of the $q$-dependent Hall conductivity cannot be applied to each valley, but only to the system as a whole. The problem of defining a "valley Hall viscosity" remains open.

A Modified Planar Graphene-Based Heterostructure (Barrier—Quantum Well)

A planar graphene-based heterostructure is considered, which behaves differently: as a barrier or a quantum well at small or large momenta of charge carriers, respectively. This heterostructure contains a strip of gapped graphene with a lower Fermi velocity, surrounded by gapless graphene with a higher Fermi velocity. In this configuration, an interface state arises at the intersection point of dispersion curves. The transformation of this interface state into a fundamental bound state is investigated.

Estimations of the Fermi Velocity and Effective Mass in Epitaxial Graphene and Carbyne

It is shown that the Fermi velocity of electrons is a natural characteristic of gapless graphene and cumulene modification of carbyne weakly coupled with the substrate. At the same time, in the presence of gap (graphene with a gap and polyyne modification of carbyne), the corresponding characteristic is the effective electron mass. The corresponding analytical estimations have been performed.

Iterative approach to arbitrary nonlinear optical response functions of graphene

Two-dimensional materials constitute an exciting platform for nonlinear optics with large nonlinearities that are tunable by gating. Hence, gate-tunable harmonic generation and intensity-dependent refraction have been observed in e.g. graphene and transition-metal dichalcogenides, whose electronic structures are accurately modelled by the (massive) Dirac equation. We exploit on the simplicity of this model and demonstrate here that arbitrary nonlinear response functions follow from a simple iterative approach. The power of this approach is illustrated by analytical expressions for harmonic generation and intensity-dependent refraction, both computed up to ninth order in the pump field. Moreover, the results allow for arbitrary band gaps and gating potentials. As illustrative applications, we consider (i) gate-dependence of third- and fifth-harmonic generation in gapped and gapless graphene, (ii) intensity-dependent refractive index of graphene up to ninth order, and (iii) intensity-dependence of high-harmonic generation.