Graphene Ribbons Research Articles

Entropy and Seebeck signals meet on the edges

We explore the electronic entropy per particle $s$ and Seebeck coefficient $\mathcal{S}$ in zigzag graphene ribbons. Pristine and edge-doped ribbons are considered using tight-binding models to inspect the role of edge states in the observed thermal transport properties. As a bandgap opens when the ribbons are doped at one or both edges, due to asymmetric edge potentials, we find that $s$ and $\mathcal{S}$ signals are closely related to each other: both develop sharp dip-peak lineshapes as the chemical potential lies in the gap, while the ratio $s/\mathcal{S}$ exhibits a near constant value equal to the elementary charge $e$ at low temperatures. This constant ratio suggests that $\mathcal{S}$ can be seen as the transport differential entropy per charge, as suggested by some authors. Our calculations also indicate that measurement of $s$ and $\mathcal{S}$ may be useful as a spectroscopic probe of different electronic energy scales involved in such quantities in gapped materials.

Electronic Properties of Single‐Layer and Bilayer Graphene Nanoribbons

Herein, a tight‐binding description is utilized to investigate electronic structures and density of states of single‐layer (SL) and bilayer (BL) graphene ribbons with and without the influence of external electric fields. Analyses are implemented to reveal the similarity and difference among electronic properties of three types of structures (specifically SL and BL ribbons with AA and AB stackings). Moreover, both armchair and zigzag edge orientations are considered. It is indicated in the results that variation in electronic properties of these structures in the presence of external electric fields depends on both structural form and edge orientation. The following two points are demonstrated: 1) a transverse field has a significant effect on adjusting bandgap of the zigzag configurations, whereas a vertical electric field has a distinct impact on energy bands of armchair edge structures, and 2) among considered structures, AB‐stacking BL ribbons are invariably the structures that are most strongly influenced by external fields. Interestingly, AB‐stacking BL ribbons are also capable of enlarging bandgap with both edge terminations. Herein, an insight into how the electronic structure and charge distribution of both SL and BL graphene nanoribbons can be controlled not only in armchair but also in zigzag edge terminations using electric stimulants is provided by the results.

Theory of Edge Effects and Conductance for Applications in Graphene-Based Nanoantennas

In this paper, we present a theory of edge effects in graphene for its applications to nanoantennas in the THz, infrared, and visible frequency ranges. The novelty of the presented model is reflected in its self-consistency, which is reached due to the formulation in terms of dynamical conductance instead of ordinary surface conductivity. The physical model of edge effects is based on using the concept of the Dirac fermion and the Kubo approach. In contrast with earlier well-known and widely used models, the surface conductance becomes non-homogeneous and non-local. The numerical simulations of the spatial behavior of the surface conductance were performed in a wide range of values, known from the literature, for the graphene ribbon widths and electrochemical potential. It is shown that if the length exceeds 800 nm, our model agrees with the classical Drude conductivity model with a relatively high degree of accuracy. For rather short lengths, the conductance exhibits a new type of spatial oscillations, which are not present in the ordinary conductivity model. These oscillations modify the form of effective boundary conditions and integral equations for electromagnetic field at the surface of graphene-based antenna. The developed theory opens a new way for realizing electrically controlled nanoantennas by changing the electrochemical potential via gate voltage. The obtained results may be applicable for the design of different carbon-based nanodevices in modern quantum technologies.

Graphene-based optofluidic tweezers for refractive-index and size-based nanoparticle sorting, manipulation, and detection

This work proposes a novel design composed of graphene nanoribbons-based optofluidic tweezers to manipulate and sort bio-particles with radii below 2.5 nm. The suggested structure has been numerically investigated by the finite difference time domain (FDTD) method employing Maxwell's stress tensor analysis (MST). The finite element method (FEM) has been used to obtain the electrostatic response of the proposed structure. The tweezer main path is a primary channel in the center of the structure, where the microfluidic flow translates the nanoparticle toward this channel. Concerning the microfluid's drag force, the nanoparticles tend to move along the length of the main channel. The graphene nanoribbons are fixed near the main channel at different distances to exert optical forces on the moving nanoparticles in the perpendicular direction. In this regard, sub-channels embedding in the hBN layer on the Si substrate deviate bio-particles from the main path for particular nanoparticle sizes and indices. Intense hotspots with electric field enhancements up to 900 times larger than the incident light are realized inside and around the graphene ribbons. Adjusting the gap distance between the graphene nanoribbon and the main channel allows us to separate the individual particle with a specific size from others, thus guiding that in the desired sub-channel. Furthermore, we demonstrated that in a structure with a large gap between channels, particles experience weak field intensity, leading to a low optical force that is insufficient to detect, trap, and manipulate nanoparticles. By varying the chemical potential of graphene associated with the electric field intensity variations in the graphene ribbons, we realized tunability in sorting nanoparticles while structural parameters remained constant. In fact, by adjusting the graphene Fermi level via the applied gate voltage, nanoparticles with any desired radius will be quickly sorted. Moreover, we exhibited that the proposed structure could sort nanoparticles based on their refractive indices. Therefore, the given optofluidic tweezer can easily detect bio-particles, such as cancer cells and viruses of tiny size.

Frequency Converters for the Terahertz and Infrared Ranges

A method for solving the problem of nonlinear diffraction on two-dimensional periodic gratings of graphene ribbons has been developed. The third-order nonlinear conductivity of graphene under the action of two waves is taken into account, which is determined by the field of the pump wave, for which we use the field on graphene ribbons obtained by solving the linear diffraction problem. Numerical analysis shows the efficiency of nonlinear frequency conversion in the terahertz and infrared ranges when the frequencies of the incident pump and signal waves coincide with the resonant frequencies of the fundamental and higher order modes of surface plasmon polaritons in graphene ribbons.

Polarization-sensitive multi-frequency switches and high-performance slow light based on quadruple plasmon-induced transparency in a patterned graphene-based terahertz metamaterial.

A periodic patterned graphene-based terahertz metamaterial comprising three transverse graphene strips and one longitudinal continuous graphene ribbon is proposed to achieve a dynamically tunable quadruple plasmon-induced transparency (PIT) effect. Further analysis of the magnetic field distribution along the x-direction shows that the quadruple-PIT window can be produced by the strong destructive interference between the bright mode and the dark mode. The spectral response characteristics of the quadruple-PIT effect are numerically and theoretically investigated, and the results obtained by the finite-difference time-domain (FDTD) simulation fit well with that by the coupled mode theory (CMT) calculation. In addition, two hepta-frequency asynchronous switches are achieved by tuning the Fermi energy of the graphene, and their maximum modulation depths are 98.9% and 99.7%, corresponding to the insertion losses of 0.173 dB and 0.334 dB, respectively. Further studies show that polarization light has a significant impact on the quadruple-PIT, resulting in a polarization-sensitive switch being realized with a maximum modulation depth of 99.7% and a minimum insertion loss of 0.048 dB. In addition, when the Fermi energy is equal to 1.2 eV, the maximum time delay and group refractive index of the quadruple-PIT can be respectively as high as 1.065 ps and 3194, and the maximum delay-bandwidth product reaches 1.098, which means that excellent optical storage is achieved. Thus, our proposed quadruple-PIT system can be used to design a terahertz multi-channel switch and optical storage.

Nonreciprocal Thermal Emission Using Spatiotemporal Modulation of Graphene

We present a nonreciprocal thermal emitter based on the dynamic modulation of graphene. A graphene ribbon grating situated on a dielectric slab is designed to excite high-quality resonances in the long-IR region. We show that upon space–time modulation of the Fermi energy of graphene, asymmetric modal splitting results in large nonreciprocity, leading to a strong violation of Kirchhoff’s law of thermal radiation. We further show that the graphene system allows the creation of “absorptivity holes” and “emissivity holes” in the spectrum that are asymmetric. By changing the modulation frequency, the location of these holes can be adjusted, giving rise to a new dimension of tunable thermal emission in nonreciprocal systems. In this system, while Kirchhoff’s law is violated, we numerically observe certain symmetry properties between absorption and emission. We establish that these symmetry properties follow compound symmetry considerations.

On-Surface Synthesis and Evolution of Self-Assembled Poly(p-phenylene) Chains on Ag(111): A Joint Experimental and Theoretical Study.

The growth of controlled 1D carbon-based nanostructures on metal surfaces is a multistep process whose path, activation energies, and intermediate metastable states strongly depend on the employed substrate. Whereas this process has been extensively studied on gold, less work has been dedicated to silver surfaces, which have a rather different catalytic activity. In this work, we present an experimental and theoretical investigation of the growth of poly-p-phenylene (PPP) chains and subsequent narrow graphene ribbons starting from 4,4″-dibromo-p-terphenyl molecular precursors deposited at the silver surface. By combing scanning tunneling microscopy (STM) imaging and density functional theory (DFT) simulations, we describe the molecular morphology and organization at different steps of the growth process and we discuss the stability and conversion of the encountered species on the basis of calculated thermodynamic quantities. Unlike the case of gold, at the debromination step we observe the appearance of organometallic molecules and chains, which can be explained by their negative formation energy in the presence of a silver adatom reservoir. At the dehydrogenation temperature, the persistence of intercalated Br atoms hinders the formation of well-structured graphene ribbons, which are instead observed on gold, leading only to a partial lateral coupling of the PPP chains. We numerically derive very different activation energies for Br desorption from the Ag and Au surfaces, thereby confirming the importance of this process in defining the kinetics of the formation of molecular chains and graphene ribbons on different metal surfaces.

High-Surface-Area Graphene Oxide for Next-Generation Energy Storage Applications

Synthesis of high-surface-area graphene oxide for application in next-generation devices is still challenging. In this study, we present a simple and green-chemistry procedure for the synthesis of oxygen-enriched graphene materials, having very large surface areas compared with those reported for powdered graphene-related solids. Using the hydrothermal treatment of carbon nanohorns by a green-chemistry H2O2 oxidant under elevated pressure, the progressive creation of a stable carbon nanomaterial, denoted as open-sensu-shaped graphene oxide (OSSGO) by us, is observed. This oxygen-enriched nanographene contains π–π stacked few-layered graphene ribbons curved at the termini derived from the original cone tip. OSSGO is intensively analyzed and cross-characterized by spectroscopy, diffraction, adsorption, and elemental analysis methods. Based on the obtained results, we propose a mechanism of transformation from horns to a structure with several layers of sensu-form stacked graphene oxide. As this transformation process proceeds gradually, one can obtain numerous transition nanoarchitectures of tunable morphology and surface physicochemistry, including materials with an extremely high surface area. As OSSGO bears a fraction of the electron-withdrawing and O–H acidic functionalities, electrochemical studies, especially galvanostatic charge–discharge curves and specific capacitance values (significantly higher than those for other carbon-based materials), show potential applications in next-generation supercapacitors. As a result of the large surface areas, we also predict future applications in programmable adsorbents and catalysts with broad-range activity, while the list of applications is incomplete.

Geometric filterless photodetectors for mid-infrared spin light

Free-space circularly polarized light (CPL) detection, requiring polarizers and wave plates, is well established, but such a spatial degree of freedom is unfortunately absent in integrated on-chip optoelectronics. The filterless CPL photodetectors reported so far suffer from an intrinsic small discrimination ratio, vulnerability to the non-CPL field components and low responsivity. Here we report a distinct paradigm of geometric photodetectors in the mid-infrared, exhibiting a substantial discrimination ratio of 84, a close-to-perfect CPL-specific response, a zero-bias responsivity of 392 V W−1 at room temperature and a detectivity of ellipticity down to 0.03° Hz−1/2. Our approach makes use of a plasmonic nanostructures array with judiciously designed symmetry, assisted by graphene ribbons, to electrically read their near-field optical information. This geometry-empowered recipe for infrared photodetectors provides a robust, direct, strict and high-quality solution to on-chip filterless CPL detection and unlocks new opportunities for integrated functional optoelectronic devices.

Band structures of graphene, black phosphorus, and MoS2 ribbons under stress: a comparison study

The application of electronic devices becomes increasingly extensive and their performance optimization receives broad attention. Electronic devices constructed from two-dimensional materials have revealed broad prospects. However, the performance of two-dimensional electronic materials in the presence of stress has rarely been researched, which will restrict their application in an environment with intense deformation or temperature variation. Here, we adopt a first-principle method to investigate three kinds of ribbons: graphene, black phosphorus, and MoS2. We find that the bandgap of graphene and MoS2 ribbons increase with the rise of stress, while the bandgap of black phosphorus reduces when subject to both positive and negative stress. The abnormal trend of black phosphorus is owing to the indirect bandgap properties under negative stress, which becomes direct bandgap under positive stress. The present research has instructive meaning for the application of two-dimensional material on electronic devices under stressed conditions.

Perfect optical absorption in a single array of folded graphene ribbons.

Due to its one atom thickness, optical absorption (OA) in graphene is a fundamental and challenging issue. Practically, the patterned graphene-dielectric-metal structure is commonly used to achieve perfect OA (POA). In this work, we propose a novel scenario to solve this issue, in which POA is obtained by using free-standing folded graphene ribbons (FGRs). We show several local resonances, e.g. a dipole state (Mode-I) and a bound state in continuum (BIC, Mode-II), will cause very efficient OA. At normal incidence, by choosing appropriate folding angle θ, 50% absorptance by the two states is easily achieved; at oblique incidence, the two states will result in roughly 98% absorptance as incidence angle φ≈40∘. It is also interesting to see that the system has asymmetric OA spectra, e.g. POA of the former (latter) state existing in reverse (forward) incidence, respectively. Besides the angles θ and φ, POA here can also be actively tuned by electrostatic gating. As increasing Fermi level, POA of Mode-I will undergo a gradual blueshift, while that of Mode-II will experience a rapid blueshift and then be divided into three branches, due to Fano coupling to two guided modes. In reality, the achieved POA is well maintained even the dielectric substrates are used to support FGRs. Our work offers a remarkable scenario to achieve POA, and thus enhance light-matter interaction in graphene, which can build an alternative platform to study novel optical effects in general two-dimensional (2D) materials. The folding, mechanical operation in out-of-plane direction, may emerge as a new degree of freedom for optoelectronic device applications based on 2D materials.

Disordered graphene ribbons as topological multicritical systems

The low energy spectrum of a zigzag graphene ribbon contains two gapless bands with highly non-linear dispersion, $\epsilon(k)=\pm |\pi-k|^W$, where $W$ is the width of the ribbon. The corresponding states are located at the two opposite zigzag edges. Their presence reflects the fact that the clean ribbon is a quasi one dimensional system naturally fine-tuned to the topological {\em multicritical} point. This quantum critical point separates a topologically trivial phase from the topological one with the index $W$. Here we investigate the influence of the (chiral) symmetry-preserving disorder on such a multicritical point. We show that the system harbors delocalized states with the localization length diverging at zero energy in a manner consistent with the $W=1$ critical point. The same is true regarding the density of states (DOS), which exhibits the universal Dyson singularity, despite the clean DOS being substantially dependent on $W$. On the other hand, the zero-energy localization length critical exponent, associated with the lattice staggering, is not universal and depends on the topological index $W$.

Photoreduction behavior of Cr(VI) on oxidized carbon nanoparticles: From photocatalytic efficiency to oxygenated groups

Clarifying the reaction process and specific mechanism between variable-valence elements and oxidized carbon nanoparticles is essential to evaluate the environmental impact of carbon nanomaterials. In this study, the photocatalytic reduction of Cr(VI) on oxidized carbon nanotubes (OCNTs), oxidized graphene ribbons (OGRs), and graphene oxide sheets (GOs) was explored by batch experiments and spectroscopic analyses. The reaction efficiencies strongly depended on the number of oxygenated groups in the oxidized carbon nanoparticles. The abundant oxygenated groups enabled the GOs to exhibit the highest photocatalytic activity, followed by the OGRs and OCNTs. As a result, the photoreduction efficiency of Cr(VI) reached 96% for GOs, whereas those of OGRs and OCNTs were only 40% and 13%, respectively. In addition, different types of oxygenated groups exhibited various activities based on molecular model tests, following the sequence carboxylic > hydroxyl > carbonyl > ether > aldehyde > edge. Based on the underlying relationship between the oxygenated groups, topological structures, and mechanical strain in the carbon nanoparticles, we speculate that mechanical strain plays a critical role in the formation of oxygenated groups, thereby regulating their photocatalytic activities. The findings in this work provide novel insights into the roles of oxygenated groups and the mechanical strain of carbon nanoparticles in their environmental behavior.

Tuning phononic and electronic contributions of thermoelectric in defected S-shape graphene nanoribbons

Thermoelectrics as a way to use waste heat, is essential in electronic industries, but its low performance at operational temperatures makes it inappropriate in practical applications. Tailoring graphene can change its properties. In this work, we are interested in studying the transport properties of S-shape graphene structures with the single vacancy (SV) and double vacancy (DV) models. The structures are composed of a chiral part, which is an armchair graphene nanoribbon, and two zigzag graphene ribbons. We investigate the changes in the figure of merit by means of the Seebeck coefficient, electronic conductance, and electronic and phononic conductances with the vacancies in different device sizes. The transport properties of the system are studied by using the non-equilibrium Green’s function method, so that the related Hamiltonians (dynamical matrices) are obtained from the tight-binding (force constant) model. The maximum figure of merit (ZT) obtains for the DVs in all lengths. Physical properties of such a system can be tuned by controlling various parameters such as the location and the type of the defects, and the device size. Our findings show that lengthening the structure can reduce phononic contribution, and single vacancies than double vacancies can better distinguish between electronic thermal conductance behavior and electronic conductance one. Namely, vacancy engineering can significantly increase thermoelectric performance. In the large devices, the SVs can increase the ZT up to 2.5 times.

Nano optical temperature sensor based on fiber Bragg grating using graphene

In this paper, a novel Graphene-Assisted Microfiber based temperature sensor is proposed that changing the surrounding temperature has a severe effect on the refractive index of the graphene, so these changes result in the transmission power of microfiber. In the proposed structure, the position of the graphene sheet affects the interaction of light and graphene, effectively. Simply, by examining the change in transmission power, the temperature sensitivity of 0.1038 dBC in the heating process and 0.1072 dBC in the high-resolution cooling process of 0.0098 ℃ is obtained, which is 16 times more than bare fiber. Moreover, in this paper, both MgF2 layer and the graphene ribbon affect fiber refractive index so a high sensitivity, compact size, low cost, linear operation and suitable transmission coefficient temperature sensor is achieved. This sensor has great potential in the field of measurement, especially surrounding temperature measurement. Also, a comprehensive and detailed study of the properties of surface conductivity, electric dispersion, refractive index and permittivity for graphene with sensitivity simulation is accomplished.

Multi-frequency switch and excellent slow light based on tunable triple plasmon-induced transparency in bilayer graphene metamaterial ∗ ∗Project supported by National Natural Science Foundation of China (NSFC) (61605018, 11904032, 61841503).

We propose a novel bilayer graphene terahertz metamaterial composed of double graphene ribbons and double graphene rings to excite a dynamically adjustable triple plasma-induced transparency (PIT) effect. The coupled mode theory (CMT) is used to explain the PIT phenomenon, and the results of the CMT and the finite-difference time-domain simulation show high matching degree. By adjusting the Fermi levels of graphene, we have realized a penta-frequency asynchronous optical switch. The performance of this switch, which is mainly manifested in the maximum modulation depth (MD = 99.97%) and the minimum insertion loss (IL = 0.33 dB), is excellent. In addition, we have studied the slow-light effect of this triple-PIT and found that when the Fermi level of graphene reaches 1.2 eV, the time delay can reach 0.848 ps. Therefore, this metamaterial provides a foundation for the research of multi-frequency optical switches and excellent slow-light devices in the terahertz band.

Half-integer Wannier diagram and Brown-Zak fermions of graphene on hexagonal boron nitride

The moir\'e potential of graphene on hexagonal boron nitride (hBN) generates a supercell sufficiently large as to thread a full magnetic flux quantum $\Phi_0$ for experimentally accessible magnetic field strengths. Close to rational fractions of $\Phi_0$, $p/q \cdot\Phi_0$, magnetotranslation invariance is restored giving rise to Brown-Zak fermions featuring the same dispersion relation as in the absence of the field. Employing a highly efficient numerical approach we have performed the first realistic simulation of the magnetoconductance for a 250 nm wide graphene ribbon on hexagonal boron nitride using a full ab-initio derived parametrization including strain. The resulting Hofstadter butterfly is analyzed in terms of a novel Wannier diagram for Landau spectra of Dirac particles that includes the lifting of the spin and valley degeneracy by the magnetic field and the moir\'e potential. This complex diagram can account for many experimentally observed features on a single-particle level, such as spin and valley degeneracy lifting and a non-periodicidy in $\Phi_0$.

Particlelike valleytronics in graphene

Particlelike scattering states allow for noiseless transport through quantum dots by closely retracing bundles of classical trajectories. We identify such raylike states for electron transport through graphene ribbons. Remarkably, we find that these quasiclassical scattering states can be unambiguously associated with well-defined quantum numbers of the valley degree of freedom specific to graphene. Trigonal warping---i.e., deviations of the band structure from a perfectly isotropic two-dimensional Dirac equation due to the hexagonal lattice structure---results in preferred propagation directions and scattering time delays that depend on the valley the particlelike wave travels in. By implementing a truncated mode basis of Bloch states, we achieve simulations of micrometer-sized quantum dots starting from an atomic-scale tight-binding Hamiltonian.

Computational study of the effect of different doping elements on the thermal conduction properties of graphene nanoribbons

The dopant's atoms of various elements can be incorporated into the crystal lattice of graphene for the purpose of modulating its structural, optical and electrical properties. While the dopant's presence negatively affects the thermal conductivity, the exact effect of doping is still poorly understood and the mechanisms involved remain obscure. The effect of different doping elements on the thermal conductivity of graphene ribbons was investigated by performing molecular dynamics simulations to understand how impurities affect the thermal conduction properties of the nanostructured material. Graphene ribbons were doped with silicon, boron, or nitrogen elements to modify their nanostructure and thermal properties. The importance of edge structure was evaluated in comparison with that of doping. The Callaway model and the Einstein's model were used to provide the theoretical upper and lower bounds on the thermal conductivity. The contribution of optical phonons at different temperatures was evaluated in order to further understand the microscopic mechanisms of thermal conduction in the two-dimensional doped crystal. A computational analysis of thermal behavior was carried out in terms of the maximum density of states. The results indicated that a small number of dopant atoms can greatly change the ability to conduct heat. The thermal conductivity of the doped nanomaterial decreases successively in the order of nitrogen, boron, and silicon. Acoustical phonons still dominate the thermal conduction in the doped crystal, but the contribution of optical phonons become larger, especially at higher temperatures. The contribution of phonons in the optical branches increases with the doping concentration and can be as large as 6.0 %. In the presence of doping, the edge structure does not significantly affect the thermal conductivity and the maximum density of states. When graphene is heavily doped, the effect of ribbon length is insignificant while doping becomes dominant. The results have significant implications for the understanding of the relations between doping elements and thermal conduction properties.